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3D CHARACTERIZATION AND MECHANICS OF BRITTLE DEFORMATION IN
THRUST FAULT RELATED FOLDS
A DISSERTATION
SUBMITTED TO THE DEPARTMENT
OF GEOLOGICAL AND ENVIRONMENTAL SCIENCES
AND THE COMMITTEE ON GRADUATE STUDIES
OF STANFORD UNIVERSITY
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
Patricia E. Fiore
November 2006

© Copyright by Patricia E. Fiore 2007
All Rights Reserved
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Abstract
This thesis addresses the proposition that a better understanding of fractures
will aid in the optimization of hydrocarbon recovery in thrust fault related folds.
Fault planes, stratigraphic layers, and stratigraphic growth features interpreted
within a three-dimensional volume of seismic reflection data collected over the Elk
Hills Oil Field, Kern County, CA are integrated with mechanical models to develop a
four-dimensional fault evolution history that is structurally, stratigraphically, and
mechanically consistent. The developed fault chronology has direct implications for
the migration and emplacement of hydrocarbons. The method introduced here, by
which structural and stratigraphic interpretations are incorporated into a sequence of
forward mechanical models, represents an effective means of constraining the
structural evolution of a fault network that developed within a syn-depositional
tectonic setting.
The development of fractures in the sedimentary layers of Sheep Mountain
anticline, a Laramide asymmetric fault-cored fold of the Bighorn Basin of Wyoming,
is documented and interpreted as a method of constraining the kinematic evolution of
the fold. The relative chronology, mode of formation (opening vs. shearing), and
structural locations of these fractures provide the following constraints interpretations
of fold kinematics: there was little or no lateral fold propagation and no hinge
migration; limb rotation or limb flexure and stretching operated at different structural
locations during folding.
Field observations of sheared fractures in various structural locations across
Sheep Mountain document the role of fracture reactivation. Differences in
observations of shearing constrain spatial and temporal variations of the stress state
across the anticline during folding. Differences in both the formation and reactivation
of fracture sets in the forelimb and backlimb indicate that the stress state in the
forelimb was significantly influenced by the underlying fault.
The coupling of fracture mapping with analysis of high precision GPS
positions collected across patches of bedding surfaces at Sheep Mountain provides
insight into the curvature-fracture relationship. Comparison of principal curvature
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magnitudes with fracture measurements indicates that greater curvature correlates with
greater spherical variance of fracture sets. Fracture intensities, however, correlate only
loosely with curvature, so fracturing mechanisms other than flexure must be taken into
account.
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Preface
Small scale structural heterogeneities (joints, faults, sheared joints) affect the
flow properties of reservoirs as discontinuities in the permeability of the rock volume,
disrupting both the vertical and lateral transport of fluids. Accurate characterization of
these structures within reservoirs is thus sought for economic purposes. Typically,
these structures are below seismic resolution and direct observation of their patterns is
unfeasible, except within boreholes, where spatial coverage is limited. Fracture
clusters often localize near faults or on folds. Thus, new multi-scale methods for
predicting fracture patterns from subsurface data in which faults and folds are imaged
would play a crucial role in the development of hydrocarbon reservoirs.
Additionally, it is often beneficial from a geological point of view to reverse
this relationship and consider faulting and folding with respect to observed fracturing.
In this way, insight into the tectonic forces existing within the crust may be gained.
The establishment of a link between faulting, folding, and fracturing would aid
geologists in deducing the deformational history of a rock mass based on field
interpretation of fractures present within thrust fault related folds. A complete
understanding of the mechanics of faulting, folding and fracturing is a prerequisite for
this process.
This thesis consists of four chapters that are focused on relating common
geological structures, namely faults, folds, and fractures. Elk Hills Anticline, a thrust
fault related growth fold in Kern County, California, and Sheep Mountain Anticline, a
Laramide thrust fault related fold in the Bighorn Basin of Wyoming, are two field sites
that provide, respectively, the subsurface and the outcrop data that form the basis for
the analyses included in this work. Three chapters provide insight into the link
between fault and fold evolutions (chapters one, two, and three), two chapters have
implications linking faulting and fracturing (chapters two and three), and three
chapters link folding and fracturing (chapters two, three, and four).
In chapter one, I use elastic models to investigate the evolution of the fault
system beneath the Elk Hills anticline. My coauthors for this work are David Pollard,
Bill Currin, and David Miner. Currin and Miner were employees at Occidental of Elk
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Hills, Inc. at the time of the study. They provided the fault and horizon interpretations
that served as input (fault surfaces) and calibration (structure contour maps of specific
horizons) for the modeling effort. I interpreted growth structures within the seismic
reflection data and worked with David Pollard to develop a method of forward
modeling for observed deformation within a growth faulting environment through a
series of iterative steps in which fault geometry evolves. I drafted the manuscript and
all included figures with significant edits suggested by David Pollard. This manuscript
has been accepted for publication in American Association of Petroleum Geologists
Bulletin and is currently in press.
The work presented in chapter two represents the initial results of a fruitful
collaboration with Nicolas Bellahsen, who, at the time, was a post-doctorate fellow
with David Pollard. Bellahsen spearheaded field efforts in which we collected fracture
measurements at outcrops around Sheep Mountain Anticline. By considering fracture
orientations, modes of deformation, and abutting relations, we developed a
chronological fracturing story and were able to use this story to investigate the
kinematics of folding at Sheep Mountain. I am second author on this paper after
Bellahsen. I led the thin section interpretation and curvature analysis work, generating
the corresponding figures. I also worked side-by-side with Bellahsen during the
development of many of the concepts presented in the paper and through the drafting
of the paper. David Pollard provided significant conceptual direction during the project
and suggested significant reorganization and edits of the paper. This manuscript was
published in the May 2006 issue of Journal of Structural Geology (v. 28, n.5).
[Reprinted from Journal of Structural Geology, v. 28, Bellahsen, N., P. E. Fiore, and
D. D. Pollard, The role of fractures in the structural interpretation of Sheep Mountain
Anticline, Wyoming, p. 850-867, Copyright 2006, with permission from Elsevier.]
In chapter three, I document the reactivation of fractures observed throughout
Sheep Mountain Anticline. This work is coauthored with Nicolas Bellahsen and David
Pollard. To dispel the notion that reactivation of fractures at Sheep Mountain may be
lithology dependent, we first present fracture measurements in four different
lithologies. We then discuss how differences observed in shearing at locations across
the fold may constrain the state of stress at the time of deformation. Nicolas Bellahsen
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worked with me in the field, identifying sheared fractures and investigating the spatial
extent of shearing for different fracture sets. David Pollard also contributed to field
work and provided invaluable direction and editing for a manuscript resulting from
this work. Submission of this manuscript to Journal of Structural Geology is
anticipated.
In chapter four I compare characteristics of the fracture pattern mapped across
patches of bedding surfaces with the magnitude of curvature of those surfaces.
Although this was the last chapter completed, it was the first concept proposed to me
by David Pollard upon my arrival at Stanford – that we should work toward a better
understanding of how the shapes of surfaces relate to the fractures developed across
those surfaces. I carried out all of the field work and analysis involved in this study
and drafted the manuscript. Nicolas Bellahsen and David Pollard are coauthors on this
paper. Work with Nicolas Bellahsen provided a foundation for the fracture
characterization included in this project. David Pollard provided conceptual advice
central to the development of the project. The manuscript is currently in preparation
for submission to Journal of Structural Geology.
Appendix one took shape while I was considering tectonic boundary conditions
for the modeling included in chapter 1. During an internship at Occidental of Elk Hills,
it became clear to me that geoscientists are still in debate over the tectonic setting in
which the anticline formed. In part to justify my work at Elk Hills to Occidental
employees, I felt it necessary to defend our view of Elk Hills as developing in response
to a thrusting mechanism. David Pollard, my coauthor for this paper, suggested that we
carry out kinematic calculations for suggested wrenching scenarios. The completion of
this task, and the results of a mechanical modeling effort in which wrenching drives
the deformation, is summed up in a manuscript that has not yet been placed for
publication.
Appendix two is a field guide for Sheep Mountain anticline that I compiled with
assistance from Nicolas Bellahsen and David Pollard for the June 2006 Rock Fracture
Project field trip. It consists of a lengthy background section that includes excerpts
from many previous studies at the anticline and then discusses much of the work
conducted by Nicolas Bellahsen, David Pollard and me. Much of chapter two of this
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thesis is included in the field guide. Some of the concepts developed in chapter three
are included as well, although many of these concepts are in their infancy. Since
publication is not intended, I have included the field guide as an appendix for archival
purposes.
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Acknowledgements
I am grateful to the many people who have contributed to the research presented
in this thesis. Foremost, I thank Dave Pollard for his guidance over the past five years.
He has been an excellent advisor and I truly appreciate the countless hours he has
dedicated to helping me develop both my research and the ability to communicate it to
others. In particular, I thank Dave for thinking of my future career when helping me to
consider projects and internships. I also thank my committee members: Atilla Aydin,
Mark Zoback, Steve Graham, and Ronnie Borja for invaluable suggestions and
feedback over the years. I am appreciative of the GPS support provided by George
Hilley and Trevor Hebert.
Thanks to my fellow colleagues within the geomechanics research group who
have engaged me in interesting research discussions and enlivened day to day tasks.
Through the years, I have greatly benefited from the field assistance, technical
discussion, and supportive working environment provided by Stephan Bergbauer, Phil
Resor, Kurt Sternlof, Ian Mynatt, Ashley Griffith, Ole Kaven, Pete Lovely, Nico
Bellahsen, Frantz Maerten, Laurent Maerten, Eric Flodin, Nick Davatzes, Brita
Graham, Jordan Muller, Fabrizio Agosta, Laura Chiaramonte, Joe Gonzales, and Chris
Wilson. In particular, Nico Bellahsen has been a great field partner and collaborator. I
have learned a vast amount through interactions with Nico in both the field and the
office, and much of my Sheep Mountain work would not have been possible without
his efforts and enthusiasm.
Beyond the Stanford community, I owe thanks to Stan Stearns and Radu
Girbacea for helping turn a summer internship project with Occidental Oil and Gas
into a true research project and to Peter Hennings for introducing me to Sheep
Mountain six years ago during an internship at Phillips Petroleum Co.
Financial support for my studies came from many sources. Project specific funds
were provided by an NSF Tectonics Program Grant No. EAR-0125935 and an NSF
Collaboration in Mathematical Geosciences Program Grant No. EAR-04177521.
Additional funds were provided by the Stanford Rock Fracture Project, the Stanford
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University Department of Geological and Environmental Sciences, and the Stanford
McGee Grant.
My family has provided endless support throughout my education. From an
early age, my parents fueled my curiosity and encouraged my learning. I owe the
dedication required to complete this thesis to them. My three sisters have been a
constant source of personal support, providing prospective and a fun outlet from the
geological world. Finally, I am indebted to my husband, Jeff, for his unwavering love,
support, and patience during my final months at Stanford, despite the many miles
between us.
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PEF, November 20 th , 2006

Table of Contents
Abstract ………………………………...………………………………………….…. v
Preface ………………………………………………………………………………. vii
Acknowledgements ………………………………………………………………….. xi
Table of Contents …………………………………………………………………... xiii
List of Tables …………………………………………………………...………… xviii
List of Illustrations …………………………………………………………………. xix
Chapter 1: Mechanical and stratigraphic constraints on the evolution of faulting
at Elk Hills, CA …………………………………………………………………. 1
Abstract ....................................................................................................................1
Introduction ..............................................................................................................1
Regional geological setting ......................................................................................4
Elk Hills Field .......................................................................................................... 6
Structural interpretation............................................................................................7
Velocity model .........................................................................................................9
Stratigraphy ............................................................................................................10
Stratigraphic constraints .........................................................................................10
Pseudowells ........................................................................................................ 10
Pseudowell interpretations: Western Elk Hills................................................ 12
Pseudowell interpretations: Eastern Elk Hills ................................................. 15
Bedding relationships ......................................................................................... 15
Bedding relationship interpretations................................................................ 15
Isochores............................................................................................................. 17
Isochore interpretations: McDonald to Base Reef Ridge................................ 19
Isochore interpretations: Base Reef Ridge to Calitroleum.............................. 21
Isochore interpretations: Calitroleum to Wilhelm........................................... 23
Isochore interpretations: Wilhelm to MYA 4-A ............................................. 24
Stratigraphic constraints on fault evolution............................................................24
Mechanical modeling ............................................................................................. 24
Boundary conditions........................................................................................... 26
Model increments................................................................................................ 30
Model calibration ............................................................................................... 32
Model results....................................................................................................... 33
Discussion ..............................................................................................................35
Modeled and interpreted discrepancies.............................................................. 36
Tectonic strain analysis ...................................................................................... 37
Implications for hydrocarbon migration ............................................................ 39
Conclusions ............................................................................................................41
Acknowledgements ................................................................................................42
References ..............................................................................................................42
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Chapter 2: The role of fractures in the structural interpretation of Sheep
Mountain anticline, Wyoming ………………………………………………… 49
Abstract ..................................................................................................................49
Introduction ............................................................................................................49
Geological and tectonic setting ..............................................................................53
Methods ..................................................................................................................56
Fracture sampling .............................................................................................. 56
Data processing .................................................................................................. 59
Curvature calculation......................................................................................... 61
Structural data ........................................................................................................63
Northeastern forelimb ........................................................................................ 63
Southwestern backlimb ...................................................................................... 68
Hinge................................................................................................................... 71
Northern nose ..................................................................................................... 75
Interpretation .......................................................................................................... 76
Pre-existing fractures ......................................................................................... 76
Early Laramide compression: onset of faulting and folding .............................. 78
Fold growth: intermediate stage......................................................................... 81
Fold growth: late stage....................................................................................... 82
Conclusions ............................................................................................................83
Acknowledgements ................................................................................................84
References ..............................................................................................................84
Chapter 3: Fracture reactivation at Sheep Mountain anticline: insight on the
mechanics of folding and constraints on the stress field …………………….. 91
Abstract ..................................................................................................................91
Introduction ............................................................................................................92
Geological background...........................................................................................93
Field data ................................................................................................................99
Systematic fracture sets ...................................................................................... 99
Forelimb ........................................................................................................ 102
Backlimb........................................................................................................ 102
Hinge ............................................................................................................. 104
Shearing datas .................................................................................................. 104
Forelimb ........................................................................................................ 106
Backlimb........................................................................................................ 110
Hinge ............................................................................................................. 113
Analysis of field data............................................................................................113
Interpretation of shearing................................................................................. 113
Forelimb ........................................................................................................ 113
Backlimb........................................................................................................ 115
Lithological control on fracturing .................................................................... 115
Set V fractures................................................................................................... 118
Stress field constraints...................................................................................... 120
Constraints on spatial variation in stress orientation: conjugate shearing..... 121
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Spatial variation in stress orientation: opposite senses of shearing............... 121
Constraints on spatial variation in stress field magnitude: set I fractures ..... 128
Discussion ............................................................................................................134
Kinematics of shearing and folding.................................................................. 134
Implications for the mechanics of fracturing in a thrust fault related folds..... 134
Acknowledgements ..............................................................................................136
References ............................................................................................................ 136
Chapter 4: Curvature and fracturing based on GPS data collected at Sheep
Mountain anticline, WY ……………………………………………………… 141
Abstract ................................................................................................................141
Introduction ..........................................................................................................141
Geological setting.................................................................................................142
Methodology ........................................................................................................143
GPS data collection .......................................................................................... 143
GPS data filtering ............................................................................................. 147
Curvature calculation....................................................................................... 148
Fracture data collection ................................................................................... 148
Fracture data analysis...................................................................................... 148
Field data ..............................................................................................................149
GPS data........................................................................................................... 149
Fracture data .................................................................................................... 151
Curvature analysis ................................................................................................158
Discussion ............................................................................................................ 163
Curvature analyses ........................................................................................... 163
Relating curvature analysis to fracture measurements .................................... 163
Conclusions ..........................................................................................................167
Acknowledgements .............................................................................................. 167
References ............................................................................................................ 167
Appendix 1: Tectonic shortening style in the Southern San Joaquin Valley,
Revisited ………………………………………………………………………. 171
Abstract ................................................................................................................171
Introduction ..........................................................................................................172
Previous work.......................................................................................................175
Shearing calculations............................................................................................177
Pure shear ...................................................................................................... 178
Simple shear................................................................................................... 178
Implications of shearing-related rotation on relative plate velocities........... 179
Discussion ............................................................................................................180
Analysis of shearing calculations................................................................... 180
Variation in isochore trends at Elk Hills ....................................................... 184
Analysis of a wrenching growth mechanism at Elk Hills............................... 184
Conclusions ..........................................................................................................186
Acknowledgements ..............................................................................................188
References ............................................................................................................188
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Appendix 2: The Rock Fracture Project field trip, Sheep Mountain Anticline,
WY, 2006………………………………………………………………………. 193
Introduction ..........................................................................................................194
Themes: ................................................................................................................194
Fracture characterization at the outcrop ......................................................... 194
Fracture characterization over the fold............................................................ 195
Fold-thrust fault relationships based on fracture patterns............................... 195
Tectonic history revealed by fracture patterns................................................. 195
Field Trip Stops:...................................................................................................196
First Day ........................................................................................................ 196
Second Day.................................................................................................... 196
DAY 1 ..................................................................................................................199
Stop 1: Geology of the greater region ..................................................................200
Objectives.......................................................................................................... 200
Key Points......................................................................................................... 200
Tectonic setting of Laramide Orogeny ............................................................. 200
Structural styles of Laramide folds and thrust faults........................................ 202
Stratigraphy of the Bighorn Basin.................................................................... 204
Structures surrounding Sheep Mountain .......................................................... 207
Structural interpretations for Sheep Mountain anticline.................................. 213
Stop 2: Fold shape ................................................................................................222
Objectives.......................................................................................................... 222
Key Points......................................................................................................... 222
Stop 3: Fracture introduction; nose fractures .......................................................224
Objectives.......................................................................................................... 224
Key Points......................................................................................................... 224
Previous fracture studies at Sheep Mountain................................................... 224
Methods of fracture characterization ............................................................... 229
Fracture interpretation..................................................................................... 231
Fracture characterization in the nose .............................................................. 233
DAY 2 ..................................................................................................................237
Stop 4: Backlimb fractures ...................................................................................238
Objectives.......................................................................................................... 238
Key Points......................................................................................................... 238
Overview ........................................................................................................... 239
Kinematic Indicators ........................................................................................ 241
Fracture characterization in the backlimb ....................................................... 242
Stop 5: Backlimb fractures and shearing of Set I.................................................248
Objectives.......................................................................................................... 248
Key Points......................................................................................................... 248
Shearing of Set I fractures in the backlimb....................................................... 249
Stop 6: Backlimb fractures ...................................................................................253
Objectives.......................................................................................................... 253
Key Points......................................................................................................... 253
Fracture characterization................................................................................. 254
Shearing at site ................................................................................................. 258
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Role of thumb in fracture variation .................................................................. 264
Stop 7: Forelimb and hinge fractures ...................................................................267
Objectives.......................................................................................................... 267
Key Points......................................................................................................... 267
Fracture characterization in the forelimb ........................................................ 268
Shearing (reactivation) of Set I fractures in the forelimb................................. 271
Bedding plane slip in the forelimb.................................................................... 272
Fracture characterization at site ...................................................................... 275
Fracture characterization in the hinge............................................................. 281
Shearing in the hinge ........................................................................................ 285
Stop 8: Fracture synthesis..................................................................................... 286
Objectives.......................................................................................................... 286
Key Points......................................................................................................... 286
Stages of fracturing........................................................................................... 288
Pre-existing fractures..................................................................................... 288
Early Laramide compression: onset of faulting and folding ......................... 288
Fold growth: intermediate stage .................................................................... 289
Fold growth: late stage .................................................................................. 289
Constraints on fold kinematics ......................................................................... 292
Fixed hinge .................................................................................................... 292
Understanding spatial variations .................................................................... 293
Set III fractures.............................................................................................. 293
Set II fractures ............................................................................................... 295
Role of shearing of set I fractures..................................................................... 299
References ............................................................................................................ 302
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List of Tables
Table 1.1. Ages of stratigraphic horizons; model increments; applied strains.............31
Table 4.1. Fisher statistics for fracture sets at surveyed pavements...........................155
Table 4.2. Extreme values of principal normal curvatures.........................................159
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List of Illustrations
Figure 1.1. Location of the Elk Hills Oil Field...............................................................5
Figure 1.2. Structure of the Elk Hills Oil Field ..............................................................8
Figure 1.3. Tertiary stratigraphic column for the Elk Hills Oil Field...........................11
Figure 1.4. Cross sections and pseudowells .................................................................13
Figure 1.5. Stratigraphic bedding relationships............................................................16
Figure 1.6. Tracing of seismic line exhibiting stratigraphic bedding relationships......18
Figure 1.7 Interpreted and modeled isochore maps.....................................................20
Figure 1.8. Isochore signatures related to fault activity................................................22
Figure 1.9. Conceptual model of fault evolution..........................................................25
Figure 1.10. Remote boundary conditions applied to one step models ........................29
Figure 1.11. Interpreted and modeled structure contour maps .....................................34
Figure 1.12. Remote boundary conditions applied to iterative models ........................38
Figure 2.1. Geology of Sheep Mt. ................................................................................52
Figure 2.2. Cross section through Sheep Mt.................................................................54
Figure 2.3. Stratigraphic column for Sheep Mt. ...........................................................54
Figure 2.4. Fracture measurements in the limbs and hinge at Sheep Mt......................57
Figure 2.5. Fracture measurements in the nose at Sheep Mt. .......................................58
Figure 2.6. Sample sites for microscope analysis.........................................................60
Figure 2.7. Curvature map of Sheep Mt. ......................................................................62
Figure 2.8. Fracture patterns in the forelimb ................................................................64
Figure 2.9. Thin section of a set I fracture in the forelimb...........................................65
Figure 2.10. Reactivated set I fractures in the forelimb................................................66
Figure 2.11. Fracture pattern in the backlimb...............................................................67
Figure 2.12. Thin section of a set I fracture in the backlimb........................................67
Figure 2.13. Thin sections of set II, III, and IV fractures in the backlimb ...................69
Figure 2.14. Set IV fractures in the backlimb...............................................................70
Figure 2.15. Thin sections of set I and II fractures in the hinge ...................................70
Figure 2.16. Fracture pattern in the hinge.....................................................................72
Figure 2.17. Fracture pattern in the hinge of the nose ..................................................73
Figure 2.18. Fracture pattern in the backlimb of the nose ............................................74
Figure 2.19. Stages of fracturing at Sheep Mt..............................................................77
Figure 3.1. Geology of the Bighorn Mts./Bighorn Basin area......................................94
Figure 3.2. Geological map of Sheep Mt......................................................................96
Figure 3.3. Stratigraphic column for the Bighorn Basin ..............................................97
Figure 3.4. Schematic drawing of Sheep Mt. fracture pattern .....................................98
Figure 3.5. Forelimb, backlimb, and hinge fracture measurements ...........................100
Figure 3.6. Abutting relationships for set V joints .....................................................103
Figure 3.7. Locations and types of shearing observations at Sheep Mt. ....................105
Figure 3.8. Set I reactivated fractures in the forelimb ................................................107
Figure 3.9. Sheared set I fracture in the forelimb .......................................................108
Figure 3.10. Sheared set I fractures and set II joints in the backlimb.........................109
Figure 3.11. Sheared set V joints in the backlimb......................................................111
Figure 3.12. Sheared set I fractures in the backlimb ..................................................112
Figure 3.13. Fracture pattern in the hinge...................................................................112
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Figure 3.14. Shearing domains ...................................................................................114
Figure 3.15. Conceptual model of fracture, fold, and shearing development ............116
Figure 3.16. Sets II and V abutting relationship.........................................................119
Figure 3.17. Conjugate shearing along sets II and V..................................................122
Figure 3.18. Spatial constraints on local principal stress directions...........................123
Figure 3.19. Conceptual drawing of opposite senses of shear along parallel joints...123
Figure 3.20. Stress states for which pre-existing fractures will slip...........................126
Figure 3.21. Remote strains consistent with shearing observations ...........................129
Figure 3.22. Mohr-Coulomb analysis investigating mechanics of set I reactivation 131
Figure 3.23. Thin sections of set I fractures in the hinge and backlimb.....................133
Figure 3.24. Kinematics of shearing at Sheep Mt. .....................................................135
Figure 4.1. Geological map of Sheep Mt....................................................................144
Figure 4.2. Various methods of post-processing GPS data ........................................146
Figure 4.3. GPS data collected at Sheep Mt. ..............................................................150
Figure 4.4. Fracture orientation data...........................................................................152
Figure 4.5. Fracture sets present at studied pavements ..............................................154
Figure 4.6. Intensity mesurements..............................................................................157
Figure 4.7. Relative elevations of collected GPS data................................................160
Figure 4.8. Filtered GPS data .....................................................................................161
Figure 4.9. Maximum and minimum normal curvatures across GPS6 and GPS7 .....162
Figure 4.10. Photographs of GPS6 and GPS7 ............................................................164
Figure 4.11. Spherical variance of fracture sets at study sites....................................165
Figure A1.1. Location of Elk Hills .............................................................................173
Figure A1.2. Schematic model of a compressional flower structure..........................174
Figure A1.3. Structure of Elk Hills.............................................................................181
Figure A1.4. Isochore maps at Elk Hills.....................................................................183
Figure A1.5. Elastic displacement field for a flower structure model of Elk Hills ... 187
Figure A2.0. Aerial photograph of Sheep Mt.............................................................193
Figure A2.1. Tectonic map of Wyoming....................................................................194
Figure A2.2. Sheep Mt. field trip stops ......................................................................196
Figure A2.3. Geological map of Sheep Mt.................................................................197
Figure A2.4. Structural map of Sheep Mt...................................................................198
Figure A2.5. Road map to Sheep Mt. .........................................................................199
Figure A2.6. Day 1 field trip stops .............................................................................199
Figure A2.7. Two modes of subduction .....................................................................201
Figure A2.8. Thrust fault interpretation of Laramide deformation ............................202
Figure A2.9. Drape fold interpretation of Laramide deformation ..............................203
Figure A2.10. Stratigraphic column of Bighorn Basin...............................................205
Figure A2.11. Photograph of stratigraphy at the NW nose of Sheep Mt....................206
Figure A2.12. Stratigraphic column of Sheep Mt.......................................................206
Figure A2.13. Geological map of the NE Bighorn Basin...........................................207
Figure A2.14. Major folds within the NE Bighorn Basin...........................................208
Figure A2.15. Synthetic structure contour map of the NE Bighorn Basin .................209
Figure A2.16. Strain energy density models of the NE Bighorn Basin......................211
Figure A2.17. Cross section through the Bighorn Mts. and NE Bighorn Basin.........212
Figure A2.18. Interpretation of Sheep Mt. structure: Hennier and Spang, 1983........313
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Figure A2.19. Interpretation of Sheep Mt. structure: Forster et al., 1996 ..................214
Figure A2.20. Interpretation of Sheep Mt. structure: Brown, 1984 ...........................214
Figure A2.21. Relationship btwn Sheep Mt. and Bighorn Mts.: Forster et al., 1996 .215
Figure A2.22. Interpretation of Sheep Mt. structure: Stanton and Erslev, 2002 ........215
Figure A2.23. Structure of the Torchlight Field ........................................................216
Figure A2.24. Tectonic map of the NE Bighorn Basin ..............................................217
Figure A2.25. Structure contour map of Sheep Mt. ...................................................218
Figure A2.26. Model setup to test fault geometry at Sheep Mt..................................219
Figure A2.27. Results of heuristic tests of fault geometry at Sheep Mt.....................220
Figure A2.28. Basemap for 2D seismic reflection profiles near Sheep Mt................221
Figure A2.29. Photographs of hinge...........................................................................222
Figure A2.30. Photograph showing topographic high................................................223
Figure A2.31. Fracture pattern map: Harris et al., 1960.............................................225
Figure A2.32. Iso-fracture map: Harris et al., 1960....................................................226
Figure A2.33. Joint frequencies: Johnson et al., 1965................................................228
Figure A2.34. Characterizing fracture orientations ....................................................229
Figure A2.35. Characterizing mode of deformation...................................................229
Figure A2.36. Characterizing abutting relationships..................................................230
Figure A2.37. Fracture pattern in the hinge of the nose .............................................231
Figure A2.38. Stereonets for fracture measurements at site 2....................................231
Figure A2.39. Photo and interpretation of fractures at site 2......................................232
Figure A2.40. Photo and interpretation of fractures at site 2......................................232
Figure A2.41. Rose diagrams of fracture measurements in the nose ........................ 234
Figure A2.42. Fracture pattern in the hinge of the nose .............................................235
Figure A2.43. Fracture pattern in the backlimb of the nose .......................................236
Figure A2.44. Field trip driving route ........................................................................237
Figure A2.45. Stop 4 location.....................................................................................238
Figure A2.46. Pavement at site 8................................................................................239
Figure A2.47. Fracture pattern at site 8 ......................................................................240
Figure A2.48. Rib marks and hackle along joint surface at site 8..............................241
Figure A2.49. Shear along a set II fracture at site 8 ...................................................241
Figure A2.50. Aerial photograph of backlimb of Sheep Mt.......................................242
Figure A2.51. Backlimb stereonet..............................................................................243
Figure A2.52. Backlimb fracture measurements ........................................................244
Figure A2.53. Thin section of a set I fracture in the backlimb...................................245
Figure A2.54. Thin section of a set II fracture in the backlimb..................................245
Figure A2.55. Thin section of a set III fracture in the backlimb ................................246
Figure A2.56. Thin section of a set IV fracture in the backlimb .............................. 246
Figure A2.57. Photographs of set IV fractures in the backlimb .................................247
Figure A2.58. Fractured pavement at site 72 in the backlimb....................................248
Figure A2.59. Left-lateral shear along set I fractures at site 72 in the backlimb........249
Figure A2.60. Left-lateral shear along a set I fracture at site 72 in the backlimb ......250
Figure A2.61. Left-lateral shear along a set I fracture at site 72 in the backlimb ......250
Figure A2.62. Left-lateral shear along set I fractures at site 74 in the backlimb........251
Figure A2.63. Interpretation of fractured pavement at site 72....................................252
Figure A2.64. Photograph of stop 6 sites ...................................................................253
xxi

Figure A2.65. Stereonets of fracture measurements at stop 6 sites ............................254
Figure A2.66. Interpretation of fractured pavement at site 81....................................255
Figure A2.67. Set IV fractures at site 81 ....................................................................255
Figure A2.68. Photograph and interpretation of site 22 pavement.............................256
Figure A2.69. Photograph and interpretation of fractures at site 22 ..........................257
Figure A2.70. Interpretation of stages of fracture formation at site 22 ......................257
Figure A2.71. Photograph and interpretation of conjugate shearing at site 22 ..........258
Figure A2.72. Left-lateral shear along a set V fracture at site 22...............................259
Figure A2.73. Right-lateral shear along a set II fracture at site 22.............................259
Figure A2.74. Interpretation of a sheared set V fracture at site 22.............................260
Figure A2.75. Left-lateral shear along a set V fracture at site 22...............................261
Figure A2.76. Right-lateral shear along a set II fracture at site 15............................ 262
Figure A2.77. Bedding plane slip at site 22 in the backlimb......................................263
Figure A2.78. Backlimb fracture data highlighting set V fractures ...........................264
Figure A2.79. Left-lateral shear along a set V fracture in the backlimb ....................265
Figure A2.80. Elastic model setup with idealized main and thumb thrust faults .......266
Figure A2.81. Most tensile stress field resulting from slip along underlying faults...266
Figure A2.82. Photograph of the forelimb of Sheep Mt.............................................267
Figure A2.83. Forelimb fracture measurements.........................................................268
Figure A2.84. Forelimb fracture patterns ...................................................................269
Figure A2.85. Thin section of a set I fracture in the forelimb ....................................270
Figure A2.86. Reactivated set I fractures in the forelimb...........................................271
Figure A2.87. Splay fractures indicating bedding plane slip in the forelimb.............272
Figure A2.88. Polished underside of a bedding plane in the forelimb .......................273
Figure A2.89. Slickenlines along a bedding plane in the forelimb ............................273
Figure A2.90. Conceptual model of flexural slip: Twiss and Moores, 1992..............274
Figure A2.91. Interpretation of bedding plane slip along the rivercut at Sheep Mt. ..274
Figure A2.92. Photograph of the forelimb; location of site 12...................................275
Figure A2.93. Stratigraphy at site 12..........................................................................276
Figure A2.94. Tensleep pavement at site 12...............................................................276
Figure A2.95. Stereonets of measurements in the Tensleep at site 12. ......................277
Figure A2.96. Set I reactivated fractures at site 12.....................................................277
Figure A2.97. Slickenlines along set I reactivated fracture surfaces at site 12 ..........278
Figure A2.98. Limey sandstone pavement at site 12..................................................279
Figure A2.99. Stereonets of measurements in the limey sandstone at site 12............279
Figure A2.100. Phosphoria pavement SE of site 11...................................................280
Figure A2.101. Stereonets of measurements in the Phosphoria at site 12..................280
Figure A2.102. Photograph of the hinge ....................................................................281
Figure A2.103. Hinge fracture measurements............................................................282
Figure A2.104. Thin sections of set I and set II fractures in the hinge.......................283
Figure A2.105. Fracture pattern in the hinge..............................................................284
Figure A2.106. Dispersion in orientation of hinge fracture sets.................................285
Figure A2.107. Intense fracturing within the Madison Fm. in the hinge ...................285
Figure A2.108. Photograph of site 10.........................................................................286
Figure A2.109. Sandstone fracture measurements in the limbs and hinge.................287
Figure A2.110. Stages of fracture and fold development...........................................291
xxii

Figure A2.111. Mechanism of hinge perpendicular jointing: Gross et al., 1998 .......292
Figure A2.112. Curvature map of Sheep Mt. .............................................................293
Figure A2.113. Geometry for elastic model investigating set II development...........295
Figure A2.114. Modeled elastic displacements and most tensile stress field.............296
Figure A2.115. Correlation of model results and field observations..........................297
Figure A2.116. Conceptual model of folding at Sheep Mt.........................................298
Figure A2.117. Conceptual model of set IR fractures formed in the forelimb...........299
Figure A2.118. Stages of fracturing and shearing of set I fractures ...........................300
Figure A2.119. Proximity of a stress state to brittle failure........................................301
xxiii

xxiv

Chapter 1
Mechanical and stratigraphic constraints on the evolution of faulting
at Elk Hills, CA
Abstract
To unravel the four-dimensional evolution of the Elk Hills Oil Field, Kern
County, CA we integrate seismically interpreted fault surfaces, stratigraphic units, and
stratigraphic features with mechanical models. Correspondence of synthetic
stratigraphic surfaces, deformed by modeled vertical displacement fields, to
seismically interpreted stratigraphic surfaces represented on structure contour maps
suggests that the tectonic history described here is structurally, stratigraphically, and
mechanically consistent, placing constraints on the regional deformation mechanism
and local structure. During the time period investigated, Middle Miocene to present,
the eastern and the western parts of the Elk Hills Anticline developed in response to a
regional horizontal shortening oriented at about 035°. The apparent bend in the trend
of the anticline, from northwest-southeast in the western part of the field, to east-west
in the eastern part of the field is generated by the intersection of two distinct fault
systems. In both fault systems, north dipping fault surfaces are backthrusts of older
south dipping faults. These results have direct implications for the migration and
emplacement of hydrocarbons at Elk Hills, suggesting that Upper Miocene Stevens
turbidite oil pools were derived from sources to the south. Additionally, this study
indicates that the method by which stratigraphic and structural interpretations are
incorporated into a sequence of forward mechanical models represents an effective
means of constraining the structural evolution of a fault network that developed within
a syn-depositional tectonic setting.
Introduction
At Elk Hills Oil Field, Kern County, CA better knowledge of the present day and
evolutionary structure of the underlying faults would improve recovery efforts. Gross
fault geometry has implications for the existence of hydrocarbon traps and the
trajectories of wellbores, while evolutionary structure has implications for the timing
1

of hydrocarbon migration and entrapment. Previous studies have considered the
current day fault geometry at Elk Hills (Nicholson, 1990; Imperato, 1995), and a
recently published geochemical analysis of various oils constrains the timing of
emplacement of specific oil pools (Zumberge et al., 2005). To date, however, there has
not been a well documented study of the growth of the subsurface faults at Elk Hills
through time.
A three-dimensional seismic reflection volume acquired over the field in 1999
images the shallow fold and fault geometry, for the first time making such a study
feasible. Although the existence of this seismic reflection volume greatly enhances
efforts to determine the history of faulting at Elk Hills, two issues require further
attention. As in many cases, the resolution of the data at Elk Hills decreases with
depth, and so the deep fault geometry, specifically how faults intersect at depth,
remains debatable. Additionally, evolutionary structure is not directly observable
within the three-dimensional seismic reflection data volume, as time is not
represented.
Recent literature offers a methodology to help constrain fault geometry and
timing using mechanical models. Savage and Cooke (2004) present the displacement
fields resulting from heuristic models with simple fault geometries for a field area
where no faults are directly observable, asserting that the geometry of mechanically
interacting faults can be constrained by the distributions of their displacement fields.
Muller and Aydin (2005) and Resor et al. (2005) use mechanical models to investigate
recent earthquakes where fault geometry is obscure, citing plausible fault geometries
as those that produce modeled elastic displacement fields closely resembling observed
displacements. These studies represent one episode of deformation, wherein fault
geometry is static. Elk Hills is a growth fold, and the seismic reflection data reveal that
not all faults have the same history of activity, so this modeling approach must be
tailored to incorporate the different stages of fault evolution.
Prior structural studies document how various geological and geophysical
observations can be integrated to constrain the growth history of faults in cases where
faults and folds are imaged adequately. For example, Medwedeff (1989), Suppe et al.
(1992), Bloch et al. (1993), Shaw and Suppe (1996), and Shaw et al. (2002) show that
2

growth wedges can be analyzed to determine intervals of fault movement along a
single fault plane and to distinguish pre-, syn-, and post-faulting strata. Stratigraphic
signatures present within the seismic reflection data at the Elk Hills Oil Field indicate
that structural development and deposition were coeval, thus motivating a similar
analysis. At Elk Hills, however, activity along multiple intersecting faults presents a
complex history, requiring that numerous growth signatures be interpreted.
In our study of Elk Hills, we show how these two previously published
techniques can be combined to develop a fault history that is structurally,
stratigraphically, and mechanically consistent. In light of profiles of interval
thicknesses, stratigraphic bedding relationships, and isochore maps, we constrain the
sequence of faulting. This interpreted growth sequence is then tested by comparing the
displacement field inferred from structure contour maps to model displacement fields.
The structure contour maps are taken as a cumulative representation of the elastic
displacement fields modeled through each stage of fault evolution. It is tacitly
assumed that the elastic stress perturbations due to individual slip events relax
between events in such a way that the displacement fields for multiple events over ten
million years are simply additive.
Where stratigraphic signatures are not adequate to determine the activity of a
specific fault during a given period, or the resolution of the data does not permit a
complete understanding of fault geometry with depth, alternate fault geometries and
faulting histories were considered. A series of forward mechanical models was
constructed to test each possible fault network evolution. In this paper, we focus on
the growth sequence that led to the best correlation between modeled and interpreted
displacement fields. We note in the sections on structural interpretation and
stratigraphic constraints on fault evolution where certain interpretations required
additional testing.
This study uses stratigraphic and mechanical principles to constrain the four-
dimensional evolution of the fault system beneath the Elk Hills Anticline. It provides
insight into the tectonic framework in which the field developed and the geometry and
timing of faulting, thus having significant implications for hydrocarbon migration.
Additionally, this study represents an extension of previous work on mechanical
3

forward modeling of deformation in compressional tectonic settings (Shamir and Eyal,
1995; Savage and Cooke, 2004), developing a methodology to consider both multiple
faults and multiple time steps in an analysis that combines faulting kinematics and
mechanics.
Regional Geological Setting
Elk Hills is located 25 km (15.5 mi) north of the bend in the San Andreas Fault
(Fig. 1.1) in the southern San Joaquin Valley within the fold and thrust belt that lines
the west side of the valley (Nicholson, 1990). Deformation within this belt is linked to
tectonism along the San Andreas Fault, which lies just west of the Temblor Range that
bounds the western limit of the valley. Coalinga, Kettleman Hills, and Lost Hills are
similarly oriented antiforms proximal to Elk Hills. Interpretation of the causal tectonic
mechanism for these folds has varied. In the 1970s, Wilcox et al. (1973) and Harding
(1974, 1976) suggested that these echelon folds are the result of a wrenching
mechanism related to slip along the San Andreas Fault. In the following decade,
interpretation of a seismic reflection profile across Kettleman Hills (Wentworth et al.,
1984) led to the reclassification of these anticlines as thrust related. This interpretation
was later strengthened by the analysis of earthquakes near New Idria in 1982 (M=5.5),
Coalinga in 1983 (M=6.5) and Kettleman Hills North Dome in 1985 (M=6.1), which
indicated the activity of thrust faults striking subparallel to the trend of these folds
(e.g. Namson and Davis, 1988; Ekstrom et al., 1992; Stein and Ekstrom, 1992). In situ
borehole studies that estimated the regional maximum horizontal compression
direction as northeast-southwest (e.g. Mount and Suppe, 1987; Zoback et al., 1987;
Castillo and Zoback, 1994), when combined with the northwest-southeast trend of the
anticlinal hinges, are also consistent with the thrust related hypothesis.
A proposition that the folds formed initially with trends oblique to the San
Andreas Fault and subsequently were rotated to their subparallel orientations, with
deformation style transitioning from wrench-related shearing to fault-perpendicular
shortening (Miller, 1998). In this paper, we show that mechanical models do not
generate representative uplift at Elk Hills when the slip along the underlying faults is
4

36 0 00’
Diablo Range
New Idria
Coalinga
Coalinga
120 0 00’
San Andreas Fault
N
Kettleman Hills
Temblor Range
0 mile 20
0 km 30
120 0 00’
San Joaquin
Valley
Lost Hills
Elk Hills
Buena Vista
119 0 00’
Taft
Midway Sunset
Sierra Nevada Range
Bakersfield
San Emigdio Mtns
119 0 00’
Figure 1.1. Location of the Elk Hills Oil Field within the southwestern San Joaquin
Valley of California.
5
36 0 00’
35 0 00’

predominantly strike-slip; and we present mechanical model results for the data
included in this study that are consistent with a thrust fault related growth mechanism.
Elk Hills Field
Elk Hills was first classified as oil land based on field work by Arnold and
Johnson (1910) that correlated surface morphology and lithologies at Elk Hills to that
of other known oil fields in the San Joaquin Valley. Shallow tests proved the existence
of oil in 1911 (Maher et al., 1975). In 1912, Elk Hills was set aside as Naval
Petroleum Reserve No. 1 and remained largely shut-in until 1976 (Reid and McIntyre,
2001). During this time, several geological studies, based on field data and
increasingly deeper subsurface data, were conducted at Elk Hills (e.g. Thoms and
Smith, 1922; Pemberton, 1929; Woodring et al., 1932; Maher et al., 1975).
As a result of the multitude of wells drilled on site since the discovery of oil and
field studies carried out within the greater San Joaquin Valley, the upper Tertiary
stratigraphy at Elk Hills is well documented (e.g. Maher et al., 1975; Sarna-Wojcicki
et al., 1979; Loomis, 1990; Sarna-Wojcicki et al., 1990; Bloch, 1992; Miller, 1999).
The Monterey Formation, comprising the mid to late Miocene interval, is the best
known stratigraphic sequence at Elk Hills. It has been the subject of much study in the
past few decades due to its function as both source rock and reservoir for
hydrocarbons, with the diagenesis of its constituent porcelanites (e.g. Graham and
Williams, 1985; Eichhubl and Behl, 1998; Reid and McIntyre, 2001) and the
deposition and trapping mechanisms of its constituent turbidites (e.g. MacPherson,
1978; Webb, 1981; Reid, 1990; Reid, 1995; Shultz, 2003) receiving specific attention.
These studies combined with investigations into the larger San Joaquin Valley
petroleum system (e.g. Peters et al., 1994), have bolstered recovery efforts at Elk Hills.
Today, over 2,000 wells are producing from four petroleum zones. As of 2004,
cumulative production at Elk Hills exceeded 1.2 billion barrels of oil and 1.8 trillion
cubic feet of natural gas, making it the seventh largest oil field in the continental U.S
(California Division of Oil and Gas, 2005).
6

Structural Interpretation
The Elk Hills structure has an overall northwest-southeast anticlinal trend (Fig.
1.2a, 1.2b). At shallow depths, Elk Hills is a broad structure with two slight highs
representing left stepping echelon anticlines called 29R and 31S (Fig. 1.2a). At depth,
these anticlines are distinct and a much lower amplitude fold called the Northwest
Stevens structure lies to the northwest of the echelon folds (Fig. 1.2b). Collectively,
these three structures constitute the Elk Hills Anticline and Oil Field.
The fault interpretation at Elk Hills is based primarily upon the three-
dimensional volume of seismic reflection data that was collected over the field from
1999 to 2000. Along with borehole data from over 700 wells, the seismic data place
constraints on the large scale faulting in the field. In the western part of the field, four
main structure bounding faults have been identified, all of which strike northwest-
southeast (Fig. 1.2a and 1.2b). Three of these faults, 1R, 2R, and 3R, are thrust faults
with dips that decrease with depth (Fig. 1.2c). The decollement surface for the 1R fault
is placed within the Late Oligocene Lower Santos shale, approximately 1 km above
that inferred for the 2R and 3R faults, which sole into the Early Oligocene Tumey
shale. These decollement levels are somewhat ambiguous within the seismic reflection
data, and have been located with the help of mechanical models. Mechanical models
have also helped to interpret the fourth fault, 5R, as a backthrust of the 1R fault.
Correlating the spatial location of these faults with the shape of deformed seismic
reflectors as displayed on structure contour maps, we associate the 2R fault with the
Northwest Stevens anticline, the 3R fault with the 31S anticline, and the 1R and 5R
faults with the 29R anticline (Fig. 1.2).
Cross sections through the eastern part of the field reveal a different structural
configuration (Fig. 1.2d). Here, the 7 fault is a steep and nearly planar fault dipping to
the south. It trends east-west, as does the 6R fault, which dips to the north.
Stratigraphic features within the seismic data imply that the 6R fault is much younger
than the 7 fault (Fig. 1.2c). An anticlinal crest comparable to the anticlinal crest
located slightly to the south of the 7 fault has not developed adjacent to the 6R fault at
depth, suggesting that early in the structural history of Elk Hills, the 7 fault was the
only fold forming fault present in the eastern part of the field. Mechanical
7

SW NE
S N
8
8
0 km 2
0 km 2
7
0 mile 1
7
0 mile 1
6
6
5
5
depth (km) 0
McDONALD
3R
2R
1R
4
BASE REEF RIDGE
3
5R
CALITROLEUM
2
NWS
anticline
WILHELM
31S
anticline
MYA4-A
1
29R
anticline
depth (km) 0
6R
4
McDONALD
7
BASEREEFRIDGE
3
2
CALITROLEUM
31S
anticline
WILHELM
1
MYA4-A
(c) (d)
A A’
B B’
NE
119 0 32’00”
119 0 26’00”
119 0 20’00”
119 0 32’00”
119 0 26’00”
119 0 20’00”
0 km 2
8
B
0 km 2
B
0mile1 6R
1829
305
0mile 1
N
2438
A
N
6R
1R
610
A
1R
5R
3048
35 0 16’00” 35 0 20’00”
914
3658
7
5R
31S anticline
31S anticline
29R anticline
1219
4267
7
1524
29R anticline
4877
3R
depth (m)
3R
depth (m)
NWS anticline
B’
NWS anticline
B’
2R
A’
35 0 20’00”
35 0 16’00” 35 0 20’00”
2R
A’
35 0 20’00”
C.I. = 76 m (250 ft)
C.I. = 152 m (500 ft)
(a) (b)
119 0 32’00”
119 0 26’00”
119 0 20’00”
119 0 32’00”
119 0 26’00”
119 0 20’00”

Figure 1.2 (opposite page). (a) Structure contour map of a Late Pliocene stratigraphic
unit. The traces of the six seismically interpreted, structure bounding faults are drawn
on the map and labeled. Dashed lines represent faults that are below the contoured
surface. (b) Structure contour map of a Middle Miocene stratigraphic unit. At this
depth, the slight highs seen in figure 1.2a, the 31S and the 29R anticlines, are clearly
two distinct anticlines. A fold of much lower amplitude, the Northwest Stevens
structure, lies to the north. (c) A cross section through the western part of the field
running along the line A to A’ in (a) and (b). (d) A cross section through the eastern
part of the field running along the line B to B’ in (a) and (b). Labeled anticlinal crests,
faults, and marker horizons are the structural and stratigraphic elements factoring into
this study.
modeling has indicated that the 6R fault is a backthrust of the 7 fault and does not
cross-cut the 7 fault.
Velocity Model
We created a three-dimensional velocity model to convert surfaces interpreted
within the seismic data volume from the time domain to the depth domain. The three
dimensionality of this model is very important to the preservation of the shapes of the
faults as they are interpreted, and these shapes provide the input geometry for the
mechanical models. As noted, the majority of faults at Elk Hills are not planar. Thus,
the two-dimensional method, commonly applied within fields where planar faults
exist, of converting fault polygons (hanging wall and footwall cuts) from time to depth
at various horizons and then extending a planar surface between these polygons to
generate a three-dimensional fault surface, is not adequate for the Elk Hills field.
The velocity model was calibrated with the Base Reef Ridge horizon (see
below). This horizon was selected as a calibration surface based primarily on the
exceptional well control of 704 data points. It was chosen over other surfaces of
comparable well control due to its position lower in the stratigraphic column, thus
providing calibration to deeper levels. The velocities within the model range from
1,400 m/sec (4,600 ft/sec) near the surface to 6,000 m/sec (19,700 ft/sec) at depth.
This velocity profile corresponds to the two-way travel time interval extending from 0
to 5 seconds, the lower limit of the seismic volume.
9

Stratigraphy
Five stratigraphic markers were selected for use in this study: the Middle
Miocene McDonald horizon, the Early Pliocene Base Reef Ridge horizon (BRR), the
Early Pliocene Calitroleum horizon, the Middle Pliocene Wilhelm horizon, and the
Late Pliocene Mya 4-A horizon (Fig. 1.3). Due to strong seismic reflections (large
impedance contrasts), each horizon can be correlated throughout the three-dimensional
volume. Well picks, numbering into the hundreds for each of these horizons, serve as
calibration for the geophysical seismic reflection volume. No horizons older than the
mid Miocene McDonald horizon are included in this study because both well control
and clarity of the seismic reflection imaging diminish greatly below the McDonald
marker. The results of this study therefore have implications for the development of
Elk Hills during the time period extending from the Middle Miocene to the present.
Stratigraphic constraints
Stratigraphic analyses contribute significantly to the interpretation of fault
evolution at Elk Hills because the faulting is syn-depositional growth faulting. As
evident in cross sectional views (Fig. 1.2c and 1.2d), stratigraphic intervals thin
toward faults within their hanging wall and thicken discontinuously across the fault
planes into the footwall. These and similar stratigraphic features can be identified and
used to interpret the timing of relative motion. These techniques provide sufficient
constraints on fault evolution so particular fault initiations can be bracketed between
the deposition times of different stratigraphic layers.
Pseudowells
We term the first method of stratigraphic analysis pseudowells because they are
artificial profiles of interval thicknesses. To construct pseudowells, we generated
depth converted cross-sections running perpendicular to the strike of the faults. We
then drew two well-path trajectories for each fault, one in the hanging wall and the
other in the footwall, both parallel to and equidistant from the fault (Fig. 1.4a). Where
a trajectory intersects with the center of an interval, a bedding perpendicular
10

PERIOD
QUAT.
NEOGENE
PALEOGENE
EPOCH
PLEIST.
PLIOCENE
MIOCENE
OLIGOCENE
EOCENE
FORMATION MEMBER / ZONE
SAN JOAQUIN
ETCHEGOIN
MONTEREY
TEMBLOR
sandstone
pebbly sand
clay shale
silty shale
TULARE
DRY GAS ZONE
SHALLOW OIL ZONE
REEF RIDGE
ANTELOPE SHALE /
MCDONALD
DEVILWATER / GOULD
MEDIA
CARNEROS
UPPER SANTOS
CASTLEROCK
LOWER SANTOS
SALT CREEK / CYMRIC
OCEANIC
TUMEY
STEVENS
PHACOIDES
KREYENHAGEN
siliceous shale
dolomitic shale
LITH.
interbedded sandstone
and siltstone
sandstone lens
Mya 4-A
Wilhelm
Calitroleum
Base Reef
Ridge
(BRR)
McDonald
Figure 1.3. Stratigraphic column of the mid to upper tertiary sediments at Elk Hills
based on Maher et al. (1975). The stratigraphic positions of the five markers used in
this study are noted to the right of the column. The lithology column is highly
simplified.
11

thickness was measured and plotted. The thickness of each interval is hung on the top
horizon of that interval (Fig. 1.4b). Because the strike of the faults in the eastern part
of the Elk Hills field is much different from that in the western part, we consider these
parts separately.
Pseudowell interpretation relied heavily upon cross-sections. For instance, the
cross section in figure 1.4a shows a regional thickening of sediments toward the
southwest during McDonald to BRR time of depostion. For the other three time
intervals considered, the regional thickening direction is reversed, with thickening
toward the northeast. When looking at the pseudowell plot (Fig. 1.4b), we note
interruptions in the regional trends. Fault activity is identified based on both
stratigraphic thinning and sharp changes in thickness across faults. An anomalously
thin interval is correlated with the location of a structural high, where thinning is
interpreted as the result of erosion (or lesser deposition) of sediments caused by uplift
associated with slip on the underlying fault. Eroded sediments from the uplifted
hanging walls are subsequently deposited on the footwalls, creating a difference in
thickness of the interval from one side of the fault to the other.
Pseudowell interpretations: Western Elk Hills
Figure 1.4b shows that during the period from McDonald to BRR time, there is a
departure from the trend of thickening toward the southwest at pseudowells H2R and
H3R. These pseudowells are positioned in the hanging walls of the 2R and 3R faults,
respectively. The cross section in figure 1.4a shows a change in thickness across the
2R fault and a larger change across the 3R fault, suggesting that both faults were
active during this interval. The thickness of the McDonald to BRR interval in figure
1.4a is slightly different across the 1R fault. We tentatively infer that 1R was less
active (or inactive) during this time relative to 2R and 3R, but reexamine this activity
more closely in subsequent examples. There is no thinning of the McDonald to BRR
interval in the 29R anticline during this time, and the hanging wall and footwall
thicknesses across the 5R fault are constant, indicating that the 5R fault was inactive.
12

(a)
depth (km)
0
1
2
3
4
5
6
7
8
(c)
1
2
3
4
5
depth (km) 0
6
7
8
0 mile 1
0 km 2
SW NE
H6R
F6R
0 mile 1
0 km 2
F5R H5R
1R
31S
anticline
6R
29R
anticline
7
5R
H1R F1R H3R F3R
3R
H7 F7
31S
anticline
2R
NWS
anticline
MYA4- A
S N
H2R F2R
NE
MYA4-A
(b)
(d)
m
0
400
0
400
800
0
400
800
1200
0
400
800
F5R H5R H1R F1R H3R F3R H2R F2R
MYA4-A
WILHELM
CALITROLEUM
BRR
1200
SW NE
m
0
400
0
400
0
400
0
400
800
F6R H6R H7 F7
MYA4-A
WILHELM
CALITROLEUM
BRR
S N
Figure 1.4. Cross sections through the (a) western and (c) eastern parts of the field
showing the locations of pseudowells used for stratigraphic analysis. The orientation
of the cross sections run from A to A’ and B to B’ in figure 1.2a. Dashed gray lines
represent pseudowell paths and white dots represent the intersection points of these
wellpaths with the centers of stratigraphic intervals. White lines represent the bedding
perpendicular thickness measurements made for each interval along wellpaths.
Pseudowell plot of the thicknesses in meters of the four stratigraphic intervals in each
well location for the (b) western and (d) eastern parts of the field.
13

The most notable feature in the interval from BRR to Calitroleum time is the
large contrast in hanging wall and footwall thickness across the 2R fault (Fig. 1.4a).
This observation is mirrored in the pseudowell plot at well F2R, where the thickness is
much greater than in well H2R, departing from the slight thickening trend. We infer
that the 2R fault was very active during this period. Similarly, this interval in well
H3R in the hanging wall of the 3R fault is thin compared to that in well F3R in the
footwall, suggesting continued slip along 3R. Little can be deduced about the activity
of the 1R fault from these plots. As in the earlier interval, the hanging wall and
footwall thicknesses across the 5R fault are constant, suggesting that no slip occurred
from BRR to Calitroleum time.
The Calitroleum to Wilhelm interval is thin in pseudowell H5R compared to
both F5R and H1R (Fig. 1.4b). This suggests that the area near H5R was a structural
high, and implies the presence of an active fault beneath the interval. Slip along either
or both the 1R and 5R faults could produce uplift at H5R. A disparity in the
thicknesses of the Calitroleum to Wilhelm interval between the hanging wall and
footwall of the 5R fault indicates that it was active during this period. It is not possible
to determine from the cross section and pseudowell plots (Fig. 1.4) how large a role, if
any, fault 1R played in the development of the structural high near well H5R. There is
no diagnostic evidence for slip on the 2R fault from Calitroleum to Wilhelm time
based on figure 1.5.
In the final interval, Wilhelm to Mya 4-A, the structure was apparently
composed of a single broad anticline. The pseudowells on the flanks of the structure,
wells F5R, H2R, and F2R, are thick compared with other wells. Based on the thin
intervals in the H1R, F1R, and F3R pseudowells, we deduce that uplift was still
occurring due to slip on faults in both the northeast and the southwest parts of the
field.
Through this analysis, we recognize that slip along the northeastern faults, 2R
and 3R, affected depositional patterns during the Late Miocene, whereas Pliocene
depositional patterns suggest slip along all of the major faults. We conclude that slip
along the 2R and 3R faults initiated before slip along the 1R and 5R faults, but that
motion along the earlier faults continued as slip along the 1R and 5R faults initiated.
14

Pseudowell interpretations: Eastern Elk Hills
The most interesting stratigraphic constraints on faulting in the eastern part of
the Elk Hills Oil Field pertain to the 7 fault and can be seen in both cross-section (Fig.
1.4c) and pseudowell analysis (Fig. 1.4d). The differences in interval thickness across
the 7 fault from well H7 to well F7, as well as the differences in interval thickness
across the anticline from well H7 to well H6R, indicate that activity along the 7 fault
decreased after the deposition of the Base Reef Ridge to Calitroleum interval.
Pseudowell analysis indicates that wells located in the hanging wall and footwall of
the 6R fault, wells H6R and F6R, have equivalent thickness for each of the studied
intervals. The 6R fault was not active during these intervals.
Bedding relationships
The second technique for constraining fault timing is the examination of
stratigraphic bedding relationships that are indicators of fault movement. Figure 1.5
provides schematic drawings of the five relationships considered: divergent fill,
disrupted reflectors, onlap fill, divergent reflectors, and disrupted fill (Mitchum et al.,
1977). Interpretation of these relationships is based upon the interaction of structure
and stratigraphy. Divergent fill indicates syn-faulting strata, disrupted reflectors
indicate pre-faulting strata, onlap fill indicates post-faulting strata, divergent reflectors
indicate syn- to post-faulting strata, and disrupted fill indicates syn-faulting strata
relative to one fault and pre-faulting strata relative to the second fault. Many such
bedding relationships are imaged within the Elk Hills seismic reflection dataset and
these provide important constraints on fault activity (Fig. 1.6).
Bedding relationship interpretations
Divergent fill is shown in figure 1.6, where beds thin onto, and truncate against,
the anticlinal crest in the hanging wall of the 3R fault within the McDonald to BRR
interval. The 3R fault was thus active during the deposition of this interval. The 1R
fault offsets this same stratigraphic package with no apparent across fault thickness
change. Consideration of the kinematics involved in the process of offsetting divergent
15

(a) (d)
(b)
(c)
(e)
2 1
Figure 1.5. The five stratigraphic bedding relationships considered in this study. Each
suggests a timing relationship between faulting and the deposition of sediments. (a)
Divergent fill indicating syn-faulting strata. (b) Disrupted reflectors of equal thickness
indicating pre-faulting strata. (c) Onlap fill indicating post faulting strata. (d) Divergent
reflectors indicating syn-faulting to post faulting strata. (e) Disrupted fill indicating that
the strata are syn-faulting relative to fault 1 and pre-faulting relative to fault 2
(Mitchum et al., 1977). This figure also suggests a timing relationship between the
two faults, with fault 1 being older than fault 2.
16

fill leads to the following conclusions: (1) the 3R fault is older than the 1R fault; (2)
stratigraphic layers above the base of the divergent fill post-date the initiation of slip
along the 3R fault; (3) the entire divergent fill package is older than slip along the 1R
fault that offsets it.
Onlap fill and divergent reflectors are seen in figure 1.6 as sags in the BRR,
Calitroleum, and Wilhelm horizons above the 1R fault. These features reflect a
slowing or termination of slip along the 1R fault at the time of deposition of the
deformed horizons. Just above the Wilhelm horizon, however, the next resolvable
reflector is fairly straight, with no kink above the 1R fault. This geometry leads to the
deduction that 1R fault activity slowed after the deposition of the Wilhelm horizon.
The interval of rock between the bent and straight reflectors consists of post faulting
strata that leveled out the paleotopography that was generated by previous slip along
the 1R fault.
At the northeast end of the cross section shown in figure 1.6, divergent
reflectors are labeled above the 2R fault. These reflectors document an incremental
infilling of paleotopography. Reflectors one through four are sequentially less
divergent, indicating that each layer was subjected to less deformation subsequent to
its deposition than the previous layer. The degree to which these reflectors are
divergent indicates that slip along the 2R fault slowed during Calitroleum to Wilhelm
time and may have ceased shortly after Wilhelm time.
Disrupted reflectors of equal thickness occur across the 5R fault just above the
Calitroleum horizon. Because there is no discrepancy in the thickness of hanging wall
and footwall beds, it is inferred that movement along the 5R fault postdates the
deposition of the Calitroleum horizon.
Isochores
The final technique for stratigraphic analysis constrains both fault height and the
timing between deposition and faulting using isochore maps that provide contours of
the vertical thickness of a given interval. We have removed overthickening effects due
to repeated sections across thrust faults from the isochore maps. Four isochore maps
17

two-way time (s)
1.0
2.0
3.0
4.0
5R
29R
anticline
onlap fill
1R
divergent fill
0 mile 1
31S
anticline
0 km 2
3R
2R
1
4
3
2
divergent
reflectors
SW NE
Figure 1.6. Line drawing of a seismic line exhibiting each of the stratigraphic bedding
relationships shown in figure 1.5. Timing relationships can be deduced from analysis
of these indicators.
18
1
2
3
4
5
approximate depth (km)

were interpreted, representing each of the studied time intervals (Fig. 1.7a, 1.7c, 1.7e,
1.7g). In analyzing these maps, we focused on two fault-related signatures, contour
merging and bed thinning. Closely spaced and merging contours (Fig. 1.8a) may
indicate that a fault cut the interval at the time of deposition (Fig. 1.8b). Sediments
eroded off the hanging wall may be deposited on the footwall side of the fault,
resulting in a sharp thickness contrast across the fault. The thinning of beds may
indicate a structural high (Fig. 1.8c). Isochore maps do not contain information about
the relative depths of any two points within a layer. Thus, thinning intervals could
result from syn-depositional faulting below the interval, so the beds of interest are
uplifted (Fig. 1.8di), or post-tectonic infilling by sediments of paleotopography (Fig.
1.8dii). We use the seismic character of divergent reflectors, as previously illustrated
in figure 1.6, to determine which interpretation is more representative of the faulting in
question.
Isochore interpretations: McDonald to Base Reef Ridge
Isochores of vertical thickness between the McDonald and the Base Reef Ridge
markers (Fig. 1.7a) show that a structural high is present along the trace of the 2R
fault, indicating an active fault beneath the interval at the time of deposition. The
structural high and close contours along the trace of the 3R fault indicate that it cut the
interval during the time of deposition. Both of these faults were previously determined
to be active prior to McDonald deposition, based on fault movement indicators.
Isochore interpretation presents an additional conclusion in terms of the relative ages
of these faults. Because the 3R fault cut further up section than the 2R fault during this
time interval and the two faults sole to the same decollement level (Fig. 1.2b and
1.4a), we infer that the 3R fault is older than the 2R fault.
A few small isolated structural highs exist along the trace of the 1R fault,
indicating that it was not slipping along its entire present day length. We infer that this
isochore map captures the very early stages of growth of the 1R fault. Because the
thickness of the McDonald to BRR interval remains roughly constant across the
location of the trace of the 5R fault, we infer that the 5R fault was inactive during this
time interval.
19

(a)
35 0 16’00” 35 0 20’00”
(c)
35 0 16’00” 35 0 20’00”
(e)
35 0 16’00” 35 0 20’00”
(g)
35 0 16’00” 35 0 20’00”
N
0mile1 0 km 2
N
0mile1 0 km 2
N
0mile1 0 km 2
N
0mile1 0 km 2
119 0 32’00”
2R
2R
2R
2R
119 0 32’00”
5R
5R
5R
5R
3R
1R
119 0 26’00”
3R
1R
1R
3R
3R
1R
119 0 26’00”
C.I. = 76 m (250 ft)
7
6R
119 0 20’00”
C.I. = 76 m (250 ft)
7
C.I. = 15 m (50 ft)
7
6R
6R
C.I. = 15 m (50 ft)
7
6R
119 0 20’00”
35 0 20’00”
thickness
(m)
1524
1219
914
610
305
35 0 20’00” thickness
(m)
35 0 20’00”
thickness
(m)
35 0 20’00”
1829
1524
1219
914
610
305
427
366
305
244
183
122
thickness
(m)
366
305
244
183
122
(b)
35 0 16’00” 35 0 20’00”
(d)
35 0 16’00” 35 0 20’00”
(f)
35 0 16’00” 35 0 20’00”
(h)
35 0 16’00” 35 0 20’00”
20
119 0 32’00”
119 0 32’00”
119 0 32’00”
119 0 32’00”
119 0 26’00”
119 0 26’00”
119 0 26’00”
119 0 26’00”
119 0 20’00”
N
0 km 2
119 0 20’00”
N
0 km 2
119 0 20’00”
N
0 km 2
119 0 20’00”
N
0 km 2
35 0 20’00”
35 0 20’00”
35 0 20’00”
35 0 20’00”
1
0.95
0.9
0.85
0.8
0.75
0.7
0.65
0.6
0.55
1
0.95
0.9
0.85
0.8
0.75
0.7
0.65
0.6
1
0.95
0.9
0.85
0.8
0.75
0.7
1
0.95
0.9
0.85
0.8
0.75
0.7
normalized thickness normalized thickness normalized thickness normalized thickness

Figure 1.7 (opposite page). Isochore maps of the intervals: McDonald to Base Reef
Ridge (a) as interpreted, (b) as modeled; Base Reef Ridge to Calitroleum (c) as
interpreted, (d) as modeled; Calitroleum to Wilhelm, (e) as interpreted, (f) as modeled;
Wilhelm to Mya 4-A (g) as interpreted, (h) as modeled. Fault traces have been plotted
and labeled on the interpreted isochore maps with solid lines representing faults that
cut through the interval at the time of deposition, dashed lines representing faults that
were below the interval at the time of deposition, and dotted line representing faults
that had not yet begun to slip at the time of deposition of the interval. The thickness
colorbar and contours for the interpreted isochores have been converted from feet
into meters. Modeled isochores show normalized thicknesses with a 0.1 contour
interval. For location referencing, an index map outlining the production blocks of the
field has been plotted on both interpreted and modeled isochore maps.
In the eastern part of the field, the structural high and close contours along the
trace of the 7 fault indicate that it was active and cut up through the McDonald to Base
Reef Ridge interval during the time of its deposition. Further to the south, along the
present day trace of the 6R fault, there is no evidence of fault activity. The 6R fault
trace lays in a low that is most likely an expression of the hanging wall subsidence that
occurs well behind the tipline of a thrust fault as a result of displacement of material
up the fault plane (Savage and Cooke, 2004).
Isochore interpretations: Base Reef Ridge to Calitroleum
The isochore map representing the time interval from Base Reef Ridge to
Calitroleum deposition (Fig. 1.7b), highlights a few changes in fault activity from the
previous interval. The very close contours and large difference in contour values
across the 2R fault (about 1000 feet), indicate that this fault was active and cut up
through the section, uplifting Base Reef Ridge to Calitroleum sediments in the
hanging wall, much of which were eroded off to create the large disparity in thickness
of this interval across the 2R fault. The 3R fault apparently was still active during this
interval based on the adjacent structural high, and the fact that it cut through this
interval. If we compare the extent of the expression of the 3R fault in the Base Reef
Ridge to Calitroleum interval with the previous interval, we see that slip migrated
toward the southeastern end of the fault, which cuts through the interval, as indicated
by the pattern of thinning across the crest of the 31S anticline. The east-west portion
of the 31S anticline is thin during this interval, indicating that uplift along the 7 fault
21

Figure 1.8. Fault related signatures seen within isochore maps. (a) Close contours
are indicative of a fault cutting the interval during deposition. (b) A cross sectional
view through the anticline along line C to C’ shown in (a). (c) Thin beds are indicative
of a structural high. The line D to D’ shows the location of a cross-section through the
anticline that can have two possible configurations: (di) thinning beds can result from
an active fault beneath the interval, causing syn-depositional uplift, (dii) thinning beds
can result from infill of paleotopography after fault slip.
22

continued into Base Reef Ridge to Calitroleum time. In contrast with the previous
interval, however, there is not a jump in the contour values along the trace of the fault,
so it did not cut through the interval. The highly asymmetric shape of the thinning
pattern, with a much steeper gradient on the northern side of the structural high,
suggests that the sediments of this interval were draped over the tip of an active fault.
To the south, in the vicinity of the 6R fault trace, the absence of a structural high, and
of close contours, reveal that the fault had not yet developed at the time the
Calitroleum was deposited.
During this interval, the 1R fault was slipping along the entire length of the
present day fault, as indicated by the extent of the structural high. To the southwest of
this structural high, where the thickness of the interval is fairly constant, there are no
signs of activity along the 5R fault. We interpret the structural highs to the southeast
of the 29R anticline as being related to uplift along faults associated with the Buena
Vista and Midway-Sunset fields (Fig. 1.1).
Isochore interpretations: Calitroleum to Wilhelm
Isochore thickness patterns and fault activity change drastically after Calitroleum
time. In the Calitroleum to Wilhelm isochore map (Fig. 1.7c), there is little
disturbance of contours in the area of the 2R fault. During this interval, the 2R fault
slipped much less than in the previous time interval, if at all. Similarly, slip along the 7
fault virtually shut off, as the average strike of the 31S anticline in this isochore map is
oriented more northwest-southeast than previously, with the east-west section not as
well-defined. The 3R fault was still active from Calitroleum to Wilhelm time, as the
northwest-southeast part of the 31S anticline remained thin. In the southwestern part
of the study area, a northwest-southeast striking depression bounded on the northeast
by close contours appears along the trace of the 5R fault. This marks the beginning of
slip along the 5R fault and expresses the uplift and erosion of hanging wall sediments.
Judging from the pattern of thinning over the 29R structure, where the gradient along
the northern limb is steep, the 1R fault also was active during the Calitroleum to
Wilhelm interval.
23

Isochore interpretations: Wilhelm to Mya 4-A
The isochore map (Fig. 1.7d) of the time from Wilhelm deposition to Mya 4-A
deposition, depicts a relatively thin stratigraphic interval. The difference between the
thickest and thinnest sections is small, and thus the contour map appears very noisy
and is more difficult to interpret, but trends are noticeable. The 31S and 29R anticline
locations remain thin through this time period, indicating that the 3R, 1R, and 5R
faults were still active. As in the previous interval, little evidence for motion along the
2R fault exists. Examination of the southern part of the isochore map indicates that the
5R fault remained active beneath the interval while the 6R fault had not yet begun to
slip.
Stratigraphic Constraints on Fault Evolution
The pseudowell, bedding relationship, and isochore interpretations made at Elk
Hills allow us to place constraints on the evolution of the fault system beneath the
anticline (Fig. 1.9). These stratigraphic interpretations indicate that in the western part
of Elk Hills, both the 2R and 3R faults were active prior to deposition of the
McDonald horizon. Initiation of slip along isolated segments of the 1R fault occurred
at some time after McDonald deposition, but before Base Reef Ridge deposition and
the 1R fault began slipping as a whole after Base Reef Ridge deposition. The 5R fault
formed during the interval between Calitroleum and Wilhelm deposition.
Interpretations for the eastern part of the field indicate that the 7 fault was active prior
to McDonald deposition and slowed greatly after Calitroleum deposition and that the
6R fault formed very late in the evolution of the anticline.
Mechanical Modeling
To test the mechanical viability of the stratigraphically interpreted fault
chronology, and to further refine the evolution (both timing and geometry) of the fault
network at Elk Hills, we turn to forward numerical models. The remainder of this
paper focuses on the method involved in developing a mechanical model to apply to
growth faulting. We do not show the results of all the scenarios tested, but only the
model that provided the best fit for the data at Elk Hills. From this model, we
24

(a)
A A’
3R
pre-McDonald
(Middle Miocene)
A A‘
A A‘
1R
5R
3R
2R
pre-Base Reef Ridge
(Early Pliocene)
A A‘
1R
3R
3R
2R
pre-McDonald
(Middle Miocene)
2R
pre-Wilhlem
(Middle Pliocene)
(b)
B B’
7
pre-McDonald
(Middle Miocene)
B B’
6R
7
post Mya-4A
(Late Pliocene)
Figure 1.9. Conceptual model of fault evolution in (a) the western part and (b) the
eastern part of the Elk Hills oil field. Each box represents a distinct stage in the
faulting history in which a new fault, shown in black, begins to slip. Faults shown in
gray have been active during a prior stage of evolution. These schematic fault crosssections
are located along lines A to A’ and B to B’ in figures 1.2a and 1.2b.
25

determined: (1) the 6R fault formed as a backthrust of the 7 fault sometime after Mya
4-A deposition; (2) the 5R fault is a backthrust of the 1R fault; (3) the 1R fault has a
different decollement surface than the 2R and 3R faults, which sole at a deeper
stratigraphic level; and (4) of the major faults included in this study, only the 7 and 2R
faults are inactive today. For all of the remaining faults, additional increments of slip
accumulated in each successive stage of deformation once the fault initiated.
For the mechanical modeling involved in this study, we use Poly3D (Thomas,
1993), a boundary element computer program based on the deformation of a linear
elastic, homogeneous, and isotropic solid. It is a three-dimensional displacement
discontinuity program that solves for the elastic stress, strain, and displacement fields
resulting from fault slip. Complex fault geometries can be investigated because the
program models faults as assemblages of triangular elements of displacecment
discontinuity. Each element is constructed by the superposition of angular dislocations
(Comninou and Dunders, 1975; Jeyakumaran et al., 1992). Previous investigators have
documented agreement between numerical approximations resulting from Poly3D and
related analytical solutions (Thomas, 1993; Willemse et al., 1996; Crider and Pollard,
1998); thus validating the reliability of the code.
Our hypothesis for Elk Hills is that the faults are first order heterogeneities and
that heterogeneity in mechanical properties of the stratigraphic layering contributed to
a lesser degree to the shape of the folds. Dealing with a homogeneous model space
allows us to investigate deformation related to fault heterogeneity in an otherwise
simple and well-constrained setting. We show that significant insight can be gained
from this approach which has the advantage of being more efficient to implement than
approaches that could address the material heterogeneities.
Boundary Conditions
Local boundary conditions are specified on each triangular element as three
components of a uniform displacement discontinuity or of the traction at the midpoint.
We prescribe local zero traction in the strike and dip directions and zero displacement
discontinuity in the direction perpendicular to the elements. These conditions allow
26

the two surfaces of each element to slip freely in a strike-slip and dip-slip sense, but
restrict the element surfaces from opening or interpenetrating.
We consider several different remote (tectonic) strain boundary conditions,
depicted in the insets in figures 1.10a – 1.10f, and observe how points along an
originally flat observation grid are displaced as the Elk Hills faults respond to the
remote loading. For this analysis of the remote boundary conditions, we simplify the
model to the application of one strain step to build a basic intuition as to how variation
in remote strain direction affects the deformation. We observe the pattern of uplift,
noting where it has the same general trends as those seen in the interpreted structure
contour maps (e.g. Fig. 1.2a). The following discussion examines these correlations
for each of the boundary conditions. We disregard slip along the 6R fault because
stratigraphic analysis has shown it to be very recent.
The first loading condition tests whether slip along the San Andreas Fault could
be wholly responsible for the deformation at Elk Hills. We specify a zero remote stress
field and apply a right lateral displacement discontinuity of 33 mm, representing the
slip accrued in one year (Toda and Stein, 2002), on a model San Andreas Fault that
extends to 1000 km depth. The use of this deep dislocation is based on studies of
transform plate boundaries using GPS data that indicate such a dislocation embedded
in an elastic half-space produces a displacement field at the free surface that is
comparable with the measured displacement field (e.g. Savage, 1990; Muller et al.,
2003). The uplift pattern mapped within the seismic volume (Fig. 1.2a) is not similar
to the computed displacement field (Fig. 1.10a), so we conclude that slip on the plate
boundary is unlikely to generate the Elk Hills uplift.
In an Elk Hills structural overview paper, Nicholson (1990) suggested that the
slip of the Elk Hills faults that generated the uplift we see today was driven by a deep
seated left lateral strike-slip fault into which the shallower faults converge. In a
representative mechanical model (Fig. 1.10b), left lateral motion along such a deep
seated fault serves as the loading for the shallower, Elk Hills faults. At shallow depths,
the model fault geometry is similar to that shown in figures 1.2, 1.4a, 1.6, and 1.9. At
depth, however, where the seismic data do not resolve the faults well, we take the
liberty of converging the faults into the proposed strike slip fault. The interpreted
27

shallow fault geometry does not converge simply into one deep strike slip fault, so two
distinct, offset, vertical fault segments are used (Fig. 1.10b). A left-lateral
displacement discontinuity of 33 mm is applied along these faults within a zero remote
stress field. A map view representation of the vertical displacement field at a
stratigraphic level comparable to the level of the Mya 4-A horizon is shown in figure
4b. No uplift is generated in the area of the 31S and 29R anticlines. Based on these
results, it seems improbable that the uplift at Elk Hills was generated by strike-slip
motion along a deep-seated left-lateral fault.
The displacement fields in figures 1.10c through 1.10f assess the orientation of
the maximum horizontal tectonic contraction on the pattern of uplift. In the first two
examples, applied remote contractions of one percent at 110° (Fig. 1.10c) and
140° (Fig. 1.10d), have only small components normal to the western faults. These
cases resolve predominantly left-lateral and right-lateral motion along the Elk Hills
faults, respectively. Neither of these examples produce results that correlate well with
the interpreted displacement fields.
Concluding that the greatest uplift is generated by a horizontal tectonic
contraction oriented perpendicular to the strike of the dipping faults, we consider
strain fields in which the maximum contraction is at 035° and 000°, perpendicular to
the average strike of the western faults (125°) and that of the eastern faults (090°),
respectively. Both displacement fields (Fig. 1.10e and 1.10f) replicate the northwest-
southeast anticlinal trend in the western part of the field and the east-west trend in the
eastern part of the field. The displacement associated with the north-south contraction
correlates better in the eastern part of the field as a larger east-west trending high
develops at the eastern end of the 31S anticline. In the western part of the field,
however, this model correlates more poorly because a localized high is generated far
to the northwest, at the tip of the 2R fault. As in figure 10d, this is a reflection of the
right lateral strike-slip that occurs along the western faults. The best correlations are
found for a tectonic strain field in which the horizontal contraction is perpendicular to
the majority of the structures. We proceed by applying a 035° contraction to the
models. To ensure that our models replicate deformation in a thrust
28

35 0 16’00” 35 0 20’00”
35 0 16’00” 35 0 20’00”
35 0 16’00” 35 0 20’00”
(a) (b)
N
0 km 2
(c) (d)
N
0 km 2
(e) (f)
N
0 km 2
119 0 32’00”
119 0 32’00”
119 0 26’00”
119 0 26’00”
SAF
119 0 20’00”
119 0 20’00”
35 0 20’00”
35 0 16’00”
35 0 20’00”
35 0 16’00”
35 0 20’00”
35 0 16’00”
35 0 16’00” 35 0 20’00”
35 0 16’00” 35 0 20’00”
N
0 km 2
N
0 km 2
N
0 km 2
normalized displacement
Figure 1.10. Model results of test cases in which one step models were run under
various remote boundary conditions. Plotted are the normalized vertical displacement
fields resulting from driving mechanisms of (a) right-lateral slip along the San Andreas
Fault; (b) slip along deep seated left-lateral strike-slip faults; (c) remote horizontal
contraction oriented at 110°; (d) remote horizontal contraction oriented at 140°; (e)
remote horizontal contraction oriented at 035°; (f) remote horizontal contraction
oriented at 000°. Insets show the geometry of the model setup with red arrows
indicating the driving mechanism for each scenario. With the exception of (b), all
insets are in map view with the Elk Hills index map shown in blue for reference. The
inset for model (b) is a three-dimensional view with the geometry of the hypothetical
deep vertical strike-slip faults drawn in dashed lines.
29
35 0 16’00” 35 0 20’00”
119 0 32’00”
119 0 32’00”
119 0 26’00”
119 0 26’00”
119 0 20’00”
119 0 20’00”
35 0 20’00”
35 0 16’00”
35 0 20’00”
35 0 16’00”
35 0 20’00”
35 0 16’00”

environment, where the minimum principal compressive stress is vertical, we apply a
small contraction of 0.1 percent in the minimum horizontal strain direction.
Model Increments
A fault chronology relative to specific stratigraphic horizons has been
constrained above. Each interval bracketed by two horizons can be represented by an
individual model step. Because certain faults are active only during the deposition of
specific stratigraphic intervals, we begin by prescribing an appropriate amount of
strain for each interval. To stay within the elastic limit of a few percent, we set a total
maximum horizontal strain of one percent from McDonald time of deposition through
the present day. We then partition this strain into increments proportional to the length
of time represented by each interval (Table 1.1a). We further partition increments
during which new faults begin to slip by assigning half of the allotted strain to a step
in which the new fault is not yet active and the remaining half of the allotted strain to a
step in which the new fault is allowed to slip. Increments 9 and 10 are an exception
because fault 6R has been found to be much younger than the Mya 4-A horizon, and
so it is allowed to slip for only one quarter of the time represented by the Mya 4-A to
surface interval.
Although a constant strain rate is questionable, it provides a basis from which to
make first order evaluations of similarities between modeled and mapped deformation.
Table 1.1a documents the ages selected for each of the horizons and the corresponding
strains applied to each stratigraphic interval. Table 1.1b documents the strains applied
to model increments that have been defined based on fault activity. Because the total
strain is less than the actual tectonic strain, the models cannot reproduce the
magnitudes of uplift. However, we postulate that the patterns of uplift are set by the
geometry and sequence of faulting and the relative magnitudes of uplift are set by the
relative magnitude of applied strain.
To address the fact that some paleotopography may have been present at the time
of deposition of each layer, we apply a pre-deformation step. An undeformed
observation grid, representing the newly deposited, undeformed horizon, is given ten
percent of the deformation that occurred across the next oldest surface during the
30

Table 1.1. (a) Documentation of the ages assigned to each horizon (approximate
error bars are given), the time period represented by each stratigraphic interval (∆t),
and the corresponding applied strains. Ages gathered from Sarna-Wojcicki et al.,
1979; Loomis, 1990; Sarna-Wojcicki et al., 1990; Bloch, 1992; Miller, 1999. Refer to
the stratigraphic column shown in figure 1.3. (b) Documentation of the model
increments defined based on fault activity, and the corresponding applied remote
strain in the maximum contraction direction, active faults, and stratigraphic interval.
Abbreviations: McD = McDonald, BRR = Base Reef Ridge, CLLM = Calitroleum,
WILM = Wilhelm.
31

previous interval to account for paleotopography. The figure of ten percent is not well
constrained, but was applied to the Base Reef Ridge, Calitroleum, Wilhelm, and Mya
4-A horizons. The McDonald horizon required special attention, as cross sections
showing the geometries of the faults (Fig. 1.2c and 1.2d) indicate that its topography
was influenced by slip prior to McDonald deposition along the 7 fault for a greater
period of time than by slip along the 2R and 3R faults. We ran a pre-deformation step
as discussed above for an interval in which the 7, 2R, and 3R faults were all active.
The amount of strain applied to this increment was a small percentage of the total
strain applied to the model from McDonald time of deposition to the present time
(Table 1.1). Before this step, we applied a deformation step in which the McDonald
horizon was at the surface, but only the 7 fault was active. We tested how differing
amounts of strain applied in this step affected the overall deformation of the
McDonald horizon.
Model Calibration
The deformed shapes of stratigraphic horizons as interpreted in the seismic data
volume were used to calibrate the model. A planar observation grid represents an
undeformed stratigraphic horizon. After the grid is slightly deformed to account for
the paleotopography at its time of deposition, the locations of points across this grid
are tracked in three dimensions through the deformation stages as faults are generated
and slip. After the final stage of deformation, the shape of the modeled horizon is
compared with the shape of a horizon at a similar stratigraphic level as interpreted
within the seismic volume. A representative model should reproduce comparable
trends and relative magnitudes of uplift in the areas of the 31S and 29R anticlines.
Depending on the depth of the specific horizon, various fault cuts should also be
reproduced. The sequence of steps that most closely reproduces the shape of the
interpreted horizon is considered to be the best model to fit the fault evolution at Elk
Hills.
Because the faults at Elk Hills developed in a syn-depositional setting, the
horizons interpreted within the seismic data volume record deformation due
32

predominantly to slip on faults during the time period since deposition of the horizon,
with a small amount of recorded deformation attributed to the existing topography at
the time of deposition of the surface. Thus, the deformation of several surfaces can be
modeled, and the results compared with the interpreted deformation of the surfaces, to
ensure that the fault system evolution through time is consistent. Therefore, we
include all five of the horizons considered within the stratigraphic analysis in the
model.
Model Results
The forward modeled deformation of the McDonald, Base Reef Ridge, and
Wilhelm surfaces (Fig. 1.11a, 1.11c, and 1.11e) and the corresponding interpreted
surfaces (Fig. 1.11b, 1.11d, and 1.11f) show that the long wavelength deformation of
Elk Hills is well represented by the models. At each of the tested levels, there is
correlation in the general trend of the Elk Hills field, with the structure trending
northwest-southeast in the western part of the field and transitioning in the middle of
the field to trending east-west in the eastern part of the field. The Calitroleum and Mya
4-A surfaces have similar deformational features as the Wilhelm surface, respectively
more and less pronounced. We omit the analysis of these results in favor of focusing
on the deeper horizons with more complicated deformation patterns.
The McDonald surface, cut by all faults included in this study and subjected to the
largest amount of cumulative strain, is expected to be the most difficult to reproduce.
Regardless, model results (Fig. 1.11a) indicate that we have accounted for all of the
major deformational features noticeable across the interpreted surface (Fig. 1.11b).
Fault cuts of the 2R, 3R, 1R, 5R, 6R, and 7 faults can be seen on the modeled surface.
The 31S, 29R, and Northwest Stevens anticlines are present, are located at reasonable
spatial positions, and are of similar relative magnitudes as in the interpreted surface.
31S is slightly more uplifted than 29R, and both of these structures are much higher
than the Northwest Stevens anticline. The east-west trending portion of the 31S
anticline also is present. The asymmetry of the 31S and Northwest Stevens anticlines
are well represented in the model results, with the steeper limb of the 31S being that
33

(a)
35 0 16’00” 35 0 20’00”
(c)
35 0 16’00” 35 0 20’00”
(e)
35 0 16’00” 35 0 20’00”
N
0mile1 0
0
0 km 2
N
mile1
km 2
N
0mile1 0 km 2
119 0 32’00”
24Z sand body
2R
119 0 32’00”
119 0 32’00”
2R
119 0 32’00”
119 0 32’00”
2R
119 0 32’00”
26R sand body
5R
5R
5R
1R
3R
3R
1R
119 0 26’00”
1R
119 0 26’00”
119 0 26’00”
119 0 26’00”
119 0 26’00”
3R
119 0 26’00”
C.I. = 152 m (500 ft)
7
6R
C.I. = 152 m (500 ft)
7
6R
C.I. = 76 m (250 ft)
7
119 0 20’00”
119 0 20’00”
119 0 20’00”
119 0 20’00”
119 0 20’00”
6R
119 0 20’00”
35 0 20’00”
depth (m)
35 0 20’00”
depth (m)
35 0 20’00”
4877
4267
3658
3048
2438
1829
3658
3048
2438
1829
1219
depth (m)
1829
1524
1219
914
607
305
(b)
(d)
(f)
35 0 16’00” 35 0 20’00”
35 0 16’00” 35 0 20’00”
119 0 32’00”
119 0 32’00”
119 0 32’00”
119 0 32’00”
119 0 26’00”
119 0 26’00”
119 0 26’00”
119 0 26’00”
119 0 20’00”
N
0 km 2
119 0 20’00”
119 0 20’00”
N
0 km 2
119 0 20’00”
N
0 km 2
Figure 1.11. Interpreted and modeled vertical displacement fields for three stratigraphic
horizons: McDonald (a) as interpreted, (b) as modeled; Base Reef Ridge (c)
as interpreted, (d) as modeled; Wilhelm (e) as interpreted, (f) as modeled. The
colorbars and contours for the interpreted maps have been converted from feet into
meters. The traces of the six seismically interpreted, structure bounding faults are
plotted on the interpreted map with dashed lines representing faults that are below
the stratigraphic surface. For location referencing, an index map outlining the
production blocks of the field has been plotted on all vertical displacement fields. In
(a), the locations of the Stevens sands reservoirs of the 31S anticline, the 2B
reservoir at the western nose of the 29R anticline, and the Asphalto field to the
southwest of the 29R anticline are outlined in solid white, while turbidite sand bodies
are outlined in dashed white (after Zumberge et al., 2005). See text for a discussion
of how fault evolution may have played a role in the charging of Stevens reservoirs.
35 0 16’00” 35 0 20’00”
34
119 0 32’00”
119 0 32’00”
119 0 26’00”
119 0 26’00”
119 0 20’00”
119 0 20’00”
35 0 20’00”
35 0 20’00”
35 0 20’00”
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
normalized displacement normalized displacement normalized displacement

which lies along the 3R and 7 faults, and the steeper limb of the Northwest Stevens
anticline being the limb that lies along the 2R fault.
At the Base Reef Ridge level, the model outputs a surface that is cut by faults
2R, 3R, 1R, 5R, and 6R (Fig. 1.11c). The uplift of the 31S and 29R anticlines is of
virtually the same magnitude, and the Northwest Stevens anticline is a lower
amplitude feature. Although the east-west portion of the 31S anticline is present in the
modeled surface, the model has not produced sufficient uplift at this location. A
structure that the model has reproduced nicely is the 29R anticline. If we compare the
modeled surface (Fig. 1.11c) with the interpreted surface (Fig. 1.11d), we see that in
both cases, the steeper anticlinal limb is along the 1R fault at the northwestern extent
of the structure, but that at the southeastern extent of the structure, the steeper
anticlinal limb is along the 5R fault.
At the shallow level of the Wilhelm surface, the three distinct anticlines of the
Elk Hills field have coalesced into one broad structure (Fig. 1.11e and 1.11f). The
model shows two localized highs in positions corresponding to the 31S and 29R
anticlines. The magnitude of uplift at the location of the 29R anticline is slightly
greater than that at the 31S anticline. The Northwest Stevens structure cannot be
distinguished as a separate feature. The east-west portion of the 31S anticline, again, is
not reproduced with sufficient uplift.
Discussion
The mechanical modeling undertaken in this study has refined the interpreted
fault activity and geometric constraints at Elk Hills. If the deformation at Elk Hills
occurred in a manner that can be approximated by linear elastic behavior during
faulting with stress relaxation between events, then the suggested fault evolution is
physically realistic. We acknowledge, however, that if the deformation at Elk Hills
occurred in a manner that differs significantly from the postulated behavior, then
faulting scenarios that our modeling efforts have deemed physically impossible, such
as continued slip along the 2R fault to present, or a common decollement surface for
the 1R and 3R faults, may in fact be possible. Correspondence between interpreted and
modeled displacement fields indicates that the models presented here do approximate
35

the deformation at Elk Hills. This method of sequential forward modeling for the total
observed deformation therefore provides an opportunity to investigate deformational
processes in an environment wherein fault geometry evolves.
Modeled and Interpreted Discrepancies
The most noticeable difference between the modeled and mapped surfaces is to
the southwest of the Elk Hills structure, where all model results show a pronounced
depression and the interpreted structure maps do not. Figures 1.11b, 1.11d, and 1.11f
show highs in this corner of the maps, related to uplift within the Midway Sunset field
(Fig. 1.1). We would not expect our models to replicate these features because we
have not included faults outside the Elk Hills field.
A discontinuity in the uplift of the 31S anticline is seen in all of the model
results where the strike of the anticline changes from northwest-southeast to east-west.
We suggest that this is a result of the limits of seismic resolution, because the data are
very noisy at this location. A complete understanding of how the northwest-southeast
and east-west fault systems intersect cannot be gained from examination of the seismic
data. The faults were extrapolated across this data gap, but the resulting geometry is
awkward and may not accurately represent the intersection of the two fault systems.
The final noteworthy difference between the modeled and interpreted
deformation for each surface is the inability of the model to reproduce the east-west
trending portion of the 31S uplift. Varying fault frictional properties and the extent of
pre-McDonald uplift are two possible explanations that we do not address in this
study. Modeling a more pronounced eastern section of the 31S anticline through time
could also be accomplished by applying a remote strain oriented more normal to the
eastern faults. We assess this possibility in the following section.
To further assess the correspondence between modeled and interpreted
deformation, we present modeled isochores of the four intervals that were
stratigraphically analyzed (Fig. 1.7b, 1.7d, 1.7f, 1.7h). These synthetic isochores have
been edited to remove overthickening effects along fault traces and thus can be
directly compared with the interpreted isochores (Fig. 1.7a, 1.7c, 1.7e, 1.7f). Many of
36

the features within the interpreted isochore maps are also present in the synthetic
isochore maps.
Tectonic Strain Analysis
We explore the effects of a clockwise rotation in relative plate motion between
the North American and Pacific plates that occurred between 5 and 8 Ma (Atwater,
1970; Engebretson et al., 1985). If the tectonic strain direction had rotated along with
this plate motion rotation, then the remote contraction direction during the early stages
of structural evolution at Elk Hills would have been oriented more N-S than the
applied 035° remote contraction. The cumulative deformation field of the McDonald
surface is shown in figure 1.12a. For this modeling scenario a remote contraction at
000° was applied for steps 1-5 (Table 1.1b), representing growth prior to 5 Ma, and a
remote contraction at 035° was applied for steps 6-10 (Table 1.1b), representing
growth after 5 Ma. As compared with figure 1.11a, figure 1.12a shows greater uplift
along the 7 fault, the oldest fault in the field that strikes sub-perpendicular to this early
contraction direction. This comparison indicates that the 7 fault accrued significant
slip during the period of structural development represented by model steps 1-5. By
applying a two step deformation pathway, we may more closely replicate the
interpreted deformation fields.
Noting that a change in remote strain applied to half of the modeling steps does
not drastically change the uplift modeled along the western faults, we revisited the
possibility of having a remote contraction oriented at 000° throughout the period of
Elk Hills growth investigated by this study using the full ten step model and observing
the modeled deformation of the McDonald surface. Figure 1.12b shows the resulting
cumulative deformation field. In comparing figure 1.12b with the interpreted
McDonald surface in figure 1.11b, we suggest that this constant 000° remote strain
results in an east-west trending uplift that is too high relative to the northwest-
southeast trending portion of the 31S anticline. This discrepancy could be reconciled
by readjusting the amount of strain applied to model increments representing
deformation occurring prior to McDonald deposition. A second discrepancy that we
37

(a) (b)
35 0 16’00” 35 0 20’00”
119 0 32’00”
119 0 32’00”
119 0 26’00”
119 0 26’00”
119 0 20’00”
N
0 km 2
119 0 20’00”
35 0 20’00”
35 0 16’00”
35 0 16’00” 35 0 20’00”
normalized displacement
119 0 32’00”
119 0 32’00”
119 0 26’00”
119 0 26’00”
119 0 20’00”
N
0 km 2
Figure 1.12. Normalized modeled vertical displacement fields for the McDonald
surface resulting from: (a) a two step remote strain history in which a change from a
remote contraction oriented at 000° to one oriented at 035° replicates the change in
relative plate motion that occurred 5 Ma., and (b) a constant remote strain oriented at
000°. For location referencing, an index map outlining the production blocks of the
field has been plotted on the vertical displacement fields.
38
119 0 20’00”
35 0 20’00”
35 0 16’00”

cannot explain away is the location of the northwest-southeast trending portion of the
31S anticline. As referenced by the index map shown in black in figure 1.12b, the
mapped location of the maximum uplift has been translated to the northwest as
compared with figures 1.11a and 1.11b. Although this tectonic strain sensitivity
analysis has indicated that changes in the orientation of the contraction between 000°
and 035° do not drastically affect the resulting deformation, we suggest that the small
change in location of the 31S anticline when modeled with a tectonic contraction at
000° provides justification for using the 035° direction.
Additional support for a remote strain oriented perpendicularly to the western
faults is derived from consideration of the relative ages of the eastern and western
faults and the mechanics of fault formation. The 7 fault (in the east of the field) strikes
E-W and is a steeply dipping planar feature. It is the oldest fault in the model and
could be a remnant of an older structural fabric. Extensional basins formed throughout
Southern California beginning around 18Ma as the triple junction passed through the
area. Maps from Tennyson (1989) show that some of these basins were oriented E-W.
Thus, it is possible that the 7 fault is a remnant of one of these basins linked to the
formation of the San Andreas Fault. With the change in the tectonic regime to
contraction after the migration of the triple junction, strain could have first localized
along this normal fault, reactivating it in reverse motion. As contraction continued, the
deformation was too great to be accommodated by this fault alone, so the fault system
in the western part of the field developed, striking perpendicular to the remote
contraction. The later development of the 6R fault in an E-W orientation could also be
attributed to the older structural fabric. Although the 035° orientation of the tectonic
contraction does not produce the optimal deformation pattern in the eastern part of the
Elk Hills field, it is the most sound orientation mechanically when we consider the
development of the thrust faults in the western part of the field.
Implications for Hydrocarbon Migration
When integrated with results from a recent geochemical study investigating
reservoir charging at Elk Hills (Zumberge et al., 2005), the structural history presented
here may constrain the direction from which hydrocarbons charged the 31S Stevens
39

turbidite oil pools. The 31S anticline is located updip from subbasins both to the north
and to the south, making migration pathways from either direction a possibility
(Zumberge et al., 2005). Biomarker maturity indicators for the 31S reservoirs show
very little thermal-maturity variation, indicating quick flooding of the reservoirs in the
Late Pliocene or Pleistocene that was possibly due to the development of a fault
system on the flanks of the anticline (Zumberge et al., 2005). Our structural study
suggests that the 7 fault on the northern flank of the anticline developed very little past
the Early Pliocene, while the 6R fault on the southern flank of the anticline began to
form during the Pleistocene. We therefore hypothesize that the oil pools residing
within the 31S Stevens turbidite sands migrated from the south.
The structural evolution of the fault system beneath Elk Hills may also explain
the existence of the oil pool within the Stevens turbidite sands at the Asphalto field,
located to the southwest of the 29R anticline (Fig. 1.11a). The geochemistry of this oil
pool matches the geochemistry of the oil pools found within the Stevens sands in the
2B reservoir at the southeast nose of the 29R anticline and across the 31S anticline
(Fig. 1.11a). The 2B reservoir was most likely charged by spillage from the 31S oil
pool. As Zumberge et al. (2005) explain, however, the existence of the Asphalto oil
pool in the Stevens turbidite sands is enigmatic. Geochemical data imply that this
reservoir was not charged by the same oils that exist in the other reservoirs in the
western part of the field, and the low permeability porcelanite within the crest of the
29R anticline should have impeded migration of oils within the 2B pool to the
Asphalto field (Zumberge et al., 2005). The 2B reservoir lies near the southeast lateral
termination of the 5R fault and the Asphalto oil field lies near the northwest lateral
termination of the 5R fault (Fig. 1.11a). Perhaps motion along the 5R fault allowed the
fault to act as a conduit (Antonellini and Aydin, 1994; Barton et al., 1995; Caine et al.,
1996; Huang et al., 1998; Aydin, 2000; Wiprut and Zoback, 2000), transporting oil
from the turbidite sands within the 2B reservoir through the porcelanite along the
length of the 29R anticline and depositing it in the turbidite sands to the southwest of
the 29R anticline. In this case, the migration of these oils would have been during
Pleistocene time, as the sequence of events would have been: (1) development of the
6R fault and charging of the 31S Stevens reservoirs; (2) spillage of oil into the 2B
40

eservoir; (3) migration of oil along the 5R fault from the 2B reservoir to the Asphalto
field.
Pleistocene migration of hydrocarbons into the 31S turbidites is feasible as long
as two conditions are met: the migration preceded the increase in Monterey
porcelanite permeability resulting from the diagenetic conversion of opal CT to quartz;
and either no other migration pathways into the 31S sands were established, or no trap
existed, prior to development of the 6R fault (S. A. Reid, 2006, personal
communication). Migration of hydrocarbons along the 5R fault into the Asphalto field
rather than the updip 24Z field is feasible as the migrating oil would not have been
able to displace oil out of the steep 24Z structure but could flood and displace oil from
Asphalto (S. A. Reid, 2006, personal communication). Although further work is
required to asses the soundness of the suggested migration constraints, the charging of
reservoirs at Elk Hills was most likely influenced by the evolving fault system.
Conclusions
The integration of numerical modeling with stratigraphic interpretation of
seismic data has refined our understanding of the fault evolution at Elk Hills, placing
constraints on decollement levels, the chronology of faulting, and the timing of
faulting relative to reference horizons. These constraints have important implications
for oil migration routes and reservoir charging histories. North dipping faults 5R and
6R are backthrusts of older south dipping faults. Consideration of the locations and
timing of these faults indicates that they have likely played a significant role in the
migration of oil from a source south of the Elk Hills oil field into Pleistocene age traps
within the Stevens sands of the Monterey Formation on the 31S anticline and, in
limited locations, the 29R anticline.
Consideration of the driving mechanism for the deformation at Elk Hills
suggests that since ~ 10 Ma, Elk Hills has been subjected to thrusting related,
predominantly northeast-southwest directed compressional tectonics. Within this
compressional setting, the apparent bend in the trend of the Elk Hills Oil Field has
developed due to the intersection of two distinct fault systems. Modeling indicates that
the faults in the east of the field are most likely the remnants of an older structural
41

fabric trending east-west, whereas the northwest-southeast trending faults to the west
are oriented perpendicularly to the tectonic compression.
Iterative mechanical models adequately approximate the deformation of
stratigraphic horizons interpreted within the seismic volume. This correlation has
provided constraints on the fault evolution at Elk Hills. More generally, the correlation
indicates that sequences of mechanical models can be used to better understand
deformation within growth-faulting settings.
Acknowledgements
This study was supported by Stanford Rock Fracture Project funds as well as
grant EAR-0125935 from the National Science Foundation Tectonics Program.
Fiore’s research was supported by an internship at Occidental Oil and Gas. The
authors thank Bill Long for obtaining permission from Occidental Oil and Gas to work
with and present results from the Elk Hills seismic data set. Discussions with Steve
Graham, Radu Girbacea, Stan Stearns, and Tony Reid significantly contributed to this
study. Critical reviews by Russell Davies, Raymond Sorenson, Laird Thompson, and
Bruce Trudgill improved earlier versions of the manuscript.
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45

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46

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47

Abstract
Chapter 2
The role of fractures in the structural interpretation of Sheep
Mountain anticline, Wyoming
The development of fractures in the sedimentary layers of Sheep Mountain
anticline, a Laramide asymmetric fault-cored fold of the Bighorn Basin, is documented
and interpreted as a method of constraining the kinematic evolution of the fold. This
study suggests the existence of a regional fracture set (set I) predating the Laramide
compression, and striking 110°, oblique to the future fold trend. A joint set (set II),
striking 045° and present in the hinge and backlimb, is associated with the NE-
oriented Laramide compression. Joints striking 135° (set III; fold parallel) are found
within the hinge and are interpreted to have developed in response to the bending of
stratigraphic layers. The two youngest fracture sets are attributed to a late stage of fold
growth: a joint set (set IV) in the backlimb striking parallel to the set I fractures, but
vertical; and a fracture set in the forelimb consisting of set I fractures reactivated as
reverse faults. The relative chronology, mode of formation (opening vs. shearing), and
structural locations of these fractures provide the following constraints on fold
kinematics: there was little or no lateral fold propagation and no hinge migration; limb
rotation or limb flexure and stretching operated at different structural locations during
folding.
Introduction
Fold-fracture relationships were conceptualized in the late 1960s and 1970s by
Price (1967), Stearns (1968), Friedman (1969), and Stearns and Friedman (1972).
These conceptual models have three shortcomings, which have been addressed in
recent investigations. First, they do not consider the temporal evolution of the fold.
The fractures described in these models are correlated with final fold geometry,
without consideration of either the effect of the initial and transitional fold shapes on
fracture development, or fracture evolution during fold growth (Fischer and
Wilkerson, 2000). Second, they neglect to account for the influence of pre-existing
49

fractures (Guiton et al., 2003a; 2003b; Bergbauer and Pollard, 2004). Third, they
disregard the effect of primary faults, which are often associated with fold formation
(Johnson and Johnson, 2002; Savage and Cooke, 2004). Fault slip perturbs the
surrounding stress field on the scale of fault length and can affect fracture formation
within this zone of influence. In this paper, we document the distribution and
characteristics of fractures at Sheep Mountain anticline and use these data to interpret
the evolution of the fold.
Kinematic models attempt to unravel the evolution of a fold with time through
both backward and forward modeling, with the present-day shape of the fold as
calibration (Suppe, 1985; Jamison, 1987; Mitra, 1990; Erslev, 1991; Cristallini and
Allmendinger, 2002; Bump, 2003). These models are based on kinematic assumptions
such as hinge migration (Suppe, 1983; Beutner and Diegel, 1985; Allmendinger,
1998) or fixed hinge (Erslev, 1991; McConnell, 1994; Spang and McConnell, 1997),
rotating limbs (Erslev, 1991) or fixed limb dip (Suppe, 1983; Suppe and Medwedeff,
1990). Recent studies have suggested that a fold may attain its maximum (along
strike) length very early during its evolution (Armstrong and Bartley, 1993; Cristallini
and Allmendinger, 2001; Bernal and Hardy, 2002; Fischer and Christensen, 2004). In
contrast, other workers have inferred that fold tips propagate laterally through time
(Fischer and Wilkerson, 2000), maintaining that vertical displacement on a fault is
accompanied by increasing length (Cowie and Scholz, 1992; Dawers et al., 1993;
Peacock and Sanderson, 1996). We propose that the kinematics of a thrust fault related
fold can be constrained through an examination of the deformation recorded within the
folded layers. This deformation includes the brittle fracturing of sedimentary layers as
recorded by joints, faults, and deformation bands. The chronology of these structural
features, when combined with their geometry and modes of deformation, provide
insight into the structural setting at the time of their formation. We show how
inferences can be made that associate each fracture set with a particular stage of fold
evolution (pre-, early-, syn-, late, or post-folding). The timing and locations of these
fractures, thereby help to inform an improved kinematic model.
Recent studies have attempted to constrain the unknown parameters of folding at
various field sites, making use of mechanical models, for which the present-day fold
50

shape and fracture distributions serve as calibration (e.g. Shamir and Eyal, 1995; Nino
et al., 1998; Zhang et al., 2000; Johnson and Johnson, 2002; Savage and Cooke, 2004,
and references therein). For example, Nino et al. (1998) examined the role of fault dip,
layer thickness, and bedding-parallel slip with elasto-plastic models that replicate the
shape of the Jabal Mquebra anticline in Syria. Johnson and Johnson (2002) showed
that viscous models reproduce the shape of some of the Rocky Mountain foreland
basement-involved folds when the appropriate underlying fault geometry, magnitude
of cover anisotropy, and nature of the basement-cover contact are prescribed. Savage
and Cooke (2004) showed how the geometry of a parasitic fault at Sheep Mountain,
Wyoming can be developed using elastic models. The mechanical models also provide
the opportunity to investigate fold-fracture relationships that may constrain fold
evolution. Theoretical fracture patterns derived from the stress fields computed in a
mechanical analysis can be compared with fracture data collected in the field to test
hypotheses about fold evolution (Guiton et al., 2003a, 2003b).
Sheep Mountain anticline, Wyoming (Fig. 2.1) is widely known for its
exceptional outcrops, most notably in the canyon cut by the Bighorn River,
approximately perpendicular to the axial trend of the anticline. Studies over the past
two decades have contributed to an understanding of the large scale deformation at
Sheep Mountain (Gries, 1983; Hennier and Spang, 1983; Stone, 1993; Brown, 1993;
Forster et al., 1996; Savage and Cooke, 2002), particularly the underlying fault
geometry. Recently, a new geometric model was developed for the subsurface
structure of the anticline (Stanton and Erslev, 2004). From the interpretation of a few
2D seismic reflection lines, as well as surface maps from previous studies (Rioux,
1958; Hennier 1984; Rioux, 1995) and stratigraphic picks within exploration wells,
Stanton and Erslev (2004) interpreted the fold to have resulted from slip along a
basement fault dipping SW that was followed by slip on a NE-dipping fault (Fig. 2.2).
Although the underlying fault geometry at Sheep Mountain has received
attention, knowledge of the fracture patterns is limited. Harris et al. (1960) described
several fracture sets in the Sheep Mountain area and related these to bed thickness and
lithology. They interpreted the systematic (planar, parallel, repetitious) fracture sets as
“of compressional deformational origin” and “related to shear stresses”. However,
51

N
(b)
108°12'
subsidiary
structure
Quaternary
Cretaceous
Jurassic
Triassic
A
108°10'
Permian (Phosphoria Fm)
Carboniferous (Pennsylvanian, Tensleep Fm)
Carboniferous (Pennsylvanian, Amsden Fm)
Carboniferous (Mississipian, Madison Fm)
Anticlinal axis Synclinal axis
108°08'
A'
Big Horn River
Sheep
Mountain
anticline
1 km
(a)
44°
43°
45°
110°
Absaroka Mnts
WIND RIVER
RANGE
108°04'
109°
BIG
HORN
WIND RIVER
108°02'
BASIN
BASIN
Owl Creek Mnts
108°
Big Horn Mnts
107°
100 km
POWDER
Figure 2.1. Geologic and tectonic maps of the Sheep Mountain anticline. (a) Detail of
the Wyoming tectonic map, with a square outlining the location of the anticline. (b)
Geological map of the anticline from Rioux (1994). The line A-A’ is the location of the
cross-section shown in figure 2.2.
52
44°36'
44°34'
Casper Arch
RIVER
BASIN

diagnostic evidence for such an interpretation (see Pollard and Aydin, 1988) was not
obtained. Furthermore, the fracture orientations were not recorded, nor were they
rotated to remove the effect of bedding orientation, and the relative age relationships
of the fracture sets were not deduced from the field observations. Johnson et al. (1965)
studied fracture geometries within two formations of significantly different ages, one
pre-Laramide and one post-Laramide, in the Bighorn Basin. The study was designed
to test the premise that differences between the fracture patterns within the two
lithologies would suggest that a pre-Laramide orogeny had occurred in the Bighorn
Basin. Although the study was inconclusive, fracture orientation (strike and dip) and
length data were collected and interpreted to suggest the mechanism by which each
fracture set formed. Two major joint sets were recorded: one trending east-west and
one trending between 105° and 155°; two minor joint sets were recorded: one trending
north-south and one trending between 025° and 065°. The modes of deformation of
these fracture sets were not observed in the field, but were instead suggested based on
angular relationships between fracture sets and fold axes.
In this paper, we present new field data collected at 60 sites across the
northwestern half of the anticline that consist of fracture mode (opening or shear) and
geometry (orientation, size, and spacing) at the macro- and microscale, along with the
chronological relationships among the fracture sets. We focus on the interpretation of
these data as an indicator of fold kinematics.
Geological and tectonic setting
Sheep Mountain anticline is located along the eastern flank of the Bighorn basin,
which trends NW/SE and is bounded to the east by the Bighorn Mountains, to the
south by the Owl Creek Mountains, to the west by the Absaroka and Beartooth
Mountains, and to the north by the Nye-Bowler Lineament (Fig. 2.1). During the
Paleozoic and Mesozoic, this basin filled with approximately 3000 m of sediments
(Thomas, 1965; Ladd, 1979). The oldest formation exposed at Sheep Mountain is the
Lower Carboniferous Madison limestone (Fig. 2.3), which is about 200m thick, and is
topped by a paleokarst surface. The Madison Formation is unconformably overlain by
the Upper Carboniferous Amsden Formation. The base of the Amsden Formation is
53

SW
0 m
2000 m
4000 m
T. P. P.
Bighorn basin
Cambrian
pre-Cambrian basement
Sheep Mountain
Figure 2.2. Cross section through Sheep Mountain (see Fig. 1b for location) as
interpreted by Stanton and Erslev (2004). The fold is asymmetric and underlain by a
basement (gray shading) thrust fault verging toward the northeast and cross cutting
only the lower sedimentary layers. Stanton and Erslev (2004) interpreted this fault to
be later cut by a southwest-verging thrust fault. The formation above the Cambrian
formation is the Madison Fm. T.P.P. is for the Amsden (Pennsylvanian), Tensleep
(Pennsylvanian), Phosphoria (Permian) and Chugwater (Triassic) Fm.
Perimian Trias
Carb.
(Penn.)
Carboniferous (Miss.)
250 Ma
292 Ma
320 Ma
Chugwater
174m
Phosphoria
68m
Tens
29m
Ams
35m
Madison
230m
Figure 2.3. Stratigraphic section for formations that outcrop at Sheep Mountain after
Ladd (1979). Miss. is for Mississipian. Penn. is for Pennsylvanian.
54
NE

marked by a crossbedded, light gray fine grained quartz arenite (Ladd, 1979). The
remainder of the formation consists of thick siltstones, sandstones, shales and
carbonates. Above the Amsden formation, the Tensleep Formation (also Upper
Carboniferous in age) is composed of interbedded thin sandstones, shales, and
carbonates in its lower part and thicker beds of crossbedded quartz arenite in its upper
part. Above the Carboniferous section is the Phosphoria Formation, Permain in age.
The lower beds of the Phosphoria Fm. are predominantly siltstones and shales, with a
thin interbedded gypsum layer (Ladd, 1979). Higher in section, the formation is
composed of thick carbonates (biolithite, micrite and biosparite). Due to minor
Ancestral Rocky Mountains uplift, the Tensleep Fm. and Phosphoria Fm. are thinned
at Sheep Mountain (Simmons and Scholle, 1990). Above these units, the base of the
Mesozoic rocks is defined by the Triassic Chugwater Formation, distinctive due to its
red color. The overlying sediments are composed of sandstones and shales that have
been eroded in the Sheep Mountain area.
At the end of the Maastrichtian and during Paleocene times, the Laramide
orogeny produced a NE-trending compression (Dickinson and Snyder, 1978;
Engebretson et al., 1985; Bird, 1998; Bird, 2002). Sheep Mountain anticline formed
during the Laramide orogeny as a basement cored, doubly-plunging, asymmetric fold
(Fig. 2.1 and 2.2). Given its orientation (NW-SE), the fold formed perpendicular to the
Laramide direction of compression (NE-SW). This orientation is similar to the
orientation of many folds within the Rocky Mountains, although others formed at
acute angles to the regional compression (Erslev, 1993). At Sheep Mountain, the steep
northeastern limb (forelimb) dips between 40° and 90° northeast. This dip is shallower
near the fold noses and steeper in the central part of the fold. In the southwestern
backlimb, bedding dips are between 10° and 40° southwest. The shape of Sheep
Mountain anticline changes along the fold axis. Near the northern termination, the fold
plunges approximately 20° northwest and the profile is very tight (Twiss and Moores,
1992, p.228). Toward the south, the asymmetry increases while the fold hinge
becomes rounder. At the southern termination, the plunge of the fold axis is
approximately 10° southwest.
55

The fold overlies a fault that has been interpreted as a southwest-dipping thrust
(Hennier and Spang, 1983; Forster et al., 1996; Stanton and Erslev, 2004). Stanton and
Erslev (2004) suggest the displacement along this fault reaches a maximum beneath
the central section of the anticline and decreases toward the north and south noses.
They conclude that this southwest-dipping thrust was later cut by a northeast-dipping
thrust (Fig. 2). This faulting chronology is in opposition to the studies of Hennier and
Spang (1983) and Forster et al. (1996), which suggest that the fault responsible for the
formation of Sheep Mountain Anticline is a SW dipping backthrust of an older NE
dipping thrust, and Stone (2004), which suggests that the SW and NE dipping thrusts
developed contemporaneously in early Laramide time.
Smaller scale faults are present at Sheep Mountain Anticline. Slickensides are
present on bedding (Hennier and Spang, 1983), indicating a component of flexural-slip
folding with slip directions approximately normal to the fold axis. Additionally, some
small reverse faults are present in the hinge and the backlimb of the anticline (Hennier
and Spang, 1983; Forster et al., 1996). In the backlimb, a smaller fold branches from
the main anticline and has an axis trending NNW-SSE. This structure apparently is
associated with a shallower thrust fault that is not linked to any basement fault
(Hennier and Spang, 1983; Forster, 1996; Savage and Cooke, 2004; Stanton and
Erslev, 2004).
Methods
Fracture sampling
Fracture populations were sampled only in the part of the anticline north of the
Bighorn River (Fig. 2.4, 2.5, 2.6). Sandstones were sampled from the Tensleep Fm. in
the anticlinal limbs and from the Amsden Fm. in the hinge. The limestone of the
Phosphoria Fm. was sampled in the fold nose to increase data coverage and to assess
fracture formation as a function of lithology. The fracture orientation data, mode of
deformation (opening or shearing), termination relationships, and evidence for
reactivation are the key data sets incorporated into our analysis of fracture evolution.
Fracture infilling, length, and spacing also were studied. Spacing measurements are
56

Site 27
N
31
Site 36
N
31
Site 08
N
NOSE
Site 28
N
Site 02
N
Site 07
N
36
116
78
57
N
Site 23
N
HINGE
86
Site 39
N
108°10'
Site 18
N
42
Site 40
N
27
02 36
28
29
39
41
07
40
30
14
43
08
44
51 Site 17
N
BACKLIMB
62
42
Site 29
N
Site 41
N
12
23
44°39'
Site 16
N
35
Site 43
N
13
18
44
45
Site 30
N
53
12
17
16
Site 01
N
Site 44
N
37
01
26
19
Site 45
N
Site 19
N
20
47
49
Site 46
N
21
Site 20
N
19
44
FORELIMB
Figure 2.4. Aerial photograph of Sheep Mountain with the backlimb, forelimb, and
hinge fracture measurement sites and the corresponding polar stereonets shown.
Great circles represent the average bedding corrected orientations of fracture sets
measured within the sandstones of the Tensleep and Amsden Formations. Black
great circles correspond to the major fracture sets that are used in the analysis of fold
kinematics. Gray great circles correspond to minor fracture sets that are most likely
due to local deformation. These minor fracture sets are not considered in the present
analysis of fold evolution. The backlimb contains four fracture sets: striking 110° and
bedding perpendicular (set I), striking 045° and bedding perpendicular (set II), striking
135° and bedding perpendicular (set III), and striking 110° and oblique to bedding (set
IV). The forelimb contains one abundant systematic set that strikes 110° and is
perpendicular to bedding (set I). Other fracture sets (are much less numerous and
predominantly trend N-S. In the hinge, three fracture sets are found: striking 110° and
bedding perpendicular (set I), striking 045° and bedding perpendicular (set II), and
striking 135° and bedding perpendicular (set III). The fractures of set III are largely
restricted to the hinge.
22
57
108°10'
Site 14
N
11
46
63
Site 13
N
51
35
50
Site 12
N
44°38'
101
10
1 km
Site 50
N
Site 11
N
24
31
32
Site 21
N
63
24
Site 51
N
Site 10
N
47, 48
26
108°08'
37
Site 31
N
Site 47
N
38
44°37'
39
Site 32
N
Site 48
N
49
37

Jurassic
Trias
Permian (Phospphoria Fm)
Carboniferous
(Pennsylvanien, Tensleep Fm)
Carboniferous
(Pennsylvanian, Amsden Fm)
Carboniferous
(Mississipian, Madison Fm)
Anticlinal axis
Hinge
site 66
N
site 65
N
46
50
site 57
site 64
N
N
Backlimb
N
37
250 m
54
site 56
site 63
N
N
site 67
site 55
57
66 56
55 67
65 68
26
64
54
63 53
62
N
N
61
60
2
site 68
site 54
Forelimb
site 26
site 53
site 02
site 62 site 61 site 60
Figure 2.5. Geologic map from Rioux (1995) of the nose of Sheep Mountain with the
nose fracture measurement sites and the corresponding polar stereonets shown.
Great circles represent the average bedding corrected orientations of fracture sets
measured within the limestone of the Phosphoria Fm. Black great circles correspond
to the major fracture sets that are used in the analysis of fold kinematics. Gray great
circles correspond to minor fracture sets not used in the analysis.
58
52
46
N
58
56
36
N
N
N
31
53
57
N
N
N
N
31
78
61
79

parallel to the bedding and are not normalized to bed thickness. At each outcrop,
fractures were sampled in areas typically a few tens of meters on a side.
The data presented here include evidence from thin sections cut perpendicular to
fracture strike (Fig. 2.6). The samples were collected at the same sites at which
fracture orientations were measured. The samples were collected to confirm, at the
microscale, the macroscopic determination of deformation mode. When the mode is
ambiguous, the structures are called fractures, where confirmed they are referred to as
joints or shear fractures. We collected several samples for each set of fractures in each
structural position. Thus, we believe that the samples are representative of the
deformation modes observed throughout the northern part of the anticline. For brevity,
we show only a few typical thin sections (Fig. 2.6).
Data processing
Four fracture sets are defined based on both orientation data and mode of
deformation. Members of a fracture set share both a common range of strike and dip
orientation, and, with the exception of set I, a common deformation mode. With one
exception, common orientation can be identified only after removal of bedding dip by
stereographic rotation. Fold plunge was not removed because it is less than 20° and it
does not significantly impact the determination of prefolding fracture orientation.
Commonality of fracture orientation after removal of bedding dip is taken as
supportive of a prefolding origin (Hancock, 1985). Fracture strikes either
perpendicular or parallel to bedding strike are not affected by rotation of bedding to
remove the dip and may be interpreted as occurring during any stage of fold growth.
We present stereonets of the orientation data at each measurement site that are not
weighted by abundance, as we believe that this can be biased by outcrop conditions.
However, we note when a fracture set is less systematic and abundant than others.
The stereonets presented in this paper have been produced with a prototype
computer code developed in the Structural Geology Department of the Institut
Français du Pétrole, using an original method for the automatic definition of fracture
clusters. As a standard represention, each fracture is represented locally as a plane
with an orientation given by the unit normal vector as a point (pole) on the unit sphere.
59

N
108°10'
SM 41, 41b
44°39'
SM 44
SM 13
SM 08 SM 44b
SM 23
SM 45
SM 18
SM 16
108°10'
44°38'
1 km
108°08'
Figure 2.6. Sample sites for microscale analysis. Samples SM08, SM13, SM16,
SM18, and SM23 are within the Tensleep Formation. Samples SM41, SM44, and
SM45 are within the Amsden Formation. All sites relate to sites shown in figure 2.4
where fracture data were collected.
60
44°37

The density of fractures is estimated at each point on this sphere using an
Epanechnikov kernel (see Diggle and Fisher, 1985 for examples with other kernels).
Outliers (fractures associated with a small density) are removed by filtering and the
density distribution is smoothed manually changing the variance of the kernel
(Wollmer, 1995). In a first step, cluster centers are identified by searching for local
maxima of the density map using the method introduced by Kittler (1976). This step
results in the definition of number of sets and a guess for the mean pole of each set.
This guess allows each fracture to be classified probabilistically using its distance
from each cluster center. Then the algorithm presented by Marcotte and Henry (2002)
is used to finalize the fracture classification. This method is based on the assumption
of a bivariate normal distribution of fractures within a set. The results of this analysis
are presented in a polar stereonet using the Lambert projection on the lower
hemisphere with great circles representing the mean plane of each fracture set (Fig.
2.4, 2.5, 2.7, 2.9, 2.10, 2.13, 2.15, 2.16, and 2.17). In these figures, the polar stereonets
depict, from left to right: fractures in present-day orientations, fractures in pre-folding
orientations, and the great circle of the calculated mean orientation of the fracture sets.
Curvature calculation
We computed a curvature map (Fig. 2.7) to assess the relative curvature of
various fold locations. Forster et al. (1996) published a structure contour map of a
reference horizon at the base of a Jurassic formation (Sundance Fm.). This map was
generated through field mapping and the construction of serial cross sections that
predict the elevation of the formation in areas where it has been eroded. We digitized
the structure contour map and calculated the maximum curvature across the resulting
three dimensional surface. The curvature was calculated using gOcad, a 3D
geomodeling software program (Mallet, 2002). The algorithm for maximum curvature
selects the prinicipal curvature with the greater absolute value and plots that curvature.
Thus, positive curvature, representative of synclinal features, may be differentiated
from negative curvature, representative of anticlinal features. In figure 2.7, areas of
lighter shades of gray have positive curvature and areas of darker shades of gray have
negative curvature.
61

Hinge
Backlimb
curvature (m -1 )
x10 -3
6
4
2
0
-2
-4
-6
Hinge
Subsidiary fold
Forelimb
Syncline
Figure 2.7. Curvature map of Sheep Mountain anticline calculated from the map in
Forster et al. (1996). See text for calculation details. Light colors represent synclinal
folding and dark colors represent anticlinal folding.
62

Structural Data
Northeastern forelimb
In the forelimb, we observe one systematic fracture set within the Tensleep
sandstone, trending 110° (Fig. 2.4, sites 10 to 14 and 29 to 32). From abutting
relationships in other structural positions of the fold, this set is interpreted as the first
formed in the area, and is thus called set I. Additionally, non-systematic sets are
locally developed (striking primarily 070° and 180°, Fig. 2.4) and are interpreted to
reflect more local rather than fold-scale or regional deformation, and so are not further
considered (Fig. 2.4).
Set I fractures are linear and several meters long (Fig. 2.8). Their spacing is on
the order of a few tens of cm. In the field, their mode of deformation is difficult to
determine, as different fractures within the set exhibit characteristics of either joint or
shear band morphology. In some cases, the fractures are open with or without mineral
fill, and in other cases, they have small positive relief. This latter attribute may be
related to either cementing (for the case of joints or dilational bands) or tighter
packing of grains within the fracture (for the case of deformation bands). At the
microscale, the fractures are defined by zones that contain smaller quartz grains with
more angular shapes, poorer sorting, less porosity, and smaller calcite cement crystals
than the surrounding rock (Fig. 2.9). These features are characteristic of deformation
bands (Aydin, 1978; Antonellini et al. 1994), and we interpret set I fractures to be such
brittle structures. However, no offset or sense of shearing was obvious either in thin
sections or in the field. Thus, we are unable to suggest a mode of deformation for
these fractures.
Bed-normal reverse faults that strike 110° and dip 30° south are present along
the forelimb (at sites 11, 13, 14, and 30 to 32 on Fig. 2.4. and see Fig. 2.10). The faults
are oblique to the fold axis and the Laramide regional compression. The oblique
striations noticeable along the fault planes indicate oblique slip, consistent with the
resolution of shear stress from the NE directed compression onto these planes (Fig.
2.10).
63

S N
a)
Nb planes 94
SE
b)
Nb planes 35
N
N
N
Figure 2.8. Field photographs of fracture patterns on a tilted bedding surface taken
at forelimb sites 12 (a) and 32 (b). Note the abundance and small spacing of set I
fractures (striking 110°). Numerous fractures of different orientations can be observed
but are non-systematic and are not considered in this paper.
N
set I
64
set I
N
N
1 m
1 m
NW

zone of def.
0.5 mm
Figure 2.9. Microscopic detail of a set I fracture in the forelimb from site SM13. This
fracture strikes 110° and dips perpendicular to bedding. In the deformed zone, there
is less porosity than in the surrounding matrix. There are also more angular quartz
grains, that are, for the most part, smaller in size than those within the matrix. There
is also a larger amount of calcitic cement within the deformed zone.
65

SE NW
a)
d)
SE
c)
S 0
N
Nb planes34
1 m
N
b)
N
10 cm
N
NW
10 cm
Figure 2.10. Reactivated set I fractures in the forelimb. (a) Field photograph of set I
(110°) small reverse faults within the sandstone of the Tensleep Fm. at site 13 that
cut a bedding surface. (b) Cross sectional view of the photograph in (a) showing
offset bedding. (c) Close up of one fault: the slip decreases toward fault tips. (d)
Striation data (thin arrows on the fault planes) that indicate an oblique reverse slip
along the faults. The large arrows are inferred direction of compression that is
compatible with the striations.
66

a)
NW SE
b)
Nb planes116
set I
N
set II
Figure 2.11. Fracture pattern in the backlimb. (a) Field photograph of the fracture
pattern at site 8 within the Tensleep sandstone on the backlimb. (b) Line drawing of
the outcrop in (a) that shows set II fractures (strike of 045°) terminating at set I
fractures (strike of 110°).
zone of def.
N
N
0.5 mm
Figure 2.12. Microscopic details of a set I (110°) fracture in the Tensleep sandstone
of the backlimb at site SM16. The fracture is characterized by a zone with less
porosity, smaller quartz grains and a larger amount of calcite cement as compared to
the host rock.
67
3 m

Southwestern backlimb
In the backlimb, four fracture sets are observed in the Tensleep sandstone (Fig.
2.4, site 1, 7-8, 16-21, 23). These sets strike 110°, 045°, 135°, and 110° again.
Set I fractures trend 110° (Fig. 2.4 and 2.11) and are bed-normal. These fractures
are 10-20 m long as compared to a height of a few meters that equals bed thickness.
The fractures are linear and their spacing varies from 1 to 3 m. They lack tail cracks,
riedel fractures, or other shearing-related secondary structures. As in the forelimb,
their mode of deformation is difficult to determine in the field. They sometimes
ressemble joints and other times ressemble deformation bands. Microscopically, set I
fractures are characterized by a decrease of grain size, a decrease of porosity, and an
increase in amount of cement (calcite) as compared to the surrounding host rock (Fig.
2.12). Again, these fractures show no kinematic evidence of shearing.
Set II fractures trend 045° (Fig. 2.4 and 2.11) and are bed-normal. They
terminate against set I fractures (Fig. 2.11) and, as a result, are only a few meters in
length. They are quite linear and their spacing is approximately 1 meter. In the field,
they have a joint morphology and a cement-filling indicating an opening mode of
deformation. As seen in thin section, the fill typically consists of large calcite crystals
without evidence of fracturing or crushing, which supports a strictly dilational origin
(Fig. 2.13a).
Set III fractures have a more restricted occurrence than sets I and II (Fig. 2.4, site
18-20, 52). They trend 135°, are bed-normal, and contain a coarse calcite mineral fill
(Fig. 2.13b) that is indicative of opening mode. The length of these fractures is on the
order of a few meters. The termination relationships with other fracture sets are
difficult to determine because of the small number of these fractures. Age
relationships are more easily determined from observations within the fold hinge,
where these fractures are more numerous.
Set IV fractures trend 110° and are parallel to set I fractures but are vertical and
not bed-normal (Fig. 2.4 and 2.14). Abutting relationships are difficult to establish
because they have been observed mainly in cross-section, which reveals only their
vertical dip. These fractures are several meters long with an approximate spacing of
one meter. In the field, most set IV fractures are open, and all lack evidence of
68

a)
b)
c)
0.5 mm
0.5 mm
0.5 mm
Figure 2.13. Microscopic detail of fractures in the Tensleep sandstone of the
backlimb. These photomicrographs all show features with distinct fracture walls and a
large crystal calcite fill. (a) Microscopic structure of a set II (045°) fracture at SM8. (b)
Microscopic structure of a set III (135°) fracture at SM23. (c) Microscopic structure of
a set IV (110°) fracture at SM18. In addition to the characteristics seen in the previous
two photomicrographs, this photomicrograph has crushed grains along the walls of
the fracture.
69

)
Nb planes 22
N
NE SW
1 m
Figure 2.14. Vertical set IV fractures in the backlimb. (a) and (b) Field photographs
of set IV (110°) fractures at site 23 in the Tensleep sandstone. (b) is a close-up
photograph. These fractures do not show any evidence of shearing.
a)
b)
N
N
0.5 mm
0.5 mm
Figure 2.15. (a) Microstructure of a set I (110°) fracture in the sandstone of the
Amsden Fm. in the hinge at site SM44. The fracture is composed of crushed matrix
grains surrounded by quartz cement. (b) Microstructure of a set II (045°) fracture in
the sandstone of the Amsden Fm. in hinge at site SM41. The fracture has distinct
walls and is filled with large crystals of calcite cement.
70
a)

shearing. Microstructural examination of preserved calcite fill shows a difference from
set II and set III morphology (Fig. 2.13c). Matrix grains at joint walls are crushed and
display an elongation direction, suggesting a shearing event prior to vein filling.
Hinge
In the hinge, fracture measurements were made in the Amsden Fm. sandstone
beds (Fig. 2.4). We observed three sets of fractures with orientations: 110°, 045°, 135°
(Fig. 2.4, sites 39 to 41, 43 to 48, and 50 and 51).
Set I fractures trend 110° and are bed-normal. They are less numerous in the
hinge than in the limbs, and their spacing is greater. In thin section (Fig. 2.15a and b),
these fractures are marked by reduced grain size and porosity as compared to the host
rock, similar to the set I fractures in the forelimb (Fig. 2.8). The alignment of elongate
grains seen in thin section (Fig. 2.15b) may be indicative of shearing during
deformation. As can be noted from figure 2.4 and 2.5, this set is not visible at many
locations. Looking at the data (Fig. 2.16), we see that the fracture set striking SE (see
below, set III) is actually composed of fractures striking from ESE to SE. The set I
fractures are thus often clustered with set III, because their strike is similar. This
observation is also valid for most of the sites of measurements in the hinge. This
explains why there seem to be fewer set I fractures in the hinge. It is actually only due
to the automatic cluster analysis. However, as is represented in figure 2.16, we will
consider set I fractures to be as numerous in the hinge as in the limbs.
Set II fractures trend 45°, are bed-normal, and have a coarse calcite fill similar to
that seen in the backlimb (Fig. 2.4, 2.15c, and 2.15). These fractures are joints, with
lengths of a few meters and 1 meter spacing.
Set III fractures trend 135° (parallel to the fold axis), are bed-normal, and are
observed mainly in the hinge. Set III fractures abut set II fractures in the hinge and
thus postdate set II (Fig. 2.16). Set II fractures abut set I fractures in the backlimb, so
we infer that set III fractures also postdate set I fractures.
71

a)
Nb planes 42
b)
N
N N
10 cm
Set II
N
Set III
Figure 2.16. Fracture pattern in the hinge. (a) Field photograph showing the
termination relationships between set II (045°) and III (135°) at site 39 in the
sandstone of the Amsden Fm. (b) Line drawing of the outcrop in (a) showing that 8 of
13 set III fractures terminate at set II fractures and no set II fractures terminate at set
III.
72

a)
NW
b)
Nb planes 77
Set III
N N
Set II
N
SE
10 cm
Figure 2.17. Fracture pattern in the hinge of the fold nose. (a) Field photograph
showing the fracture pattern in the sandstone of the Tensleep Fm. at site 2. (b) Line
drawing of the outcrop in (a) showing that set III (135°) fractures terminate at set II
(045°) fractures more times than set II fractures terminate at set II fractures.
73

a)
NW SE
b)
Set II
Nb planes 61
Set III
N N
N
10 cm
Figure 2.18. Fracture pattern in the backlimb of the fold nose. (a) Field photograph
showing the fracture pattern in the Phosphoria Formation at site 2. (b) Line drawing of
the outcrop in (a) showing that the chronology of fracture sets II (045°) and III (135°)
is hard to determine from abutting relationships at this location.
74

Northern nose
The fold nose is defined as the area NW of the position in the backlimb where,
due to the fold shape, bedding strike has rotated to 150° from the typical value of 135°
along the limbs (Fig. 2.4). In the nose, fracture data were collected primarily from
limestones within the Phosphoria Formation because the Tensleep Formation crops
out in limited locations (Fig. 2.4 and 2.5). Outcrops of both the Tensleep and
Phosphoria Formations are present at the southern extent of the nose, and we compare
measurements from these two formations to determine similarities and differences
between fractures within the two lithologies. The comparison was done at sites 2, 27,
and 36 in the Tensleep Fm. (Fig. 2.4) and sites 2 and 60 in the Phosphoria Fm. (Fig.
2.5).
Close to the nose hinge, in the Tensleep Fm., as described earlier, the fractures
consist of two main joint sets trending 045° (set II) and 135° (set III) (Fig. 2.4, sites 2,
27, and 36 and Fig. 2.17). From abutting relationships, the set II joints predate set III
joints (Fig. 2.16). In the Phosphoria Fm., in the nose hinge, we also observe two main
fracture sets (Fig. 2.5, site 2). One set is NE-trending and composed of joints (Fig. 2.5,
site 2 and Fig. 2.18). Another set is SE-trending (Fig. 2.5, site 2 and Fig. 2.18) and
also composed of joints. The chronology is difficult to determine (Fig. 2.18) as the
abutting relationships are not entirely consistent. However, based on strike and mode
of deformation, we suggest that theses two joint sets are similar to set II and III
described throughout the fold.The fracture pattern in the backlimb (Fig. 2.4, site 7) is
similar to the fracture pattern in the nose backlimb (Fig. 2.5, site 60). The fracture
pattern in the forelimb (Fig. 2.4, site 29) also is similar to the fracture pattern in the
nose forelimb (Fig. 2.5, site 26). The common occurrence of both set II and set III in
the sandstones and limestones at the selected sites is used to infer that fracture data
recorded within the limestones is a reasonable proxy for the fracture pattern that
existed within the eroded sandstone beds of the fold nose.
Throughout the nose, we observe that the NE-trending set II joints vary in
orientation from 045° to 070° toward the nose (Fig. 2.5). Fractures trend 045°at sites
2, 26, 53, and 60 and 070° at all but one of the remaining sites. The SE-trending set III
joints also vary in orientation throughout the nose, but to the largest extent within the
75

nose backlimb (Fig. 2.5). They trend 135° at sites 60, 61, and 62, and trend 160° at
sites 64, 65, and 66. In the nose hinge, these SE-trending joints maintain an average
orientation of 140° at all sites except site 57 (Fig. 2.5).
Interpretation
The four fracture sets found at Sheep Mountain anticline provide qualitative
constraints for the temporal and spatial evolution of deformation of the sedimentary
layers within the anticline. The following discussion synthesizes field and thin-section
observations to first present an interpretive chronological history of fracture
development and to then make inferences about fold kinematics.
Pre-existing fractures
Set I fractures are observed in most of the locations across the fold and are
systematically perpendicular to bedding. The exact nature of these fractures remains
uncertain (see previous sections and Fig. 2.9, 2.12, 2.15a and b) because we do not
know if they initiated in a shearing mode (e.g. as deformation bands) or in an opening
mode (as joints) and subsequently were sheared.
Fracture set I is oblique to the fold, striking approximately 25° counterclockwise
from the fold axis. Additionally, abutting relationships indicate that set I predates all
other fracture sets. Thus, we interpret set I as the oldest set and as having initiated
prior to the Laramide orogeny (Fig. 2.19). A similar interpretation was made by
Silliphant et al. (2002) at Split Mountain in Utah and Hennings et al. (2000) at Oil
Mountain in Wyoming, where a fracture set of similar strike (WNW-trending) was
present at nearby locations where bed dips are approximately horizontal, as well as in
each position of the fold after rotation of the bedding to horizontal.
Fractures, striking 110° when bedding is restored to horizontal, and dipping
perpendicular to bedding, also are found regionally near Sheep Mountain in the Black
Hills of western South Dakota and northeastern Wyoming (Wicks et al., 2000). In this
location, the fracture set was interpreted to predate Laramide compression.
Conversely, a set of fractures of this orientation was found near the Tensleep fault in
the Southeast Bighorn basin (Allison, 1983) and was interpreted as a late joint set. The
76

(c)
Set I
(d)
(a)
(b)
Set I
Set III
Set III
Set II
Set II
N E
Set IV
Figure 2.19. Schematic representation of the fracturing history at Sheep Mountain
anticline. (a) Set I (110°) fractures form prior to the Laramide compression in
horizontal beds. (b) Set II (045°) joints are initiated as early compression-parallel
fractures. (c) Set III (135°) joints develop in the hinge during folding. (d) Vertical set IV
(110°) joints initiate parallel to set I fractures in the backlimb, while in the forelimb, set
I fractures are reactivated as reverse faults during a late stage of (or posterior to)
folding.
77

chronology, however, was deduced from a statistical analysis of the number and
scatter of joint measurements and not from abutting relationships observed in the field.
In other places in Wyoming and Montana, fractures sub-parallel to set I have not been
observed: for example at Elk Basin in Montana (Engelder et al., 1997), at Garland and
Little Sand Draw in the southeast Bighorn basin (Garfield et al., 1992), and at Teapot
Dome (Allison, 1983; Cooper et al., 1998). This suggests that set I did not develop
uniformly across the region. Similarly, at Sheep Mountain, set I fractures are present
primarily within the limbs, are less abundant within the hinge and the nose. One
explanation is that this fracture population did not form homogeneously but left
undisturbed patches in a given layer, due to subtle differences in diagenesis or stress
state. Another explanation is that this fracture set is not well expressed in limestone
(the dominant formation cropping out in the nose) due to material properties differing
from those of the sandstone and/or the higher position in the stratigraphic column. Set
II and III however are expressed both in the Tensleep Fm. and in the Phosphoria Fm.
Lastly, these fractures may be fold-related, which would explain the heterogenous
distribution. However, we have documented that these fractures are older than those
interpreted as the Laramide compression-related fractures and other studies have
shown that they are present in places where no fold formed (Allison, 1983; Hennings
et al., 2000; Wicks et al., 2000). Thus, in the following, we consider these fractures to
be pre-Laramide in age.
If the set I fractures formed as shear fractures, they would have formed oblique
to the direction of greatest compression. Taking an estimated 30° angle, the tectonic
compression would have been in a direction of either 080° or 140°. If they formed as
joints, they would be associated with a 110°E directed compression. Further study is
needed to constrain the nature and origin of this fracture set, but this is not crucial for
constraining the fold growth as we view set I as having formed before folding.
Early Laramide compression: onset of faulting and folding
Set II joints strike parallel to the NE-SW direction of Laramide compression
(Dickinson and Snyder, 1978; Engebretson et al., 1985; Bird, 2002) and are
78

perpendicular to bedding. We showed that set II joints predate the fold-parallel hinge-
restricted set III joints. Thus, we interpret the set II joints as having formed in response
to early Laramide compression, prior to significant development of the fold (Fig.
2.19).
Joints initiating parallel to an early compressive event are documented in the
literature (Engelder and Geiser, 1980; Engelder et al., 1997). Joints with the same
orientation as set II are found in several locations in proximity to Sheep Mountain: at
Garland and Little Sand Draw in the southeast Bighorn basin (Garfield et al., 1992), at
Teapot Dome in Wyoming (Allison, 1983; Cooper et al., 1998) and in the southeast
Bighorn basin near the Tensleep fault (Allison, 1983), confirming their regional status.
Additionally, through pressure-interference tests in seven reservoirs throughout the
Bighorn basin, Haws and Hurley (1992) found a consistent permeability anisotropy in
the NE direction, supporting our interpretation of set II as a regional fracture set. At
Sheep Mountain, we find set II joints in the backlimb, the hinge, and the nose (Fig.
2.4, 2.5, and 2.19). Fractures of this set are notably absent in the forelimb, however,
suggesting that an early structure, most likely the incipient fold or the underlying
thrust fault, may have influenced their formation (Fig. 2.19).
Sheep Mountain is interpreted as a fault-related fold, and the thrust fault causing
the uplift of the anticline dips around 50° SW (Stanton and Erslev, 2004). Slip along
the thrust fault may induce a zone of enhanced compression above the fault tip
(compressive quadrant of a shearing mode discontinuity; Pollard and Segall, 1987).
We suggest that such a stress perturbation inhibited the formation of the set II
fractures in the overlying layers at a location corresponding to the forelimb during and
after folding. Set II can thus be considered a regional fracture set with local zones
where its formation was inhibited. Other studies have documented the influence of
perturbed stress fields on fracture orientation and location in extensional (Kattenhorn
et al., 2000; Maerten et al., 2002) or strike slip (Bourne and Willemse, 2001)
environments, as well as in salt tectonics settings (Cruikshank and Aydin, 1995).
We have shown that field evidence supports the interpretation that set II fractures
predate all fracture sets except set I, and thus they predate the hinge parallel set III
joints that are inferred to be fold related. Yet, these timing relationships do not require
79

set II to be pre-folding. Set III may have initiated during a later stage of the fold
evolution rather than at the onset of folding. In this case, set II joints could have
formed after the beginning of fold evolution but before the formation of set III, and
would thus be fold-related.
At Elk Basin Anticline, a basement-cored fold in Montana and Wyoming, fold
perpendicular fractures comprise only a minor fracture set, and they are interpreted as
a late set formed in response to an axis-parallel stretching (Gross and Engelder, 1995).
A mechanism for this type of joint formation is curvature related to a doubly-plunging,
non cylindrical fold geometry (Fischer and Wilkerson, 2000). For such a mechanism,
rather than a regional deformation, to be an explanation for set II fractures at Sheep
Mountain anticline, the present-day fold shape (quite cylindrical in its central part)
would have had to have evolved from a more non-cylindrical shape. However, a
perturbation in the strike of set II fractures occurs only in the present-day fold nose,
and similar perturbations, which would represent previous locations of the fold nose,
are not found. Therefore, we infer that the fold nose did not migrate laterally, and the
early fold length was very similar to the current fold length.
We consider a regional deformation as the most likely formation mechanism for
set II fractures and suggest that the paucity of set II joints in the forelimb is due to a
stress perturbation resulting from slip on the underlying basement thrust fault. The
rotation in strike of set II fractures in the nose is then most likely also related to stress
perturbations from the underlying fault. In such a case, the underlying fault would
have established its horizontal dimension prior to significant slip. This concept has
been documented for faults in extensional domains (Walsh et al., 2002) and inferred
for faults in compressional domains (Julian and Wiltschko, 1983; Armstrong and
Bartley, 1993; Fischer and Christensen, 2004). Such a mechanism is usually explained
by invoking fault reactivation (Walsh et al., 2002). Reactivated faults do not grow
laterally until their slip reaches a great enough value in comparison to length to trigger
lateral propagation. At Sheep Mountain, the view of the underlying basement fault as a
reactivated fault is consistent with previous studies (Simmons and Scholle, 1990; Ye
et al., 1996).
80

Fold growth: intermediate stage
In the hinge, joints striking parallel to the fold axis and dipping perpendicular to
bedding are classified as fracture set III. As previously noted, they could have formed
at any time during folding (Fig. 2.19). Despite this ambiguity, the localized occurence
of these joints is consistent with a fixed-hinge model of fold evolution (Allmendinger,
1982; Fischer et al., 1992; Fisher and Anastasio, 1994; McConnell, 1994). Had the
hinge migrated, we would expect to find fold-parallel joints elsewhere. The hinge is
very tight, so it is unlikely that the observed hinge curvature could have been
accommodated without joint formation.
We do find some fold-parallel joints in the backlimb (Fig. 2.4, sites 18 to 20).
These joints might be related to areas where layer curvature is greater (Fig. 2.7). The
darkening of the curvature plot toward the north along the fold axis reflects the
tightening of the fold in this direction. As we look along lines perpendicular to the fold
axis, we see that in the north, zero or near zero curvature values are reached just a
short distance from the fold axis, whereas further south, this distance is greater. The
number of set II joints increases toward the south, the direction in which the fold
shape changes from a tight to a more rounded profile (Fig. 2.7). This supports our
hypothesis that there is a link between curvature and the existence of set III joints.
Where the hinge is tight in the north, the limbs are virtually planar with near zero
curvature and set III is confined to the hinge.
Set III joints also are found in the fold nose. In the backlimb of the nose, the
joint strike changes along the fold from 135° to 160° (Fig. 2.5). This change roughly
coincides with the change in fold limb orientation, as the strike of the layers changes
from 130° to 150°, south to north (Fig. 2.5). The layers in this area are curved and this
layer bending can explain the rotation of the set III joints. In the nose hinge zone, set
III is the main joint set, where it most likely initiated due to layer curvature. The
variation in orientation of fractures within this set also suggests that there was no fold
propagation, as we do not observe any analogous change of set III joint strike along
the cylindrical part of the fold.
81

Fold growth: late stage
During the late stage of fold growth, the fracture patterns in the hinge and in the
nose did not change, although some fold-parallel joints may have continued to form.
In the limbs, however, new fractures initiated and others were reactivated (Fig. 2.19).
In the forelimb, we observe small thrust faults with oblique slip (Fig. 2.10 and
2.19). Given the geometric similarities to set I fractures, these structures are
interpreted as reactivated set I fractures. The present orientation of the faults is in
agreement with Andersonian theory: they are reverse faults that dip approximately 30°
from the horizontal, perpendicular to bedding. Thus, we infer that the reactivation
occurred late in the fold evolution. Incorporated into this interpretation is the
assumption that the set I fractures rotated passively with the strata and were
reactivated when their dip reached a value low enough to allow a thrust offset along
them. This mechanism implies a horizontal greatest compressive stress striking
perpendicular to the fold and a vertical least compressive stress.
The set I fractures also could have been reactivated earlier during the fold
growth. In some kinematic models of fault propagation folding, it is suggested that
thickening and thinning of the forelimb occurs (Jamison, 1987; Chester and Chester,
1990, Erslev, 1991, McConnell, 1994, Hardy and Ford, 1997, Allmendinger, 1998).
This thinning is apparent on cross-sections shown by Frizon de Lamotte et al. (1997),
Storti et al. (1997), and Grelaud et al. (2000). The presence of the reverse faults in the
forelimb of Sheep Mountain may be consistent with shearing of the layer
contemporaneous with this forelimb rotation and deformation.
The present orientation of set I fractures suggests that they sheared after the beds
were tilted. Reches (1978) and Allmendinger (1982) showed that compression at high
angle to fold limbs is generally characterized by conjugate reverse faults whose
bisector angle is horizontal and perpendicular to the fold. This compression is linked
to a late stage of fold evolution when the forelimb is steep and the upper fault tip is
locked such that additional slip events generate compressive stresses that could
reactivate older fractures.
Stanton and Erslev (2004) suggested that the thrust fault that created Sheep
Mountain anticline was cut by a later NE-dippping thrust fault. This event may have
82

occurred when the Sheep Mountain fault was locked and unable to propagate.
Moreover, this younger fault would uplift the anticline. In the backlimb, we observed
a second late fracture set, set IV, which is composed of vertical joints striking 110°
(Fig. 2.14 and 2.19). They are interpreted as late due to their vertical dip that is
oblique to bedding. These joints may be related to the uplift. We suggest that this joint
set was influenced by the presence of the earlier set I fractures, because they strike
oblique to the fold axis and parallel to the set I fractures. Such influence by pre-
existing fractures has been suggested recently in Guiton et al. (2003a, 2003b) and
Bergbauer and Pollard (2004).
Conclusions
The field data collected at Sheep Mountain anticline on fracture chronology and
mode of formation (opening vs. shearing) help us to constrain the deformation and
structural evolution of this anticline. We interpret these data to show that: (i) A
fracture set (set I, 110°) was present before the onset of the Laramide compression. (ii)
An early joint set (set II, 045°) initiated during the beginning of the Laramide
compression, however, the formation of this set may be influenced by the onset of
faulting and/or folding. (iii) Set III joints (135°) localized in the hinge during layer
bending related to fold evolution. Such joints also formed in the limbs where
significant limb curvature developed (south part of the fold). (iv) In the forelimb,
during late fold evolution, set I fractures were reactivated as reverse faults. (v) Also
during this late stage, vertical joints (set IV, 110°) oblique to the fold axis initiated in
the backlimb. Their strike direction was controlled by the pre-existing fractures of set
I. These fracture data provide constraints on the folding kinematics. They suggest a
fixed-hinge mechanism of folding in which little lateral propagation of the thrust fault
and fold occurred. The data also indicate that little deformation of fold limbs occurred
during fold growth, except where the curvature is significant, and during late stages of
fold growth.
83

Aknowledgements
This paper benefited from discussions with M. Cooke, J.M. Daniel, M. Guiton,
and Y. Leroy. We thank E. Erslev and H. Stanton for providing a pre-print of their
paper and I. Mynatt and Y. Fujii for assistance in the collection of fracture data in the
field. J.M. Daniel and M. Guiton (Institut Français du Pétrole) are thanked for their
help and for providing the software used to calculate mean fracture orientations and
plot the data. The manuscript greatly benefited from the reviews of W. Dunne and C.
Zahm. This work was supported by the National Science Foundation Tectonics
Program Grant No. EAR-012935 and the Collaboration in Mathematical Geosciences
Program Grant No. EAR-04177521, the Stanford Rock Fracture Project, and the
Institut Français du Pétrole.
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90

Chapter 3
Fracture reactivation at Sheep Mountain Anticline: insight on the
mechanics of folding and constraints on the stress field
Abstract
Field observations of sheared fractures in various structural locations across
Sheep Mountain Anticline, Wyoming, document the role of fracture reactivation in
folding related deformation. Most of the observed shearing is kinematically consistent.
Differences in both the formation and reactivation of fracture sets in the forelimb and
backlimb indicate that the stress state in the forelimb was highly influenced by the
underlying fault.
Differences in observations of shearing also constrain spatial and temporal
variations of the stress state across the anticline during folding. At some locations,
conjugate shearing has occurred along a set of joints (striking 045°) that formed early
in the folding process and a set of joints (striking 075°) that formed during the
development of a secondary fold at Sheep Mountain. These observations constrain the
local principal stress directions if both sets sheared at the same time. The local σ1
direction (maximum compression) is further constrained at locations where we have
recorded left-lateral and right-lateral conjugate shearing of selected members of single
sets of joints. Temporally, the σ1 direction apparently varied enough to resolve shear
stress with opposite senses on these sub parallel joints. Frictional faulting analysis
allows constraints to be placed on the state of stress prevailing during the reactivation
of these joints. A fracture set that pre-dates the folding has sheared in the limbs in a
sense that is consistent with the kinematics of folding, but no shearing of this fracture
set has been recorded in the hinge. Again, frictional faulting theory is implemented to
understand what physical conditions may allow for this variation in deformation. We
determine that the pre-existing fracture set must have been infilled at the time of
reactivation.
91

Introduction
Multi-scale problems in which patterns of secondary deformation are derived
from knowledge of a larger scale of deformation have gained attention over the last
decade (e.g. Sassi and Faure, 1996; Allmendinger, 1998; Fischer and Wilkerson, 2000;
Hart, 2006; 2006 AGU Fall Meeting session entitled: Fracturing and Faulting During
Folding of Sedimentary Strata: Field Observations and Mechanical Models), in part
due to economic motivations to better understand poorly observed fractured reservoirs.
Ultimately, mechanical models, which track stress, strain, and displacement fields
related to an imposed deformation, have the ability to predict physically plausible
fracture patterns relating to observable deformations. The use of mechanical models is
becoming more prevalent, but as indicated by sensitivity analyses carried out in prior
studies (e.g. Kattenhorn et al., 2000; Bourne and Willemse, 2001; Maerten et al.,
2002; Maerten et al., 2006), boundary conditions have a significant effect on the
resulting stress calculations. For problems in which few data are available for
calibration, methods of constraining boundary conditions with these small quantities
of data become crucial. We suggest that observations of reactivated fractures can be
used to constrain plausible boundary conditions.
Two types of fractures exhibit slip (displacement discontinuity parallel to the
fracture surfaces), but have formed under different circumstances. Shear fractures (e.g.
Griggs and Handin, 1960; Stearns, 1968; Bergbauer and Pollard, 2004) initiate and
propagate while slipping within the same remote stress field. Shear fractures are
interpreted to contain the intermediate principal stress (σ2) and are inclined at an angle
of less than 45° to the most compressive principal stress (σ1) based on analogous
relationships documented in lab rock mechanics experiments (e.g. Griggs and Handin,
1960). In contrast, sheared joints (e.g. Peacock, 2001; Bergbauer and Pollard, 2004;
Myers and Aydin, 2004; Davatzes et al., 2005) or faulted joints (e.g. Segall and
Pollard, 1983; Cruikshank et al., 1991; Willemse and Pollard, 1998; Wilkins et al.,
2001; Silliphant et al., 2002) initiate and propagate while opening and later are sheared
under different remote stress conditions. Sheared joints form as dominantly opening
mode fractures, with surfaces normal to the least compressive principal stress (σ3;
Pollard and Segall, 1987; Renshaw and Pollard, 1994). At some later time, the joints
92

close and become misaligned with the principal stress axes due to either a material or
stress field rotation, so shear traction is resolved along joint surfaces. Under suitable
combinations of shear and normal (compressive) tractions, a slip event initiates and
propagates along these surfaces and a sheared joint is born. We refer to this
phenomenon as “fracture reactivation”. Clarification of the class of fracture studied at
a field site is essential to understanding the evolution of the stress field through time,
as shear fractures and sheared joints imply different alignment of fracture planes with
the principal stresses.
In this study, we investigate fracture reactivation at Sheep Mountain anticline
(SMA) and, more generally, demonstrate how shearing observations can be used to (1)
place quantitative constraints on the principal stresses and strains active within a fold
at the time of deformation, and (2) identify the mechanical processes involved in the
development of the fracture pattern. We present fracture data collected from different
lithologies within the same structural locations, documenting the location, orientation,
and sense of motion of sheared fractures. With these data we are able to investigate
what effect, if any, lithological differences have on the formation and reactivation of
systematic fracture sets and to interpret spatial and temporal variations in shearing
directions and magnitudes. Analyses implementing frictional faulting theory place
constraints on the relative magnitudes of principal strains active during the Laramide.
Geological background
SMA is a northwest-southeast trending anticline located west of the Bighorn
Mountains on the eastern flank of the Bighorn Basin within the Laramide Rocky
Mountain foreland of Wyoming (Fig. 3.1a). Structurally, the fold is interpreted as a
third order feature. Gravity magnetic profiles, seismic reflection profiles, and borehole
data indicate that the eastern thrust of the Bighorn Mountains is a basin boundary fault
that thrusts the Bighorn Mountains over the Powder River Basin to the northeast and
triggers deformation distributed throughout the Bighorn Basin to the southwest (Fig.
3.1b; Robbins and Grow, 1992; Stone, 1993). At the latitude of Sheep Mountain, this
deformation is linked to slip along a northeast dipping backthrust, the Rio thrust
(Gries, 1983; Stone 2004). Based on cross sections drawn through the
93

(a)
(b)
(c)
43°
45°
44°
110°
Absaroka Mnts
A
WIND RIVER
RANGE
Bighorn Basin
A
109°
BIGHORN
WIND RIVER
BASIN
Sheep Mt.
BASIN
Owl Creek Mnts
108°
Bighorn Mnts
107°
100 km
Rio
Thrust
POWDER
Casper Arch
RIVER
BASIN
SMA
Thrust
Bighorn Mts.
Western Thrus t
Bighorn
Mountains
Bighorn Mts.
Eastern Thrust
Powder
River
Basin
N
10 km
Figure 3.1. (a) Tectonic map of Wyoming showing the location of SMA as the doubly
plunging fold represented by the thick black line and the area of (b) in gray. Modified
from Bellahsen et al., 2006a. (b) Digital Orthophoto Quarter Quadrangles (DOQQs) of
the Bighorn Mt. and Bighorn Basin area. Quadrangles downloaded from
http://wgiac.state.wy.us/. Black line shows the location of SMA. Dashed white lines
trace the surface projections of major thrust faults. Light gray line shows the location
of the cross-section in (c). (c) Schematic cross section through the Bighorn Basin and
Bighorn Mountains. The SMA thrust can be considered a third order structure related
to the Rio thrust fault and the eastern thrust of the Bighorn Mts.
94
A‘
A‘

Bighorn Mountain eastern thrust fault and the Rio thrust fault to the south (Stone,
1993; Stone 2004), we interpret the Sheep Mountain thrust fault to be a southwest
dipping backthrust of the Rio thrust fault (Fig. 3.1c).
Uplift at SMA is measured by more than 1 km of structural relief across pre-
Laramide bedding that is accommodated primarily through folding. Three hundred
meters of this structural relief can be viewed in cross-section where the Bighorn River
transects the fold almost perpendicular to the hinge (Fig. 3.2), which strikes
approximately 135°. The steeply dipping (40° to 90° NE) forelimb of SMA lies to the
northeast of the hinge, and the more gently dipping (10° to 40° SW) backlimb lies to
the southwest of the hinge. Approximately 2 km northwest of the river cut, a
secondary fold intersects the backlimb of SMA with a trend that is rotated 20°
clockwise from that of the main fold. After Savage and Cooke (2004), we call this
secondary fold the thumb.
At SMA, Paleozoic and Mesozoic marginal marine sedimentary rocks overlay
granitic PreCambrian basement (Thomas, 1965; Fig. 3.3). The Cambrian, Ordovician,
and Devonian sequence consists of about 500 meters of shale, limestone, and dolomite
that are not exposed at SMA. The Mississippian Madison Fm. is comprised of massive
limestone and interbedded dolomite and represents the oldest formation that outcrops
at Sheep Mountain, as well as the oldest lithology examined in this study (Fig. 3.2).
Above the Madison Fm., the Pennsylvanian Amsden and Tensleep Fms. consist of
interbedded sandstones, shales, and limestones. The sandstone beds provide many of
the outcrops where fractures that form the basis for this study were measured. The
Permian Phosphoria limestone forms the resistant, outermost beds on both the
forelimb and backlimb of the anticlinal edifice. The Triassic Chugwater Formation lies
stratigraphically above the Phosphoria. At SMA, the Chugwater shales and younger
Triassic, Jurassic, and Cretaceous Bighorn Basin sediments have all been eroded off
the topographic high.
95

N
108°12'
Quaternary
Cretaceous
Jurassic
Backlimb
Thumb
Forelimb
108°10'
Triassic (Chugwater Fm)
Permian (Phosphoria Fm)
Carboniferous (Pennsylvanian, Tensleep Fm)
Carboniferous (Pennsylvanian, Amsden Fm)
Carboniferous (Mississipian, Madison Fm)
Anticlinal axis Synclinal axis
Bighorn River
108°08'
44°38'
108°06'
1 km
108°04'
44°36'
Figure 3.2. (a) Geological map of SMA after Rioux, 1994 and modified from
Bellahsen et al., 2006a. Fracture data were collected from outcrops northwest of the
river cut.
96

K
J
TR
P
P
M
D
O
C
pC
Mesa Verde
Cody
Frontier
Mowry
Thermopolis
Cloverly
Morrison
Sundance
Gypsum Springs
Chugwater
Phosphoria
Tensleep
Amsden
Madison
Jefferson -
Three Forks
Bighorn
Gallatin
Gros Ventre
Flathead
Granite
Shale
Sandstone
Limestone
Dolomite
Gypsum
Granite
Figure 3.3. Stratigraphic column for the Bighorn Basin. After Hennier, 1984.
97

Set II
Set IV
Set III
Set I
Set I
reactivated
Figure 3.4. Schematic cross-section for SMA depicting the orientations of four
previously interpreted fracture sets. The hinge of the fold trends approximately 135°.
From Bellahsen et al., 2006a.
98

Field data
Systematic fracture sets
Previous work at SMA based on sandstone outcrops of both the Tensleep and
Amsden Fms. has defined four systematic fracture sets (Fig. 3.4; Bellahsen et al,
2006a). Set I is found in all structural locations on the fold, strikes 110° when bedding
is rotated to horizontal, is perpendicular to bedding, and is interpreted as forming
before the folding event. Set II strikes 045°, is perpendicular to bedding, and formed
early in the folding process, parallel to the inferred maximum regional compression
direction. This set is sparse in the fold forelimb. Set III, striking 130°, is parallel to the
fold hinge and perpendicular to bedding. It is interpreted as the primary folding-related
fracture set and is localized in areas of greatest curvature. Set IV is interpreted as a
late-folding fracture set that strikes 110°, parallel to set I fractures, but dips obliquely
to bedding and is vertical as observed in the field. Both field observations of hackle
along fracture walls and thin section identification of distinct vein boundaries support
the interpretation of sets II, III, and IV initiating as joints with purely opening mode
offset between adjacent fracture surfaces (Bellahsen et al, 2006a). Field and
microscopic observations of set I fractures have been inconclusive: they may have
formed either in a shearing mode or in an opening mode and then were sheared.
For this study, we highlight an additional set of systematic joints striking 075°
and perpendicular to bedding. This was noted as minor in the Bellahsen et al. (2006a)
study because it was found in limited locations. We refer to these joints as set V.
Evidence for reactivation was collected within the Tensleep sandstone and Phosphoria
limestone along the limbs, and in the Madison limestone and Amsden sandstone along
the hinge. An understanding of the distribution of systematic joint sets in the different
lithologies at SMA required additional data relative to those previously studied.
In figure 3.5, we provide data documenting the locations and orientations of
systematic joint sets in four stratigraphic units: Madison Fm. limestone, Amsden Fm.
sandstone, Tensleep Fm. sandstone, and Phosphoria Fm. limestone. Study sites were
exposures of dimensions typically tens of meters on a side. At each study site, fracture
sets were distinguished based on orientation data, abutting relations, and deformation
mode. The average orientations of the sets at each site are represented by great circles
99

(a)
(b)
Site 7-8
N
Site 18
N
40
20
N
Site 58
N
N
91
108°10'
Site 25
N
Site 72
N
108°10'
38
Site 77a
N
Site 12
N
15
40
21
Site 71
N
Site 80
N
Site 84
N
Site 14
N
Fracture Sets
Set I
Set II
Set III
Set IV
Set V
minor set
7-8
26
24
07
37
25
Site 78
N
Site 22
N
08
26
Site 07
25
N
23
44°39'
29
58
30
14
14
13
13
17
Site 13
N
Site 29
N
25
44°39'
36
35
Site 08
N
116
108°09'
Site 23
N
18 18
71 17
72 16
80
01
78
19
20
81
15
22
22
Site 81
N
Site 76
N
Site11
N
35
32
Site 30
N
40
Site 77b
N
22
12
12
108°09'
Site 10
N
N
77
76
30
Site 85
100
Site 14
N
63
84
25
63
11
11
86
85
Site 13
N
Site 18
N
N
Site 83
N
51
Site 17
83
21
29
35
Site 33
N
42
59
Site11
N
Site 12
N
16
44°38'
Site 16
N
Site 15
N
24
74
1 km
Site 59
N
101
10
10
44
48
139
73
Site 31
N
Site 70
N
75
31
33
32
Site 01
N
N
37
Site 22
Site 74
N
39
Site 10
N
10
37
Site 69
N
44
Site 19
36
Site 32
N
108°08'
70
69
N
108°08'
N
56
37
47
Site 20
N
44
Site 73
44°37'
Site 21
N
44°37'
35
N
63
Site 75
22

(c)
Site 39
N
Site 40
N
62
42
N
108°10'
Site 41
N
Site 43
N
53
12
Site 44
N
Site 45
N
49
26
Site 46
N
Site 51
N
26
19
Site 37
N
44°39'
Site 50
N
Site 47
N
38
21
24
Site 38
N
Site 48
N
Figure 3.5. DOQQs showing locations of fracture measurements and their
orientations. (a) Forelimb and (b) backlimb fracture measurements. Phosphoria sites
are labeled with white numbers and dots with the corresponding stereonets to the
lower left of the DOQQs. Tensleep sites are labeled in black numbers and dots with
the corresponding stereonets to the upper right of the DOQQs. (c) Hinge fracture
measurements. Amsden sites are labeled with white numbers and dots with the
corresponding stereonets to the lower left of the DOQQs. Madison sites are labeled in
black numbers and dots with the corresponding stereonets to the upper right of the
DOQQs.
101
108°09'
49
35
Site 42
N
36
Site 25
N
44°38'
40
1 km
Site 49
N
43
108°08'
44°37'

in lower hemisphere stereonets. The number of fracture measurements represented is
at the lower right of the stereonet and a total of nine orientations (five major, four
minor) are represented in this data set from 150 measurement sites. All orientations
have been unfolded before plotting on these stereonets so they are shown as relative to
horizontal bedding. For analysis purposes, we present data for the forelimb, backlimb,
and hinge separately.
Forelimb
Fracture data in the forelimb are taken from the Tensleep sandstone and
Phosphoria limestone (Fig. 3.5a). In the Tensleep, set I is the dominant fracture set,
found at nine of the ten observations sites; sets II and III are sparse; a minor north-
south fracture set is present at seven sites; and fracture set V is present at six sites. The
characteristics of set V are most evident in the backlimb and are discussed below. In
the Phosphoria, set V is the only consistent fracture set present, occurring in five of
eight measurement sites. Set I, set II and the minor north-south set are found locally.
Backlimb
Tensleep sandstone and Phosphoria limestone units provide outcrops for study
and data collection in the backlimb (Fig. 3.5b). Set V fractures are found in both
lithologies, and are perpendicular to bedding and several meters long, with an average
spacing on the order of meters. These fractures are typically joints with weathered
surfaces and apertures of a few centimeters in the Phosphoria Fm. and veins filled with
calcite in the Tensleep Fm.. Data collected from sites 16, 81, 101, 109, and 110 in the
backlimb (Fig. 3.5) provide the clearest abutting relationships for set V fractures (Fig.
3.6). There, set V abuts consistently against set I fractures and is abutted consistently
by set III fractures. Set V and set II termination relationships alternate, although set V
abuts against set II for seventy percent of the observed occurrences. Set V is found in
nine of the thirteen Tensleep sites, with most occurrences in the area where the thumb
intersects the main fold. In the Phosphoria, set V is found in seven of eighteen sites.
Fracture sets I, II, III, and IV also are found in the backlimb. Set I is found in
eight of thirteen sites in the Tensleep; but in only eight of eighteen sites in the
102

N S
0.5 m
N S
0.5 m
set I
set II
set III
set V
N-S set
Figure 3.6. Field photograph and interpretation of set III (heavy gray lines) and set V
(heavy black lines) abutting relationships at site 15 in the backlimb.
103

Phosphoria, and is absent in many of the sites along the thumb. Set II is found in
eleven of the thirteen Tensleep sites and ten of the eighteen Phosphoria sites.
Occurrences of set III fractures increase toward the southeast in the Tensleep. In the
Phosphoria set III is more widespread, and is present at all but one of the sites to the
southeast of the thumb intersection. Set IV is found in sparse locations in both the
Tensleep (at six sites) and the Phosphoria (at two sites); all but one are in the area near
the intersection of the thumb with the main fold.
Hinge
In the hinge, fracture data were collected in the Madison limestone and Amsden
sandstone (Fig. 3.5c). Amsden measurement sites are spread along the length of the
anticline. For exposure reasons, Madison sites are absent for over one kilometer
northwest and two kilometers southeast of the thumb intersection with the main fold.
Set I is found at three of five measurement sites in the Madison and four of eleven
sites in the Amsden. Set II is found at all five sites in the Madison and eight of eleven
sites in the Amsden. Set III is found at four of five sites in the Madison and eight of
eleven sites in the Amsden. Set IV is present in just one site in the hinge, Amsden
measurement site 48 (Fig. 3.5). Set V is present at two sites in the Madison and three
sites in the Amsden.
Shearing data
Fractures were classified as having sheared where distinct and consistent offsets
of markers and splay cracks were found. Sheared fractures were documented at just
over fifty of the one hundred fifty visited sites. Admittedly, numerous outcrops in the
nose, hinge, and forelimb are so intensely fractured that shearing-related features may
be present but are impossible to distinguish. Alone, apparent offset of one fracture
along another fracture was commonly not diagnostic of shear, as the direction of offset
of different fractures within the same set varied along the length of the fracture in
question. The interpretation in these cases was that the apparently offset fractures
actually are the terminations of two different fractures within that set, rather than a
through-going fracture that was later offset. Along the same lines, at certain outcrops,
104

Set I - thrust Phosphoria
Set I - LL Tensleep
Set II - RL
Set II - LL
Set V - RL
Set V - LL
km
0 0.25 0.5 1
Figure 3.7. DOQQs of the NW part of SMA. Locations and types of shearing
observations in the Tensleep sandstone are shown in black and in the Phosphoria
limestone are shown in white.
105

fractures one might identify as splay cracks are subparallel to minor fracture sets, and
thus are interpreted to be fractures of a later set abutting obliquely against earlier
formed fractures. As a result, few fractures were identified as sheared based on offset
alone. The most diagnostic evidence for shear was derived from observations of
isolated fractures with distinct splay cracks. In figure 3.7, the location, sense of
shearing (RL = right lateral, LL = left lateral), lithology, and set classification of
sheared fractures are plotted on the Digital Orthophoto Quarter Quadrangles (DOQQs)
that span the field area. Shear has been detected along fractures of sets I, II, and V.
Forelimb
In the forelimb, the most prevalent form of offset is thrusting along set I
fractures (Fig. 3.8). Where this thrusting occurs, with offset on the order of
centimeters, it is distributed along most, if not all, of the fractures within that set.
Small thrust faults were noted at six measurement sites along the length of the fold,
primarily in the Tensleep Formation (Fig. 3.8b). Morphologies of Madison outcrops in
the forelimb (Fig. 3.8a) suggest the existence of thrust faults as well. Where outcrops
are accessible, however, weathering has smoothed fracture walls, eliminating the
prospect of finding kinematic indicators.
Strike-slip shearing in the forelimb has been found only within Tensleep
outcrops. Field evidence suggests this shearing is not widespread. Where found, it
exists along a few members of the fracture set at most. The only consistent sense of
strike-slip shearing found in the forelimb is left-lateral slip along set I fractures. Splays
emanating from set I fractures were found at sites 145, 13, 12, 11, 10, and 146 (Fig.
3.9). These sites are northwest of, southeast of, and at the thumb intersection; and they
span a distance of three kilometers along the fold. Shear along set II fractures has been
recorded at three sites, all more than a kilometer northwest of the thumb intersection.
Right-lateral motion is found along set II at sites 131 and 145, whereas left-lateral
motion is found along set II at site 13. Instances of shear along set V are also recorded.
The sense of motion along this set is in some cases inconsistent within the same
measurement site. Right-lateral motion along set V is found at sites 10, 11, 12, and
150, and left-lateral motion is found at sites 10, 12, 13, 145 (Fig. 3.7).
106

E W SE NW
(b)
(a) 5 m (c)
0.5 m
SE NW
Figure 3.8. (a) Madison limestone; (b) Tensleep sandstone; (c) Phosphoria
limestone outcrops with set I fractures reactivated as small thrust faults. The
orientation and thrust direction of these fractures are shown in white lines and barbs.
Black traces in (a) represent bedding planes.
107
5 m

SE NW
0.5 m
SE NW
0.5 m
Figure 3.9. Field photograph and interpretation of a set I fracture sheared leftlaterally
in the Tensleep sandstone of site 10.
108

N
N
(a)
10 cm
10 cm
N
10 cm
N
10 cm
(b)
N
N
(c)
10 cm
10 cm
Figure 3.10. Field photographs and line interpretations of sheared fractures in the
backlimb. (a) Left-lateral shear along a set I fracture at site 72 in the Phosphoria Fm.
(b) Left-lateral shear along a set II fracture at site 8 in the Tensleep Fm. (c) Rightlateral
shear along a set II fracture at site 16 in the Tensleep Fm.
109

Backlimb
Sheared set I fractures consistently display left-lateral motion in the backlimb.
This shearing is found throughout the backlimb: in the area around sites 141 and 142
near the nose; in the area around sites 8, 135, and 124 along the backlimb of the main
fold northwest of the thumb intersection; along the thumb at sites 101, 81, and 115; at
the intersection of the thumb with the main fold around site 122; and east of the thumb
along the backlimb of the main fold around sites 130 and 114 (Fig. 3.10a). Set I
fractures are sheared in both Tensleep and Phosphoria outcrops.
Left-lateral shearing along set II (Fig. 3.10b) is found at five locations, all
northwest of the thumb intersection. Three of the sites where left-lateral shear is
recorded also contain or are within tens of meters of right-lateral shearing along set II
(Fig. 3.10c). Additional observations of right-lateral shearing along set II in the
backlimb were made in the nose area, along the thumb, at the thumb intersection, and
along the main fold southeast of this intersection. Like set I, set II fractures are sheared
in both the Tensleep Fm. and the Phosphoria Fm.
Set V also is sheared in opposite senses in the backlimb, often along members of
the set that are meters, or even decimeters (Fig. 3.11a), apart. These opposite
directions of shearing along set V are found in the nose area, at the intersection of the
thumb with the main fold, and along the backlimb of the main fold southeast of the
thumb intersection. Set V is sheared in an exclusively left-lateral sense (Fig. 3.11b) in
the area immediately northwest of the thumb intersection. Exclusively right-lateral
shearing along set V (Fig. 3.11c) has been recorded along the thumb and northwest of
the thumb intersection in the area around site 8 for a stretch of one kilometer along the
backlimb. Set V shearing occurs in left-lateral and right-lateral senses at both Tensleep
and Phosphoria outcrops, although the occurrence of opposite senses of shearing at the
same site has been noted only at Tensleep outcrops.
In most locations where shearing is recorded in the backlimb, it is detected along
just a handful of fractures within the set. Exceptions occur at sites 72, 144, 74, 16, and
22, where more than half of the fractures of a given set sheared: set I at sites 72, 114,
and 74, set II at site 16, and sets II and V at site 22 (Fig. 3.12).
110

N
N
(a)
10 cm
10 cm
N
N
N
N
(b)
10 cm
10 cm
(c)
10 cm
10 cm
Figure 3.11. Field photographs and line interpretations of sheared set V fractures in
the Tensleep Fm. at site 130 in the backlimb. (a) Opposite directions of shear along
set V fractures that are within decimeters of each other. (b) Left-lateral motion along
an isolated set V fracture. (c) Right-lateral motion along an isolated set V fracture.
111

N
10 cm
Figure 3.12. Field photograph and interpretation of a number of set I fractures
reactivated in left-lateral motion in the Phosphoria Fm. at site 74 in the backlimb.
10 cm
Figure 3.13. Field photograph and interpretation of fractures at site 44 in the
Madison Fm. in the hinge. Gray areas are rubble zones where it is difficult to view or
interpret fractures.
112
N
N
10 cm

Hinge
No evidence for shearing was found along the hinge (Fig. 3.7). The major
notable observation within the hinge is the occurrence of set III fold parallel joints.
Where found, set III is a regularly formed set with individual fractures spaced on the
order of ten centimeters apart (Fig. 3.13).
Analysis of field data
Interpretations of shearing
To interpret the shearing of fractures at Sheep Mountain, we divide the fold into
six domains, discussing the shearing specific to each domain (Fig. 3.14). Because no
shearing has been documented in the hinge (Fig. 3.14, domain 6) we do not discuss it
here. The forelimb is referred to as domain one. The backlimb, because the thumb
creates distinct, second order structural units, is subdivided into four different
structural domains. Domain two represents the backlimb of the nose, defined to be the
area northwest of where backlimb bedding strike changes from 135° to 150°
(Bellahsen et al., 2006a). Domain three represents the area along the backlimb of the
main fold to the northwest of, and removed from, the thumb intersection. Domain four
includes the areas of both the main fold backlimb in the vicinity of the intersection of
the thumb and the thumb structure itself. The boundary between domains three and
four is drawn about a half kilometer northwest of the thumb intersection. Domain five
is the area of the main fold backlimb at and to the southeast of the thumb intersection.
Forelimb
In the forelimb, two forms of reactivation in shear are observed, both occurring
along the set of fractures that pre-dates the fold, set I (Fig. 3.14). A small number of
these fractures have slipped in a left-lateral sense (note apparent RL sense on view of
underside of bedding in Fig. 3.16). We interpret this shearing to have occurred during
folding, while set I fractures were subjected to Laramide compression (Fig. 3.15c,
3.15d, 3.15e). Other set I fractures now are small thrust faults, having been reactivated
during folding. A previous study has suggested that this motion occurred late in the
folding history, when the fractures had achieved dips shallow enough to promote
113

V
III
I
II
II
V
V
III
V
I
III
III
I
I
II
II
III
V
2
I
II
3
6
Figure 3.14. Six shearing related structural domains at SMA: one in the forelimb,
four in the backlimb, where the shearing pattern is complex due to the existence of
the thumb, and one in the hinge. Gray ellipses represent centers of domains and
block diagrams illustrate the fracture sets and shearing directions observed in each
domain.
4
114
I
II
1
5
III
I
IR

thrust offset (Fig. 3.15f; Bellahsen et al., 2006a). Evidence for shearing along the other
fracture sets in the forelimb is both sparse and inconsistent (Fig. 3.7). Perturbations in
fold shape are common in the forelimb, where bedding approaches vertical, leading to
the interpretation of the rare instances of shear along set II and V fractures as resulting
from local phenomena.
Backlimb
Throughout the backlimb, left-lateral shearing along set I fractures is attributed to the
same mechanism as in the forelimb: oblique Laramide compression during folding
(Fig. 3.15c, 3.15d, 3.15e). In domain three, set II fractures show mixed directions of
shearing, sometimes within the same site (Fig. 3.7). We suggest that this represents
minor changes in a stress field in which the local maximum principal compressive
stress (σ1) was oriented subparallel to set II fractures, but varied enough temporally to
resolve shearing in different directions along the fractures. Set V is sheared in a left-
lateral sense, most likely the result of a northeast directed compression resolved along
the fracture planes (Fig. 3.15e). In domain four, the lack or degradation of outcrops
near the thumb intersection has limited the number of observation sites. To the
northwest of this domain, we see left-lateral slip along set II fractures and right-lateral
slip along set V fractures. These slip directions reverse toward the southeast of the
domain (Fig. 3.7; Fig. 3.14). An explanation for the shearing observed within this
domain will be investigated below. Domain five contains set II fractures that have
sheared in a right-lateral sense and set V fractures that have sheared in opposite senses
(Fig. 3.14). We interpret the observed shearing as a result of a local clockwise rotation
in the σ1 direction: set II sheared as σ1 rotated away from the northeast direction and,
just as in domain three, set V sheared in the opposite sense when σ1 was oriented
subparallel to set V fractures, but varied slightly temporally.
Lithological control on fracturing
Analysis of stereonets for sites within the Madison, Amsden, Tensleep, and
Phosphoria Fms. at SMA (Fig. 3.5) leads to the deduction that lithological differences
account for little variation in the average orientations of the main fracture sets at SMA.
115

(a)
(b)
(c)
Set II
Set III
Set I
(d)
(e)
(f)
Set IV
thumb thrust
Set V
1
thumb thrust
3
thumb thrust
2
SMA thrust
SMA thrust
SMA thrust
Set I
reactivated
Figure 3.15. Conceptual model of fracture, fold, and shearing development modified
from that for folding and fracturing presented in Bellahsen et al. (2006a) to include the
initiation of set V fractures, the development of the thumb, and shearing along set I, II,
and V fractures. (a) Set I fractures in undeformed rock. (b) Set II forms as Laramide
contraction and slip along the SMA thrust begin. (c) Set I shears in a left-lateral sense
in the backlimb and forelimb; set III forms in the hinge; additional set II fractures form
as contraction continues and sedimentary layers begin to bend. (d) The thumb thrust
begins to slip, accommodating some of the strain at SMA, causing slip along the SMA
thrust to decrease; set V forms as either local or remote maximum principal
compressive stress rotates; set II shears in a right-lateral sense; set I continues to
shear in a left-lateral sense; additional set III fractures form. (e) Continued folding of
both the thumb and main fold lead to the formation of additional set II, III, and V
fractures and increased shearing along sets I, II, and V. At this late stage of fold
development, several shearing signatures constrain the stress field, including: (1)
conjugate shearing along sets II and V (1); (2 & 3) opposite senses of shear along
fractures of the same set. (f) A late stage of fold growth in which set I fractures in the
forelimb reactivate with small thrust offset and set IV fractures form in the backlimb,
with the same strike as set I fractures, but oblique to bedding.
116

Observations of reactivation further discredit a large lithological influence, as sets I, II,
and V have sheared in both limestone and sandstone layers (Fig. 3.7).
In the backlimb, set I may appear to be influenced by lithology. In the
Phosphoria Fm., set I is present at notably fewer sites than in the Tensleep Fm. The
majority of these Phosphoria sites are in the thumb, however. The two Tensleep sites
in the thumb, site 15 and site 22, also lack set I fractures. This variation in the spatial
location of set I fractures is attributed to a heterogeneity in the stress field in the future
location of the thumb while set I was forming, and not a lithological difference.
Furthermore, it cannot be attributed to any structural phenomena as the thumb
uplifted, because set II also is interpreted to pre-date the thumb, and it is found in both
Tensleep and Phosphoria sites throughout the thumb with the same orientation as at
other locations on the fold.
Trends in the occurrence of sets III and IV in the backlimb also suggest a lack of
lithological control on fracturing. Set III exists primarily in the area around and to the
southeast of the thumb intersection. Set IV exists primarily in the area surrounding the
thumb intersection. The spatial locations in which these fractures formed imply that
the development of these two sets is related to localized structure-related stress
perturbations. Because the sets formed in both the Tensleep sandstone and Phosphoria
limestone, one may deduce that the two lithologies respond similarly to stress
perturbations.
No significant differences are noticeable in the orientation of fracture sets
formed in the Madison and Amsden Fms. in the hinge. Joints of set II and III are the
most commonly formed fractures in sites within both layers. Neither lithology
provides evidence for fracture reactivation.
As noted at other field locations, the forelimb of the fold shows more variability
in fracture orientations than other structural positions (Jamison, 1997; Wennberg et al.,
2007). One apparent difference based on lithology is that set I fractures are more
populous in the Tensleep sandstone than the Phosphoria limestone. We argue that set I
fractures do exist in many Phosphoria sites in the forelimb, but are underrepresented in
figure 3.5a due to geometric complications. The Phosphoria Fm. forms the uppermost
layer exposed in the steeply dipping forelimb, and thus access is limited. In these
117

steeply dipping beds striking approximately 320°, not many set I fractures extend to
the bottom of the exposed pavement where measurement is possible. As an example
set I fractures are visible in figure 3.8c, but most cannot be measured. Sets that are
found at numerous sites, set V and a minor N-S set, are present in both the Tensleep
Fm. and the Phosphoria Fm., while the set that is sparse, set II, is sparse in both
lithologies. Although at the microscale, mechanisms of deformation within sandstone
and limestone are different, field observations indicate that at SMA, macroscale
deformation is consistent from one lithology to another.
Set V fractures
Based on abutting relationships, we interpret set V to be composed of early syn-
folding joints that formed after set II joints and before set III joints. Although most
field observations suggest that set II predates set V, alternating termination
relationships exist at specific locations (e.g. sites 1, 16, 8). These few abutments of set
II on set V do not explicitly imply that the local principal stresses rotated back and
forth. As illustrated in figure 3.16, set II joints in some locations formed as echelon
offset segments. With a change in direction of the least principal stress (σ3), set V
fractures initiated and propagated, in some cases through the gaps between echelon set
II segments (location (a) in Fig. 3.16). The sigmoidal shape of the segment marked (b)
in figure 3.16 may record the transition of σ1 from 045 o to 075 o . The segment initiated
as a set II joint. With the transition in direction of σ1, the tips of the original segment
propagated along curved paths, becoming aligned with the newly forming set V joints
and propagating further in this orientation.
Set V apparently formed during a syn-folding stage before much bedding
curvature (and thus before set III joints) accumulated in the backlimb. In this case,
there are two scenarios that could lead to a rotation in local principal stress directions
allowing new joints to form at 075°. Both scenarios are linked to the development of
the thumb, a secondary fold on the backlimb of SMA with a fold axis rotated 20° –30°
clockwise from that of the main fold. In the first scenario, a clockwise reorientation of
the remote greatest compressive stress (σ1) could have occurred. A clockwise rotation
of the maximum contraction during the Laramide is supported by a study of the
118

N
10 cm
N
set V
(b)
(a)
set III
set II
10 cm
Figure 3.16. Field photograph and interpretation of set II and set V joints that grew
together. In most cases, set V joints truncate against set II joints, but as seen at
location (a) above, some set V joints grew through gaps in echelon set II joints. The
sigmoidal shape of the segment at location (b) records a rotation in the σ1 direction.
The part of the segment shown in bold formed first as a set II joint. As the σ1 direction
rotated, both tips of this original segment propagated along a curved path, realigning
with a σ1 direction parallel to the average set V joint strike.
119

kinematic history of the Rocky Mountain foreland that is based on existing structural,
paleomagnetic, and stress data (Bird, 1998). This rotation would have decreased the
potential for slip along the main SMA fault, while at the same time enhancing the
potential for slip along faults of a more north-south orientation, such as the one
proposed to exist beneath the thumb (Savage and Cooke, 2004). Slip along such a fault
would lead to the uplift of the thumb and, if tensile stresses exceeded rock strength, a
set of joints aligned with the direction of σ1. In the second scenario, the remote σ1
could have remained in the same orientation. As some of the applied remote load was
relieved by oblique slip along the fault beneath the thumb, the thumb fold developed,
and the potential for further slip along the main fault decreased. Formation of set V
fractures would then be linked to local perturbations in the stress field caused by the
interaction of the faults beneath the folds, pre-existing heterogeneities, bending of
bedding within the thumb, or any other mechanism by which the local stress field is
perturbed.
For either principal stress rotation scenario, we must justify the presence of set V
in the forelimb, where the paucity of set II has been attributed to elevated compressive
stresses in the hanging wall of the thrust fault beneath SMA as slip accrued during
early folding (Bellahsen et al., 2006b). The state of stress in the forelimb must have
differed during formation of the two fracture sets. In both scenarios for the formation
of set V fractures discussed above, the decrease in activity along the main thrust fault
and the accompanying relaxation in compressive stresses near the tip of that fault, is
consistent with the development of set V in the forelimb.
Stress field constraints
Field observations at SMA constrain the stress state throughout the fold at the
time of fracture reactivation. As illustrated through the failure analyses carried out
within this section, the presence or absence of shear along specific fracture sets
provides estimates of local principal stress magnitudes. The direction(s) of shearing
along fracture sets constrains the orientation of the local principal stresses.
120

Constraints on spatial variation in stress orientation: conjugate shearing
Conjugate shearing along set II and V joints places constraints on the direction
of the local principal stresses during joint reactivation, assuming that the recorded slip
occurred concurrently. In the second backlimb domain, at site 22 in the Tensleep
sandstone, set V, with an average local strike of 080°, has sheared in a left lateral
sense (Fig. 3.17a, 3.17b). Set II, composed of joints that are less pronounced than
those of set V, has an average strike of 050° and has sheared in a right lateral sense
(Fig. 3.17a, 3.17b). Although joint orientations within sets II and V are dispersed (Fig.
3.17c), a distinct cutoff for shearing direction is observed. Fractures of strike direction
066° and less shear in a right-lateral sense; fractures of strike direction 078° and
greater shear in a left-lateral sense. Assuming that σ2 is parallel to the intersection of
sets II and V, then the conjugate slip along these fracture sets constrains the σ1
direction during shearing to an orientation within this twelve degree range (Fig. 3.18).
Spatial variation in stress orientation: opposite senses of shearing
Where two sub-parallel joints within close proximity to one another are sheared in
opposite directions, the local stress direction may be constrained. Data from the
backlimb suggest that opposite senses of shearing are a result of temporal, rather than
spatial, variations in the stress field. Opposite senses of shearing along approximately
parallel joints are observed at site 8 within set II and at sites 127, 128, and 130 within
set V. Although the joints initiated and slipped within folding stages where spatial
heterogeneities in the stress field due to bedding plane slip and faulting were present
(Fig. 3.15d, 3.15e), sub-parallel fractures would be expected to shear with a similar
sense. The proximity of these features suggests that the shearing is not spatially
dependent: at site 130, the oppositely sheared set V fractures are decimeters apart (Fig.
3.11a). Instead, we suggest that the joint set has been subjected to a temporal stress
field rotation in which the σ1 direction varied around the mean strike direction (Fig.
3.19).
To analyze this interpretation, we refer to frictional faulting theory (Coulomb,
1773; Anderson, 1951) as applied to pre-existing fractures (Jaeger, 1958). Assuming
that σ1 (maximum compressive stress) and σ3 are in the horizontal plane and the
121

NNW SSE NNW SSE
(a)
1 m (b)
050 o
010 o
150 o
092 o
075 o
045 o
1 m
(c)
N
measured
N
set V
set II
unfolded
Figure 3.17. Fractures at backlimb site 22 in the Tensleep sandstone. (a) Field
photograph and (b) line interpretation of sheared fractures at the site. (c) Stereonets
of poles to fractures as observed in the field and unfolded.
122

4
5
Figure 3.18. Spatial constraints on local principal stress directions. Gray areas
represent different shearing domains. Tick marks represent σ1 directions as
constrained by shearing observations. Joints would form parallel to the orientations of
these tick marks.
(a)
(b)
(c)
Figure 3.19. Conceptual depiction of how opposite shearing may be resolved along
parallel joints as a result of a temporal rotation in the remote stress field. Black arrows
represent the maximum compression direction. (a) Joints form parallel to the
maximum compression direction. (b) The maximum compression direction rotates
slightly clockwise, causing fractures with low friction to shear left-laterally. (c) The
maximum compression direction rotates slightly counter-clockwise from the joint strike
direction, causing other fractures to shear right-laterally.
3
123
2
6
1
N

intermediate principal stress (σ2) is contained in the vertical plane of the fracture,
sliding depends upon both the angle β that the normal to the surface makes with σ1
and on the magnitudes of σ1 and σ3. An analysis following Jaeger (1959) and Jaeger
and Cook (1979), provides the combinations of angle β and horizontal stress values
that lead to frictional slip along pre-existing joints.
The Coulomb criterion for frictional sliding on a pre-existing weakness is
| σ +
(1)
s | = S o µσ n
where σs is the shear stress resolved on the fracture, So is cohesion, µ is the coefficient
of static friction, and σn is the resolved normal stress. σs and σn are related to the
horizontal principal stresses as follows:
1
1
σ n = ( σ 1 + σ 3 ) + ( σ 1 − σ 3 ) cos 2β
(2)
2
2
1
σ ( σ 1 σ 3 ) sin 2β
2
− − = s (3)
where β is the angle between the normal to the fracture and the direction of σ1. The
angles β1 and β2 define the range of orientations within which sliding will occur for
given principal stress magnitudes, friction, and cohesion:
−1
⎧⎡⎛
1
⎞ 1 ⎤ ⎫
β1 = π + φ − sin ⎨⎢⎜
( σ 1 + σ 3)
+ S o cotφ
⎟ / ( σ 1 − σ ) ⎥ sinφ
⎬ (5)
⎩⎣⎝
2
⎠ 2 ⎦ ⎭
2 3
−1
⎧⎡⎛
1
⎞ 1 ⎤ ⎫
β 2 = φ + sin ⎨⎢⎜
( σ 1 + σ 3)
+ S o cotφ
⎟ / ( σ 1 −σ
) ⎥ sinφ
⎬ (6)
⎩⎣⎝
2
⎠ 2 ⎦ ⎭
2 3
where φ is the angle of friction. We assume that the variation around the σ1 direction
that led to reactivation of the joints occurred during the same period of deformation
within which the joints initiated. It is thus unlikely that cementation of the joint walls
had occurred before reactivation. Assuming that the joint walls were bare (i.e. no vein
fill), we set So = 0. As determined by laboratory experiments investigating friction
along bare joint surfaces (Jaeger, 1958), we use φ = 30 o .
To assess these equations for the case of oppositely sheared joints at SMA,
constraints must be placed on the possible principal stress magnitudes. Assuming a
124

density of 2700 kg/m 3 for sedimentary rock and a depth of 2200 m, representing the
depth of the Tensleep Fm. during Laramide time, the layer within which we find
oppositely sheared joints would have been subjected to a vertical stress of 58 MPa. For
the reactivation observed along set II and set V joints to occur, the state of stress must
be a strike-slip faulting regime where the vertical stress is the intermediate principal
stress (σ2). Appropriate values for the horizontal principal stresses, as determined by
in situ stress measurements (McGarr and Gay, 1978; Brace and Kohlstedt, 1980) and
consideration of the strength of the crust (see Moos and Zoback, 1990; Zoback et al.,
2003), range from 0.6σv to 2.2σv.
To assess these limited ranges of σ1 and σ3, we set σ1 at 127 MPa, (2.2σv), we
allow σ3 to vary over the range 34 MPa to 58 MPa (0.6σv to σv), and we solve
equations (5) and (6) for β1 and β2. Figure 3.20a plots the critical angles for slip along
joints for the specified range of principal stress ratios: the gray area represents
conditions under which the pre-existing joint would slip, whereas the white area
represents those in which the stress state is insufficient for slip. This concept is readily
visualized on a Mohr diagram (Fig. 3.20b). For σ1 and σ3, (say σ1 =127 MPa and σ3
=37 MPa) for example, intersections with the failure envelope occur at angles
2(β1=48 o ) and 2(β2=72 o ) as measured from σ1 (dashed lines, Fig. 3.20b). The geometry
of a joint with respect to σ1 and σ3 for these two critical angles is shown in figure
3.20c. Slip will occur for all angles between β1 and β2 (θ in Fig. 3.20c), as indicated by
the gray area in figure 3.20b. For σ1 =127 MPa, σ1/σ3 = 3 represents the limiting case
for frictional slip. Slip occurs only at β1 = β2 = 60 o , as indicated by the tangency of the
Mohr circle to the failure envelope at 2β1=2β2 from σ1 (Fig. 3.20b). When σ1 =127
MPa smaller stress ratios will not cause reactivation of the joints.
Results for the above analysis when revisited including pore pressure at a hydrostatic
gradient of 10 MPa/km are shown in figures 3.20d,e,f. A plot of the ratio of the
maximum and minimum principal stresses, again where σ1 = 127 MPa and σ3 ranges
over 34 MPa to 58 MPa, versus the angle β indicates that when pore pressure is
accounted for, the stress ratio for the limiting case of slip is lowered to ~2.2. Sliding
125

(a)
Angle β (degrees)
(b)
(c)
75
70
65
60
55
50
45
2 2.
|σs|
β1 β2 β1 = 48 o
β = 72 2 o
σ1 /σ3 = 3.4
2 2. 4 2. 6 2. 8
σ1/σ3 3 3. 2 3. 4 3. 6
critical case: σ 1 /σ 3 = 3
σ 1 /σ 3 = 3.4
joint
β2 σ3 β
σ 1
3
β 2
β 1
n
θ
β
σ 2
1
2β 1
2β 1 = 2β 2
β
σ 1
1
2β 2
σ n
(d)
90
Angle β (degrees)
(e)
(f)
80
70
60
50
40
30
2 2.2 2.4 2.6 2.8
σ1/σ3 3 3.2 3.4 3.6
|σs*|
β1 β2 β1 = 36 o
σ1 /σ3 = 3.4
β 2 = 84 o
joint
σ 3 β 2
2β 2
critical case:σ 1 /σ 3 = 2.2
σ 1 /σ 3 = 3.4
β1 σ3 2β 1
2β 1 = 2β 2
Figure 3.20. Analysis of principal stress directions and magnitudes for oppositely
sheared joints of the same set. For the case of σ1 = 127 MPa and σ3 ranging from 34
MPa to 58 MPa, the β1 and β2 values (representing the angle between the normal to
the joint and the σ1 direction) at which pre-existing joints will slip are represented by
the gray envelopes in (a), representing the dry case and (d), where hydrostatic pore
pressure is included. (b) and (e) are Mohr circle depictions for the respective cases.
The solid line in each figure represents the critical angle (2β1 = 2 β2) at which slip will
occur. The dotted lines bound the 2β values of pre-existing joints that would slip
within a stress state where σ1 = 127 MPa and σ1 /σ3 = 3.4. (c) and (f) depict the
geometry of the σ1 directions with respect to the joint surface and the joint normal for
the β values representing the boundaries of the gray zones in (b) and (e). All preexisting
joints formed at angles represented by this zone, marked by the angles θ in
(b) and (e) would slip under the given stress conditions.
126
β 2
β 1
n
θ
β
σ 2
1
β
σ 1
1
σ n *

occurs when the normal to the joint and σ1 form an angle of 60 o . Numerous
combinations of σ1/σ3 and β result in slip, as shown by the gray area in figure 3.20d.
About 95% of set II and set V joints show no evidence for slip in the areas where
opposite senses of shearing were found. One may conclude that the state of stress was
at the frictional sliding limit for the weakest members only, while the majority of set II
joints at site 8 and set V joints at sites 127, 128, and 130 remained locked. Therefore
the combinations of stress states and β values situated along the boundary of the gray
envelope (Fig. 3.20a, 3.20d) are most appropriate. Because we interpret the opposite
senses of shearing to result from minor variation of σ1 around the strike direction of
the joints, the β2 curve defines the minimum critical slip angle for each state of stress.
We calculate the relative magnitudes of the regional principal strains relating to
the principal stresses at the critical point of failure for β2 = 85 o , 80 o , 75 o , and 70 o .
Values for σ3 are calculated from the corresponding principal stress ratios (Fig. 3.20d)
using σ1 = 127 MPa. Representative strains (ε1, ε3) for these principal stresses are then
calculated from Hooke’s law for the isotropic elastic medium:
+ ν ν
ε ij = σ ij − σ kkδ
ij
E E
1
Although Laramide strains were clearly beyond the elastic limit, we postulate
that the relative magnitudes of elastic strains calculated from principal stress values
are representative of discrete deformation events such as an episode of slip along the
faults beneath SMA. Elastic strains then provide reasonable boundary conditions for
mechanical models attempting to relate stress, strain, and displacement fields at SMA
during such events. Figure 3.21 plots the fracture parallel (ε1) and fracture
perpendicular (ε3) strains corresponding to specific values of σ3 for four different βs at
the critical limit when σ1 = 127 MPa. Plotted combinations of (ε1, ε3) that correspond
to the same σ3 value and the same β value represent strain configurations that are
plausible for inducing reactivation along set II and V joints as seen in the field.
The above analysis indicates that a variation of principal stress directions by as
little as a few degrees could result in shearing along joints. We conclude that
observations of opposite senses of shear along sub-parallel joints indicate that the
127
(7)

strike of the joints is a reasonable average σ1 direction. Because opposite senses have
been observed along set II in domain three and set V in domain five, we posit that σ1
varied around 045° in domain three and around 080° in domain five (Fig. 3.18) during
the time period in which the joints slipped. In the case that set V formed due to a
clockwise rotation in the remote σ1 direction, set II would have reactivated during an
earlier stage of folding than set V (Fig. 3.15). In the case that set V formed due to local
principal stress rotations, set II and V reactivation could have occurred in separate
locations concurrently.
Constraints on spatial variation in stress field magnitude: set I fractures
Here we investigate shearing along pre-existing set I fractures in the Tensleep
sandstone of the limbs and the formation of new set III joints in the Madison limestone
of the hinge. This analysis involves comparing sliding along pre-existing fractures to
tensile failure of intact rock. The majority of hinge observations were made within the
Madison limestone, which is locally dolomitized (Sonnenfeld, 1997). Representative
values for cohesion and angle of internal friction for dolomitized limestone are 17
MPa and 53 o , respectively (Kahraman et al., 2006). We also consider the failure
envelope for intact sandstone to demonstrate states of stress that are inconsistent with
field observations within the Tensleep Fm. Representative values for cohesion and
angle of internal friction for sandstone are 28 MPa and 26 o , respectively (Jaeger and
Cook, 1979).
For the backlimb, the cases where set I reactivated while set II was forming and
while set V was forming are compared in figures 3.22a and 3.22b. In the former case,
σ1 was oriented at 045 o and the angle between the normal to set I and the direction of
σ1 was 025 o (Fig. 3.22a). In the latter case, σ1 was oriented at 075 o and the angle
between the normal to set I and the direction of σ1 was 065 o (Fig. 3.22b). The
configuration of the stress states in figures 3.22a and 3.22b represent the onset of
sliding along set I fractures, given specific values of the maximum shear stress (radius
of the Mohr circle; ½(σ1 - σ3)) and the mean stress (center of the Mohr circle; ½ (σ1 +
σ3)). Sliding occurs where the line at an angle of 2β from σ1 intersects the failure
envelope for sliding along a bare fracture at (σn ,σs). The stress state for the case when
128

% strain
1.2
1.0
0.8
0.6
0.4
0.2
0
σ 3 ’/σ 1 ’ = 3.63; α = 85 o
σ 3 ’/σ 1 ’ = 2.89; α = 80 o
σ 3 ’/σ 1 ’ = 2.54; α = 75 o
σ 3 ’/σ 1 ’ = 2.34; α = 70 o
ε 1 : fracture parallel
ε 3 : fracture perpendicular
-0.2
30 35 40 45 50 55 60
σ 3 (MPa)
Figure 3.21. Plot showing possible remote strain boundary conditions derived from
frictional faulting theory applied to observations of reactivated joints. The strains
above are calculated for the case where σ1 = 127 MPa and account for hydrostatic
pore pressure.
129

σ1 was oriented at 075 o was more favorable for invoking sliding along set I fractures
than the case when σ1 was oriented at 045 o .
In the hinge, when set III fractures formed, σ1 was oriented at 135 o , parallel to
the strike of the joint set. The normal to set I fractures formed an angle β of 065 o with
σ1. If set I fractures were not cemented, sliding would have occurred along set I
fractures before failure of the intact rock for any stress state. This concept is
represented conceptually by the Mohr circle in figure 3.22c. The point (σn, σs) on the
Mohr circle (at angle 2β from σ1) representing sliding along set I intersects with the
failure envelope for bare fracture surfaces before reaching the point of tensile failure
for the dolomitic limestone represented by S0 dls /2. Because the failure envelope for
bare fracture surfaces has a y-intercept of 0, slip along set I fractures would occur
before set III fractures formed for any stress state. If set I had been infilled, then the
failure envelope shifts to represent the cohesion and the angle of internal friction of
the infilled material (Jaeger, 1958).
Thin sections of set I fractures in the hinge and backlimb indicate the possibility
of a multi-stage evolution in the backlimb. In the hinge (Fig. 3.23a), set I fractures are
marked by a zone of fine grained calcite cement. In the backlimb (Fig. 3.23b), fine
grained calcite cement lines the contact between the host rock and larger grained
calcite cement. Comparison of the two thin sections suggests that set I fractures in the
backlimb were subjected to a second stage of deformation not recorded by set I
Figure 3.22 (opposite page). Mohr circles investigating slip along set I fractures for
(a) backlimb positions in sandstone where the local σ1 is oriented at 045 o ; (b)
backlimb positions in sandstone where the local σ1 is oriented at 075 o ; and (c) hinge
positions in dolomitized limestone where the local σ1 is oriented at 135 o . (d) Mohr
circle depiction of how the failure envelope of the fracture fill may be constrained by
field observations. The a marks the point of tensile failure of the dolomitic limestone
and the b marks the point of failure of the fracture fill. (e) Mohr circle depiction of how
the addition of a bending stress affects the state of stress. As the bending stress
increases from stage t1 to t5, the initial σ1 becomes more tensile. Between stages t3
and t4, the principal stress directions have rotated 90 o . Additional increments of
bending stress move the stress state toward tensile failure, which is shown at stage
t5. In this figure, fi is the coefficient of internal friction, fs is the coefficient of sliding
friction, S0 is cohesion, bf = bare fracture, ss = sandstone, dls = dolomitic limestone,
fill = infilled material.
130

(a)
(c)
(e)
S 0 ss
S 0 ss /2
S 0 dls
S 0 fill
S 0 dls
σ 3 f
|σ s|
σ 3
S 0 dls /2
|σ s|
|σ s|
t5 t4 t 3
σ 1 f σ 3 i
σ 3
2β
(σ n , σ s )
σ 1
dls
(σ n , σ s )
dls
t 2
2β
t 1
σ 1
σn 50
(b)
S 0 ss
S 0 ss /2
|σ s|
ss ss
σ n
50
σ 1 i
131
(d)
S 0 fill
S 0 dls
σ 3
(σ n , σ s )
2β
σ1
φ i ss=26 0 ; φ s dls=53 0 ; φ s bf=30 0 ; φ s fill=28 0
S 0 ss = 28 MPa; S 0 dls = 17 MPa
S 0 bf = 0 MPa; S 0 fill = 18 MPa
σ n
S 0 ss
b
a
σ3 |σ s |
dls
σ1
lithology failure envelope
bare fracture failure envelope
fracture fill failure envelope
σn 50
ss
σn 50

fractures in the hinge. The fracture filling was broken during a later stage of
deformation, and opening provided space for the crystallization of the larger calcite
grains (Fig. 3.23b). It is plausible that set I fractures, thought to have formed during
the Sevier orogeny (Bellahsen et al., 2006a), had been infilled by the time of the
Laramide orogeny. In this case, the cohesion and angle of internal friction of the fine
grained calcite cement would determine the stress conditions under which slip along
set I fractures occurs.
Perhaps using a limestone failure envelope for calcite fracture fill would be
appropriate. However, as a literature search reveals, the frictional properties of
limestone vary over a large range. For example, two references alone provide a range
for the angle of internal friction of 27.9 o to 46.9 o and a range for cohesion of 15 MPa
to 105 MPa for limestone (Handin, 1969; Kahraman et al., 2006). In figure 22d, we
plot selected frictional properties (φ = 30 o , S0 = 18 MPa) that are consistent with the
deformation observed at SMA. For set III fractures to form before reactivation of set I
fractures, the stress state must reach the point of tensile failure (point a, Fig. 3.22d) of
the intact rock before the calcite fails. For set I fractures to slip in the backlimb, the
stress state must reach the point where the infill material fails (point b, Fig. 3.22d)
before the intact sandstone fails.
In the Laramide tectonic setting within which SMA developed, for set III joints
to form parallel to the hinge, the bending-related stress would have to be large enough
so that the most tensile stress direction rotates by 90°. Assuming that the bending-
related stress affects only the fold perpendicular stress magnitude, we consider the
process through which the bending stress alters the stress state (Fig. 3.22e). Given an
initial stress state, generated by the onset of fold perpendicular contraction, σ1 is
oriented at 045°. With an increase in fold amplitude, a tensile bending-related stress is
introduced and acts to decrease the magnitude of σ1 (stages t1 through t3, Fig. 3.22e).
At the point when the bending-related stress reaches a magnitude greater than the fold
perpendicular tectonic σ1 magnitude, the σ1 direction rotates 90° and the
initialσ3 magnitude becomes the new σ1 magnitude (represented by stage t3 to t4, Fig.
3.22e). As the fold continues to amplify, σ3 becomes more tensile. At the point where
the magnitude of σ3 equals the tensile strength of the limestone, set III joints form.
132

(a)
(b)
Figure 3.23. Thin section of set I fracture in the (a) hinge at site 41 and (b) backlimb
at site 23. The backlimb fracture indicates an additional phase of deformation.
133

Through this analysis, it becomes clear that the state of stress in the backlimb leading
to the reactivation of set I fractures would have a greater mean stress magnitude and a
greater maximum shear stress than the state of stress in the hinge, where a bending-
related stress exists.
Discussion
Kinematics of shearing and folding
Most examples of fracture reactivation recorded during field work at SMA are
kinematically consistent. All observed strike-slip reactivation along set I is left-lateral
(Fig. 3.7). The geometry of set I fractures subjected to contraction in an orientation of
045° or 075° suggests that, should the shear stress resolved along the fracture plane
overcome the frictional resistance, slip would occur in a left-lateral sense (Fig. 3.24b,
3.24c). Set II, striking 045°, would be expected to slip in a right-lateral sense with the
clockwise reorientation of the local σ1 responsible for the initiation of set V joints
(Fig. 3.24c). Indeed, at twenty-two of the twenty-five sites where reactivation of set II
joints has been noted, right-lateral motion has been identified (Fig. 3.7). At six of
these sites, set II joints have a left-lateral sense of shear. Here we suggest that these
joints reactivated in response to a local stress perturbation that deflected σ1 counter
clockwise prior to the clockwise rotation that resulted in the development of set V.
Implications for the mechanics of fracturing within a thrust fault related fold
The asymmetry with respect to the regional tectonic stress field of both the
formation (Fig. 3.5) and reactivation (Fig. 3.7) of fracture sets at SMA highlights an
important concept for the mechanics of fracturing in a thrust fault related fold: the
influence of the underlying faults. In the forelimb, the major fracture sets developed at
measurement sites vary along the length of the fold (Fig. 3.5a). Additionally,
subdomains within which set II and set V exhibit consistent senses of shear are not
readily apparent (Fig. 3.7). Conversely, in the backlimb distinct trends are apparent in
the formation of fractures: for instance the occurrence of sets IV and V are both
localized in the thumb area (Fig. 3.5b). Trends also are observed in the reactivation of
joints (Fig. 3.14) related to structural position.
134

(a)
(b)
(c)
N
Figure 3.24. Schematic diagram illustrating the kinematics of shearing of fracture
sets at SMA. Black arrows represent σ1 directions. (a) Outcrop prior to Laramide
orogeny with set I fractures developed at 110 o . (b) At onset of Laramide orogeny,
joints form at 045 o . Small amounts of left-lateral shear may be resolved along set I
fractures. (c) Local principal stress directions rotate clockwise. Joints form at 075 o .
Left-lateral shear is resolved along set I fractures and right-lateral shear is resolved
along set II fractures.
135

In a pure buckle fold, the expected fracture pattern in the backlimb and forelimb
is symmetric about the hinge (e.g. Dietrich, 1970). Had SMA developed as a buckle
fold with forelimb and backlimb bedding dips becoming asymmetric with increasing
deformation, one would expect the fracture pattern in the forelimb to resemble a
progression of the fracture pattern in the backlimb. The development of small offset
thrust faults along the pre-existing set I fractures in the forelimb can be viewed as an
example of this progression. However, the formation and reactivation of the set II and
V fractures, which developed during the uplift of the fold, is not consistent in the
forelimb and the backlimb. This observation leads to the conclusion that consideration
of stress perturbations related to curvature and layer parallel contraction is insufficient
for prediction of the fracture pattern developed within this thrust fault related fold. The
underlying fault(s) apparently generate significant perturbations in the stress state
prevailing throughout the fold that differ between the forelimb and backlimb and must
be accounted for to understand the fracture patterns.
Acknowledgements
We thank Yukiyasu Fujii, Ashley Griffith, Ole Kaven, Ian Mynatt, and Chris
Wilson for field assistance. This study was supported by the National Science
Foundation Collaboration in Mathematical Geosciences Program Grant No. EAR-
04177521 and the Stanford Rock Fracture Project.
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140

Chapter 4
Curvature and fracturing based on GPS data collected at Sheep
Mountain Anticline, WY
Abstract
We investigate the curvature-fracture relationship at Sheep Mountain Anticline
by coupling fracture mapping with the analysis of high precision GPS positions.
Carrier-phase post-processing techniques of spatial data collected across patches of
bedding surfaces results in a high resolution dataset. Differential geometry tools form
the basis for curvature analysis, allowing for a quantitative understanding of the
shapes of these surfaces. Comparison of principal curvature magnitudes with fracture
measurements indicates that greater curvature correlates with greater spherical
variance of fracture sets. Fracture intensities, however, seem to correlate only loosely
with curvature, as fracturing mechanisms other than curvature of bedding must be
taken into account.
Introduction
Outcrop scale brittle structures such as small faults, joints, and sheared joints,
form within folding sedimentary rock. These structures represent a second order of
deformation, developing as localized deformation features within more brittle
lithologies and relieving local stress perturbations as the deforming strata bend into
various shapes. As small-scale structural heterogeneities, faults, joints, and sheared
joints affect the flow properties of reservoirs and aquifers. They represent
discontinuities in the permeability of the rock volume that disrupt both the vertical and
lateral transport of fluids. Accurate characterization of these structures within
reservoirs or aquifers is sought for economic purposes.
Sedimentary horizons and major faults can be satisfactorily imaged in seismic
reflection data (e.g. Fiore et al., in press; Kattenhorn and Pollard, 2001; Maerten et al.,
2000; Needham et al., 1996; Mansfield and Cartwright, 1994). Identifying so-called
subseismic fractures (with length scales ≤ 20 - 30 m), however, proves to be
problematic. The secondary structures on which this paper focuses fall into this
141

category, being typically below seismic resolution. Direct observation of the patterns
in which they form is unfeasible, except within boreholes, where spatial coverage is
limited. New methods for predicting fracture patterns from available subsurface data
would play a crucial role in the development of hydrocarbon reservoirs and
groundwater aquifers.
Many previous studies have hypothesized a relationship between fracture
location, orientation, and spatial density and structural position across a fold (e.g.
Woodring et al., 1940; Harris et al., 1960; Stearns, 1968; Narr, 1991; Cooper, 1992).
In recent years, curvature analysis quantifying properties of fold geometry has been
emphasized as a means of predicting fracture patterns within folds (e.g. Schultz-Ela
and Yeh, 1992; Lisle, 1994; Fischer and Wilkerson, 2000; Hennings et al., 2000).
Studies have implemented curvature analysis in various ways. Fischer and Wilkerson
(2000) relate fracture orientation to minimum curvature trajectories; Lisle (1994),
Robinson (1997), and Hennings et al. (2000) correlate joint occurrence and density
with Gaussian curvature magnitudes. These studies rely on an assortment of curvature
calculation methods, some of which present approximated values of surface curvature
(e.g. Murray, 1968; Ekman, 1988; Ivanov, 1989; Schultz-Ela and Yeh, 1992; Lisle,
1994; Lisle and Robinson, 1995; Nothard et al., 1996; Stewart and Podolski, 1998;
Johnson and Johnson, 2000; Roberts, 2001). Recently, Bergbauer and Pollard (2003)
have presented a method of surface curvature calculation that is derived from
differential geometry.
We investigate the relationship between curvature and fracturing at Sheep
Mountain anticline (SMA) by comparing the magnitudes of the principal curvatures,
derived from differential geometry calculations, of small patches of bedding surfaces
with the intensities and orientations of fractures measured across these surfaces.
Geological Setting
SMA is located on the northeast flank of the Bighorn Basin, just west of the
Bighorn Mountains. It is a basement-cored thrust fault related fold that formed in
response to Laramide tectonics. The fold trends northwest-southeast and is cut by the
Bighorn River approximately perpendicular to this trend (Fig. 4.1). The study area
142

consists of the portion of the anticline that lies to the northwest of the river cut, as well
as the area immediately southeast of the river cut and includes sedimentary rocks
ranging in age from Lower Carboniferous to Permian (Fig. 4.1). The oldest rocks are
of the Mississippian Madison Fm., a massive limestone that has been dolomitized
throughout much of the study area (Pranter et al., 2004; Sonnenfeld, 1996). The
Madison Fm. is exposed in the canyon where the Bighorn River dissects Sheep
Mountain and in the hinge of the anticline where younger layers have been eroded.
The Pennsylvanian Amsden Fm. sits above a karst surface at the top of the Madison
Fm. and is comprised of a basal sandstone unit, a middle silty shale unit, and an upper
unit of interbedded limestone and dolomite (Ladd, 1979; Hennier, 1984). The Amsden
Fm. crops out primarily in the hinge of the fold. Above the Amsden Fm., the
Pennsylvanian Tensleep Fm. consists predominantly of sandstone that is interlayered
with thin beds of dolomite and shale. The Tensleep Fm. forms large pavements in the
backlimb and forelimb of Sheep Mountain. Limited Tensleep outcrops are found in the
hinge of the fold near the northwestern nose. The youngest formation in the study area
is the Permian Phosphoria Fm., composed of interbedded siltstones and shales that are
overlain by a massive limestone. This limestone forms the flatirons along the steep
forelimb of the fold, the folded pavements over the northwest nose, and the small
pavements at the base of the backlimb slopes. For this study, we focus on the
Phosphoria Fm. because it forms fairly continuous pavements both in areas of
significant curvature (i.e. the hinge) and apparently planar areas (i.e. base of forelimb
and backlimb dipslopes).
Methodology
GPS data collection
To collect the three-dimensional spatial data analyzed in this study, we used
differential GPS technology with a two receiver set up. A Trimble TM Pro XRS
receiver served as a stationary base station and a Trimble TM Pro XL receiver with a
pole mounted antenna served as a rover. For two of the pavements considered in this
study, we walked across the bedding surfaces with the rover system, but the remaining
five pavements were too steep. For these, the rover was kept stationary at distances
143

N
108°12'
Thumb fold
Quaternary
Cretaceous
Jurassic
Triassi c
108°10'
Permian (Phosphoria Fm)
Carboniferous (Pennsylvanian, Tensleep Fm )
Carboniferous (Pennsylvanian, Amsden Fm)
Carboniferous (Mississippian, Madison Fm)
108°08'
Bighorn River
44°38'
108°06'
Anticlinal axis Synclinal axis 1 km
Figure 4.1. Geological map of SMA. The Bighorn River dissects the fold
approximately perpendicular to the fold trend. This study focuses on deformation of
the Permian Phophoria limestone. From Bellahsen et al., 2006a. After Rioux, 1994.
144
108°04'
44°36'
108°02'
44°34'

etween 5 and 20 meters and offsets to positions on the bedding surfaces were
recorded with a LaserCraft TM Contour XLRic laser range finder.
For all pavements considered in this study, data were collected and post-
processed using the carrier-phase (L1) signal, which has a much higher frequency than
the more common code signal (C/A, pseudo random code; Kaplan, 1996). The higher
frequency of the carrier signal enables greater precision and accuracy of measurements
by orders of magnitude (Kaplan, 1996). The collection of precise GPS data sets is thus
feasible on an academic budget.
To determine the effect of various post-processing techniques on collected GPS
data, we ran a test case at a biological preserve in Stanford, CA. An area of noticeable
curvature and of comparable size to pavements intended for analysis in Wyoming was
selected at the preserve. Three-dimensional spatial data were collected at
approximately regular intervals and then were post-processed by four different
methods. To investigate the difference between correcting GPS positions with an on-
site base station versus a distant base station, we post-processed the collected positions
with data from both a base station we had set up at the preserve and a community base
station 28 km away at Pigeon Point, CA. To investigate the difference between
correcting GPS positions with code data versus carrier-phase data, we post-processed
both the code data and the carrier-phase data that we had collected with the roving
GPS receiver. The resulting corrected data sets are represented by black dots in figures
4.2a – 4.2d. Basic surfaces (MATLAB’s triangle based linear interpolation) have been
fitted to these points and contoured at a 2 ft interval for comparison to a digital
elevation model of the preserve with a resolution of 2 ft (Fig. 4.2e). Our results
indicate that for post-processing code data, an on-site base station provides more
accurate measurements than a base station 28 km away. More notable is the accuracy
of carrier-phase post-processing. The contours in figure 4.2e are reproduced in figures
4.2c and 4.2d.
The decision to set up a base station at Sheep Mountain rather than using a
community base station was based on the desire to collect large amounts of high
quality data. When post-processing using carrier-phase data, a position solution is
generated at the rate of the least common multiple of the base and rover logging
145

(a)
Y (m)
(c)
Y (m)
50
40
30
20
10
0
0 10 20 30
X (m)
40 50 60
50
40
30
20
10
Code: on−site base
Carrier: on−site base
0
0 10 20 30
X (m)
40 50 60
(e)
Z (ft)
Z (ft)
25
20
15
10
5
20
15
10
5
Y (m)
Y (m)
50
40
30
20
10
Code: PPT1
0
0 10 20 30
X (m)
40 50 60
50
40
30
20
10
Collected data on DEM (2 ft countours)
Carrier: PPT1
0
0 10 20 30
X (m)
40 50 60
Figure 4.2. Results of testing various DGPS post-processing methods. GPS data are
post-processed using (a) code data with an on-site base station; (b) code data with a
TrimbleTM referenced base station located 28 km from the field site; (c) carrier-phase
data with an on-site base station; (d) with a Trimble TM referenced base station located
28 km from the field site. Surfaces have been gridded from the respective postprocessed
data. Elevation is shown in feet so that contours, plotted in black and
spaced at two foot intervals, can be compared with the DEM contours shown in (e).
(e) Collected data are shown in black. Green lines represent a 2 foot resolution DEM
of the ground surface. The black polygon represents the area that is gridded in (a) -
(d).
(b)
(d)
146
Z (ft)
Z (ft)
20
15
10
5
20
15
10
5

intervals. Most community base stations have a five second logging interval at
minimum. With five to ten position readings per location required to ensure a
measurement of reasonable precision, setting up a base station with a one second
logging rate allowed us to collect data much more efficiently. Additionally, the ability
of the post-processing method to synchronize the signals collected by the base station
and rover is inversely proportional to the baseline distance. The nearest base station to
Sheep Mountain is 180 km away, much beyond the 30 km maximum baseline distance
that is required for high precision post-processing (TSC1 Asset Surveyor Operation
Manual).
For this project, we are characterizing the shapes of individual patches of
bedding surfaces. Therefore, we require high relative accuracy and precision of points
within a single surface, but not high global accuracy (positioning of surfaces within a
global reference frame). Moving the location of the base station for each characterized
surface therefore provides the best quality data for these purposes. The base station
typically remained within 500 m of a characterized surface. The longest baseline from
the base station to the rover was 1.8 km.
GPS data filtering
To ensure that the appropriate features are analyzed during the curvature
calculation, two steps are taken. During the collection phase, to prevent aliasing
effects, the pavement is sampled at a scale that is smaller than the scale of features
being studied. During the data processing phase, small scale undulations that are not
related to the phenomenon being considered (i.e. folding) are removed using the
spectral analysis technique described by Bergbauer and Pollard (2003). Through this
technique, the data are transformed from the spatial to the frequency domain and
decomposed into a series of trigonometric functions of varying amplitude, wavelength,
and phase (Davis, 1986; Bracewell, 2000). We then specify a maximum frequency
threshold so that any data of higher frequency (shorter wavelength) than this threshold
value are discarded. This spectral analysis technique provides the opportunity to
control the wavelength content of the dataset and focus on the scale of folding that is
of interest (e.g. Stewart and Wynn, 2000).
147

Curvature calculation
The curvature calculation in this study is derived from concepts and equations of
differential geometry presented in Bergbauer and Pollard (2003). The shape of non-
planar surfaces can be completely described using the First and Second Fundamental
Forms (Struik, 1961). These quantities relate to the arc length in various directions
through a point on a surface and the shape of the surface near that point (Bergbauer
and Pollard, 2003; Pollard and Fletcher, 2005). The ratio of the Second to the First
Fundamental Form, both of which are invariants, defines the shape of the surface, also
referred to as the normal curvature (Struik, 1961). Normal curvature at a point varies
with orientation and the extreme values are termed the principal curvatures, κ1 and κ2.
Respectively, these are the maximum and minimum curvature values and they occur
along orthogonal curves in the surface.
Fracture data collection
Fracture orientation data were collected across each of the selected pavements.
Mode of deformation (opening or shearing), evidence for reactivation, and spacing
also were recorded. Intensity measurements were obtained perpendicular to the strike
of the fracture set under consideration and parallel to bedding. Bed thicknesses were
recorded at each site.
Fracture data analysis
Fisher analysis is used to determine the dispersion in orientation of fractures
within a given set. This method is based on the assumption of circular symmetry
around a point maximum (Fisher, 1953) and has been described by Ramsay (1967),
Cheeney (1983), and Fisher et al. (1987). Each fracture measurement is first converted
into a direction vector (i.e. pole to the plane). The maximum direction, or mean pole,
of the fracture set is calculated as the sum of all direction vectors. The magnitude of
the resultant vector, R, is a measure of the dispersion of the data. In an ideal case,
where all measurements are exactly the same, R is equal to N, the number of
measurements. Increasing discrepancy between R and N indicates increasing
148

dispersion of measurements and greater error in calculating the maximum. The error in
the maximum can be quantified in three additional ways: precision, k, is defined as:
spherical variance, v, is defined as:
and a confidence cone, which can be calculated as :
k = (N-1)/(N-R); (1)
v = (N-R)/N; (2)
cos (αcl) = 1 – (N-R)*(a-1)/R (3)
where cl is the confidence level, a = P 1/(1-N) and P = (1 – cl). Commonly, a 95%
confidence cone is reported, and P for this case is equal to 0.05. A collection of
fracture measurements approaches the ideal cluster where all direction vectors equal
the mean direction vector when R approaches N, k approaches infinity, v approaches
0, and α95 approaches 0°.
Field data
GPS data
Three-dimensional spatial data were collected across six pavements (Fig. 4.3).
These pavements were chosen for their locations on the fold in various structural
positions (backlimb, hinge, forelimb) and for their noticeable shape differences.
Pavement GPS5 is in the backlimb; GPS6 and GPS7 are in the hinge; GPS14, GPS15,
and GPS16 are in the forelimb. Figure 4.3 shows the location of the pavements, the
collected data points, and preliminary meshes through these points that are color coded
for elevation. These help to visualize the dimensions and shape of the pavements. The
forelimb pavements are the most limited in area, due to erosion of the steeply dipping
strata. The smallest pavement characterized is GPS15 which has dimensions of
approximately six meters long by a few meters wide. The largest pavement is GPS6
which has dimensions of approximately 15 meters by 10 meters.
For data collected with the two receiver setup and the moving rover (GPS6 and
GPS7), precision is approximately 10 cm horizontally and 5 cm vertically. Data for
GPS5, GPS14, GPS15, and GPS16 were collected with the laser range finder, which
adds an additional uncertainty on the order of +/- 0.1 m (LaserCraft TM specification
sheet).
149

Elevation (meters)
1274
1272
1270
1268
1266
10
Y (meters)
5
Elevation (meters)
0
1310
1305
1300
1295
10
Y (meters)
5
GPS5
0
GPS6
0
5
10
X (meters)
1272
1271
1270
1269
−4 0 2 4
X (meters)
6 8
1304
1302
1300
1298
Elevation (meters)
15
1320
1315
1310
0
5
Y (meters)
10
Elevation (meters)
GPS7
15
1324
1322
1320
1318
1316
0
20
Y (meters)
GPS14
5
15
10
10
1318
1316
1314
1312
1310
5
X (meters)
0
2
4
6
8
10
1324
12
1322
1320
1318
1316
1314
Figure 4.3. Digital Orthophoto Quarter Quadrangles (DOQQs) of the northwestern
part of Sheep Mountain anticline showing the locations of pavements across which
GPS data were collected and meshes generated from the post-processed data.
Meshes are color coded for elevation and provide information on the aerial extent of
the mapped pavements. DOQQs downloaded from http://wgiac.state.wy.us/.
0
150
X (meters)
Elevation (meters)
1324
1322
1320
1318
0
1
Y (meters)
2
3
4
GPS15
5
6
4
2
X (meters)
Elevation (meters)
1260
1250
1240
0
1 km
1322
1321
1320
1319
1318
1317
0
2
Y (meters)
4
6
GPS16
8
10
12
6
4
X (meters)
2
0
1256
1254
1252
1250
1248
1246
1244

Fracture data
Fracture sets with average strikes of: 020°, 045°, 065°, 080°, 135°, and 170° are
present within the collected data at the surveyed sites. Many of these sets have been
documented in previous Sheep Mountain fracture studies (Bellahsen et al., 2006a,
2006b; Fiore et al., in prep), with their relative times of formation determined based on
abutting relationships in the backlimb. The 045° is the hinge perpendicular set II of
Bellahsen et al (2006a, 2006b), which initiated during early folding in response to fold
perpendicular Laramide contraction. The 135° set is the hinge parallel set III of
Bellahsen et al. (2006a) that could have formed at any time during folding. Fractures
striking 135° are localized in the hinge, but also are found in specific locations in the
backlimb and are hypothesized to be related to areas where layer curvature exists. The
080° set is set V of Fiore et al. (in prep) that formed in response to a rotation in the
local most tensile stress direction due to either a change in the regional contraction
direction or the influence of a secondary fault developing beneath the backlimb and
forming the thumb fold (Fig. 4.1). The 020° fractures comprise a minor set
documented by Bellahsen et al. (2006a). Based on abutting relationships, 020°
fractures are younger than 045° and 080° fractures and older than at least some of the
135° fractures, although most 020° and 135° intersections are cross-cutting. The 170°
fractures were identified by Bellahsen et al. (2006a) as a minor set. Although they are
formed primarily in the forelimb, these 170° fractures also are found at the backlimb
and hinge sites included in this study. Abutting relationships indicate that the 170° set
is younger than the 080° set. Based on their preferential formation in specific
structural locations (forelimb, nose), we suggest that this 170° fracture set is folding
related.
By assuming that fractures striking 045° and 170° are fold related and
determining through the examination of abutting relationships that these two fracture
sets are the oldest and youngest sets present at the surveyed pavements, we have made
the case that all of the fracture sets included in this study formed during folding. The
majority of fracture timing relationships were worked out in the backlimb, where
abutments are consistent. In other structural positions, however, timing relationships
are more uncertain. Opposite abutments exist within the pavements in the hinge and
151

measured
measured
measured
GPS5
N = 94
GPS6
N = 55
GPS7
N = 45
unfolded
unfolded
unfolded
Fracture Sets
020 0
045 0
065 0
080 0
135 0
180 0
bedding
measured
measured
GPS14
N = 75
GPS15
N = 39
GPS16
N = 59
unfolded
unfolded
measured unfolded
Figure 4.4. Fracture orientation data collected at each pavement. Lower hemisphere
stereonets show the orientations of poles to fractures as observed in the field
(measured) and relative to horizontal bedding (unfolded). Specific fracture sets were
defined in the field based on orientation, mode of deformation, and abutting relations.
The average strike direction of each fracture set is listed in the figure legend, next to
the corresponding symbol that has been used to plot the poles for that set. Contours
are plotted at an interval of two and highlight the clustering of poles.
152

forelimb. We suggest that rather than the formation of each fracture set being confined
to specific periods of folding, infilling of previously formed fracture sets (e.g.
Bergbauer and Pollard, 2004) occurred throughout folding in the hinge and forelimb as
a result of anisotropy within the rock generated by the presence of previously formed
fractures.
For this study, the fracture characteristics we focus on are orientation relative to
horizontal bedding and intensity. All of the fracture sets included in this study dip
approximately perpendicular to bedding, suggesting that all fracture sets initiated prior
to significant rotation of forelimb beds. Unfolding observed fracture measurements
clarifies which fracture sets in the steeply dipping forelimb are equivalent to sets
observed in the more shallowly dipping backlimb and hinge. Observing the
orientations of fractures relative to horizontal bedding thus provides the opportunity to
study the differences in characteristics of sets developed in different structural
positions. In the essentially uniformly dipping beds of the forelimb and the backlimb,
the unfolding process does not affect the statistics of the fracture orientations, as all
fractures are rotated the same amount. In the hinge, unfolding the hinge parallel
curvature related fracture set (135°) tightens the clustering. Curvature related fractures
form parallel to the fold hinge and perpendicular to bedding. As mapped in the field,
set 135° fractures thus have a larger dispersion in orientation than as considered
relative to horizontal bedding. We tested the 080° set that formed obliquely to the
hinge at GPS7 and found that the spherical variance of the set as measured in the field
(0.094) is slightly more than as unfolded (0.091). We suggest that this small difference
(0.003) is due to the fact that bedding dip at GPS7 varies by 5° at most. The surveyed
pavements are not expansive enough to generate large bedding dip related apparent
orientation dispersion; the calculated dispersion is mostly (97% in the tested case) real.
Nonetheless, we unfold fracture measurements before performing Fisher analysis.
Stereonets in figure 4.4 show the distribution of poles to fractures for each of the
study sites. The data are presented both as observed and unrotated so that bedding is
horizontal. Symbols represent fractures of specific sets. Contours within the stereonets
indicate where clustering of poles occurs. Rather than being interpreted from
stereonets, distinct fracture sets were noted in the field (Fig. 4.5). Thus, despite a
153

(a) GPS5 (b) GPS6
NW SE
(c) GPS7
N
149 o
(e)GPS15
067 o
052 o
087 o
159 o
140 o
089 o
026 o
072 o
1 m
1 m
10 cm
S
SE
070 o
(d) GPS14
SE
010 o
(f) GPS16
SE NW SE
NW
0.5 m
Figure 4.5. Fracture sets present at pavements: (a) GPS5; (b) GPS6, sets with
average strikes of 040 o and 174 o also are present at this site; (c) GPS7, sets with
average strikes of 023 o and 172 o also are present at this site; (d) GPS14; (e) GPS15,
a minor fracture set striking 180 o also is present at this site; (f) GPS16. Clusters in
figure 4.4 were broken apart based on these field observations. (b) and (c) are cross
sectional views of fractures in relatively flat bedding planes. (a), (d), (e), and (f) are
photographs of bedding surfaces.
154
060 o
127 o
150 o
062 o
179 o
166 o
10 cm
081 o
0.5 m
10 cm
NW
NW

GPS 5
GPS 6
GPS 7
GPS 8
Mean Plane n R v k 95%
026°/87° 7 6.85 0.141 38.86 9.8°
052°/89° 12 11.83 0.076 65.58 22.8°
087°/83° 35 32.56 0.042 13.93 6.7°
140°/83° 10 9.88 0.095 63.15 6.1°
159°/ 83° 19 18.75 0.042 72.87 4.0°
040°/89° 10 7.95 0.117 4.39 26.1°
070°/83° 15 9.05 0.354 2.35 32.5°
150°/84° 10 5.22 0.348 2.11 47.9°
174°/ 84° 10 9.78 0.087 41.02 7.6°
023°/ 79° 8 5.94 0.152 3.40 35.5°
072°/86° 13 10.91 0.091 5.73 19.0°
149°/75° 7 2.96 0.507 1.48 83.4°
172°/83° 8 3.99 0.431 1.74 62.5°
029°/ 81° 10 9.85 0.094 58.71 6.4°
093°/87° 52 47.17 0.075 10.56 6.4°
129°/82° 40 39.34 0.009 59.23 3.0°
178°/86° 38 37.05 0.001 38.75 3.8°
GPS 14
010°/ 88° 14 13.87 0.067 102.2 4.0°
062°/88° 12 11.96 0.087 268.7 2.7°
081°/89° 17 16.82 0.051 89.09 3.8°
166°/87° 29 28.66 0.023 81.45 3.0°
GPS 15
067°/83° 15 17.64 0.038 47.68 5.1°
089°/86° 18 13.63 0.049 35.59 6.8°
GPS 16
060°/87° 41 32.81 0.180 4.89 11.3°
179°/89° 12 11.73 0.066 40.03 6.9°
Table 4.1. Fisher statistics as calculated for each of the fracture sets measured at
individual pavements. The mean fracture plane, number of measurements (n),
magnitude of the resultant vector (R), spherical variance (v), precision (k), and 95%
confidence cone (95%) are tabulated.
155

cluster on a stereonet with one maximum that seems to represent a single fracture set,
in some cases two sets within the cluster have been recorded (e.g. sets 140° and 159°
at GPS5, Fig. 4.4a, Fig. 4.5a).
Results of a Fisher analysis for each of the fracture sets are listed in Table 4.1.
We consider values of spherical variance to compare the dispersion of specific sets in
different structural locations. The 020° set exists at one site in each position: GPS5 in
the backlimb, GPS7 in the hinge, and GPS14 in the forelimb. Spherical variance is
lowest at GPS14 and highest at GPS7. The 045° set has a lower spherical variance at
GPS5 in the backlimb than at GPS6 in the hinge. The 080° set has comparable
spherical variance values at backlimb and forelimb sites GPS5, GPS14, and GPS15; it
has higher values at hinge sites GPS6 and GPS7. Although no fractures of the set with
an average strike of 135° have been recorded in forelimb sites, the spherical variance
of this set at backlimb site GPS5 is much less than that at either hinge site. The
spherical variance for the 170° set at GPS5 is intermediate to the values at forelimb
sites GPS14 and GPS16. All three of these values are less than the spherical variance
of the 170° set at hinge sites GPS6 and GPS7.
Fracture intensities for the six distinct fracture sets are represented by bar graphs
in figure 4.6. Average thickness of the bedding at each pavement is also documented
in figure 4.6. We do not normalize the intensities to bed thickness because all
thicknesses are similar. Values plotted are normalized to ten meters so that we may
compare measurements made at all locations. Highest intensities occur in the
Phosphoria pavements that are in the hinge: GPS6 and GPS7. Lowest intensities occur
in the backlimb Phosphoria pavement GPS5. Forelimb intensities are intermediary.
Intensity of the fracture set with an average strike of 080° is approximately
consistent between the hinge and the forelimb, with values at GPS6 and GPS15
similar and values at GPS7 and GPS14 similar. The intensity of the same 080° set at
site GPS5 in the backlimb is much lower. In the backlimb at GPS5 and the forelimb at
GPS16, the intensities of the 135° set are similar. The 135° set is more intense at both
hinge locations. Where the 170° set exists in the hinge at GPS7, it is three times more
intense than at GPS14. The other two forelimb sites and the backlimb site GPS5 have
intensities of the 170° set that are less than that at GPS14. In the backlimb, no fracture
156

N / 10 m
20
0
GPS5
t = 0.35 m
159° 140° 087° 052° 026°
N / 10 m
100
80
60
40
20
0
GPS6
t = 0.40 m
150°
070°
N / 10 m
100
80
60
40
20
0
GPS7
t = 0.40 m
172° 149° 072°
N / 10 m
100
80
60
40
20
0
GPS14
t = 0.30 m
166° 081° 062° 010°
GPS15
t = 0.45 m
100
N / 10 m
80
60
40
20
0
River cut
067° 089°
N / 10 m
020 0 080 0
045 0
065 0
60
40
20
0
GPS16
t = 0.40 m
179° 127° 060°
Figure 4.6. Three-dimensional sketch of Sheep Mountain with bar graphs showing
fracture intensities of the major fracture sets at each study site. Intensities have been
normalized to show the number of fractures per ten meters. To facilitate comparison
of fracture intensities among sites, symbols are plotted beneath the bar graph to
indicate which sets have been determined to be equivalent (based on orientation,
mode of deformation, abutting relations) at different sites. An average bed thickness
for each pavement is reported.
157
135 0
180 0

set has an intensity more than two fractures per meter. In the hinge, all fracture sets
have intensities greater than six fractures per meter. In the forelimb, the intensity of
fracturing varies from set to set, and even within the same set. The 065° set, for
instance, varies from less than one fracture per meter at GPS14 to approximately two
fractures per meter at GPS 15 to approximately six fractures per meter at GPS16. At
each of the three forelimb sites, a different fracture set is dominant.
Curvature analysis
We begin the curvature analysis by removing an average plane through the data.
This process effectively removes the dip of the dataset, allowing one to better compare
the relative elevations of the collected data points (Fig. 4.7). The relative elevations
color coded in figures 4.7a, 4.7d, 4.7e, and 4.7f are very noisy, indicating that there are
no consistent elevation trends within the data. Conversely, red swaths present in
figures 4.7b and 4.7c represent maxima and suggests the presence of anticlinal
curvatures. Application of curvature analysis to the datasets in their current state
would highlight the small scale undulations visible in figure 4.7. These undulations are
most likely a result of slight spatial differences in erosion or the error included in the
data collection method and do not reflect the natural shape of the bedding surface. To
remove these artifacts from the datasets and thus capture folding on the appropriate
scale, we followed the spectral analysis technique of Bergbauer and Pollard (2003).
Application of a smoothing factor that removes oscillations of wavelength 13 meters
and below discards the high frequency content of the datasets. The smoothed surfaces
are shown in figure 4.8. The lack of contours in figures 4.8a, 4.8d, 4.8e, and 4.8f
indicates that the surface elevations vary by less than 0.1 meters and are thus
approximately planar.
The maximum and minimum principal curvatures, κ and κ2, were calculated for
the area surrounding each grid node of the smoothed surfaces. The extreme values of
κ and κ2 for each surface are listed in table 4.2, which indicates that GPS5, GPS14,
GPS15, and GPS16 have very small curvatures, with extreme values ranging from
0.00034 m -1 to 0.001 m -1 . The spectral analysis filtering algorithm removed all of the
noise from the original surfaces (Fig. 4.7), producing smoothed surfaces (Fig. 4.8)
158

κ1
κ2
GPS5 0.0086 -0.0082
GPS6 0.0399 -0.0442
GPS7 0.0466 -0.0340
GPS8 0.0376 -0.0344
GPS14 0.0010 -0.0010
GPS15 0.00041 -0.00034
GPS16 0.0034 -0.0038
Table 4.2. Extreme values of the maximum principal normal curvature (κ1) and
minimum principal normal curvature (κ2) calculated across each pavement.
159

meters
meters
meters
meters
meters
(a) GPS5 (b) GPS6
5
4
3
2
1
0
0 2 4 6 8 10
meters
(c) GPS7
6
5
4
3
2
1
0
0 5 10
meters
15 20
(d) GPS14
1.5
1
0.5
0
0
(e) GPS15
2.5
2
1.5
1
0.5
12
25
relative elevation (m)
0.8
0.4
0
−0.4
−0.8
relative elevation (m)
meters
14
12
10
8
6
4
2
0
0 2 4 6 8
meters
1 2 3 4 5 6 7 8 9 10 11
meters
0
0 1 2 3 4 5
meters
(f) GPS16
4
3
2
1
0
0 2 4 6
meters
8 10
6
0.4
0.2
0
−0.2
−0.4
−0.6
Figure 4.7. Relative elevations across surfaces constructed from unfiltered GPS data
at pavements (a) GPS5; (b) GPS6; (c) GPS7; (d) GPS14; (e) GPS15; (f) GPS16.
relative
elevation (m)
0.2
0.1
0
-0.1
-0.2
160
12
0.6
0.4
0.2
0
-0.2
-0.4
relative
elevation (m)
0. 5
0
−0. 5
relative
elevation (m)
10
0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
relative elevation (m)

meters
meters
meters
meters
meters
(a) GPS5 (b) GPS6
5
4
3
2
1
0
0 2 4 6 8 10
meters
(c) GPS7
6
5
4
3
2
1
0
0 5 10
meters
15 20
(d) GPS14
1.5
1
0.5
0
0
(e) GPS15
2.5
2
1.5
1
0.5
12
meters
0
0 2 4 6 8
meters
1 2 3 4 5 6 7 8 9 10 11
meters
0
0 1 2 3 4 5
meters
(f) GPS16
4
3
2
1
0
0 2 4 6
meters
8 10
6
Relative Elevation (m)
−1 −0. 5 0 0. 5 1
Figure 4.8. Smoothed relative elevations across surfaces constructed from filtered
GPS data collected at pavements (a) GPS5; (b) GPS6; (c) GPS7; (d) GPS14; (e)
GPS15; (f) GPS16. Contour interval is 0.1.
161
25
14
12
10
8
6
4
2
12
10

meters
meters
meters
(a) GPS6 - κ 1
14
12
10
8
6
4
2
0
0 2 4 6 8
meters
(c) GPS7 - κ 1
6
5
4
3
2
1
10
meters
(b) GPS6 - κ 2
14
12
10
8
6
4
2
Curvature (m -1 )
0
0 2 4 6 8
meters
0
0 5 10 15 20
meters
(d) GPS7 - κ 2
6
5
4
3
2
1
0
0 5 10
meters
15 20
−0.02 −0.01 0 0.01 0.02 0.03 0.04
Figure 4.9. Plots of maximum (κ1) and minimum (κ2) normal curvature values across
surfaces for which magnitudes are greater than a threshold value of 0.005 m-1. The
corresponding directions of κ1 and κ2 are represented by black tick marks. (a) κ1
values and directions across GPS6; (b) κ2 values and directions across GPS6; (c) κ1
values and directions across GPS7; (d) κ2 values and directions across GPS7.
162
25
25
10

with curvatures that are negligible, of magnitude less than the value of 0.005 m that
we designate as the curvature threshold. When we apply the threshold value, GPS6
and GPS7 are the only two pavements that have significant curvatures. The values and
directions of κ and κ across these surfaces are plotted in figure 4.9 with a normalized
colorbar so that magnitudes of curvature can be compared between the datasets.
Discussion
2
Curvature analyses
In the maximum and minimum principal curvature plots (Fig. 4.9), warm colors
represent anticlinal folding and cool colors represent synclinal folding. GPS6 and
GPS7 are very near to the hingeline of the fold (Fig. 4.4). To the naked eye, these
surfaces appear to have distinct curvatures (Fig. 4.10a). Analysis confirms the
existence of this curvature (Fig. 4.9). As expected, GPS7, which is closer to the
hingeline, has higher magnitudes of curvature than GPS6. The curvature analysis for
GPS6 highlights that the surface has two directions of curvature, one parallel to the
hinge of the fold and one perpendicular to the hinge of the fold. This phenomenon is
noticeable in field photos as well (Fig. 4.10a). GPS6 is located in the nose of the fold,
where bedding strike rotates, and so the existence of a hinge parallel component of
curvature at this location is not surprising. Localized flexures of bedding surfaces also
are found in the nose. The curvature analysis for GPS7 reflects one instance of this
localized flexure. In figure 4.9c, the left edge of the data set represents the area closest
to the hinge. A traverse from left to right across this plot approximates the dip
azimuth. In the curvature plot, the existence of anticlinal curvature across the majority
of the pavement is apparent, but an area of synclinal curvature exists at extreme down
dip locations. This synclinal curvature also is noticeable in field photos (Fig. 4.10b).
Relating curvature analysis to fracture measurements
The most noticeable correlation between curvature and fracturing relates to
fracture orientation. In figure 4.12, we plot spherical variance for the fracture sets
mapped in this study. Large spherical variances occur only at sites GPS6 and GPS7,
the two pavements of notable curvature. Thus, in pavements that have higher
163
-1

(a)
(b)
synclinal area
anticlinal area
hinge
parallel
folding
hinge perpendicular
folding
Figure 4.10. Photographs of the pavements at (a) GPS6 and (b) GPS7. The black
line outlines the approximate area of surveying. In (a), two directions of curvature are
apparent, one parallel to the hinge and one perpendicular to the hinge. In (b), both
anticlinal and synclinal curvature are apparent in a direction parallel to the hinge. In
the photo, shading highlights the faces of fractures striking ~080 o .
164
1 m
1 m

Spherical Variance
0.5 020 o set
0.25
0
0.5 045 o set
0.25
0
0.5 065 o set
0.25
0
0.5 080 o set
0.25
0
0.5 135 o set
0.25
0
0.5 170 o set
0.25
0
GPS15 GPS14 GPS16 GPS5 GPS6 GPS7
Figure 4.11. Spherical variance for the fracture sets mapped at study sites.
Pavements are plotted on the x-axis in the order of increasing curvature magnitudes.
165

curvature values, the clustering of distinct fracture sets is less pronounced than in
pavements of lower curvature values.
We look at minimum normal curvature (κ2) trajectories to determine if fracturing
was enhanced by folding in the direction perpendicular to the maximum curvature. At
pavement GPS6, κ1 is parallel to the hinge. Thus, curvature related fractures would be
expected to form in the dip direction (Fig. 4.9b), which ranges from 065 o to 080 o . Both
the intensity (Fig. 4.6) and the spherical variance (Table 4.1) of the fracture set of
average strike 070 o are large. We pointed out previously, however, that two directions
of curvature are present at this pavement (Fig. 4.10a). Fracturing may thus be expected
in the direction perpendicular to this set, formed at a strike of ~ 160 o . The spherical
variance and intensities of a set striking 150 o at GPS6 are also large. At GPS7, κ2 is
parallel to the hinge (Fig. 4.9d). GPS7 is at a location in the hinge where the plunging
northwestern nose controls the local strike direction, which varies between 077 o and
100 o . Curvature related fractures would thus be expected to form parallel to this
direction. Although the spherical variance and intensity of the 072 o set is great
compared to sets at pavements GPS5, GPS14, GPS15, and GPS16, the values of
spherical variance for the 149 o and 172 o sets at GPS7 are greater. The intensity of the
149 o set is slightly less than that of the 072 o set and the 172 o set is much more intense.
Fracture statistics at GPS6 and GPS7 suggest that, if fracturing in the hinge is due
primarily to curvature, sets in addition to the fracture set that forms in the minimum
curvature direction due to outer arc extension of a flexed bedding surface
(Timoshenko, 1934) are affected by folding.
Fracture intensities may correlate loosely with curvature. The highest intensity of
fracturing and the highest values of curvature are found at GPS6 and GPS7 from the
hinge (Fig. 4.6). Lowest intensities are found at GPS5 in the backlimb. Where the
lowest curvature magnitudes exist at GPS14, GPS15, and GPS16, however, high
intensity of fracturing has been recorded. Fracturing in the forelimb is not related to
present day curvature. It is most likely not related to paleo-curvatures (i.e. migration
of forelimb beds through the hinge) either, as characteristics of fracturing in the hinge
and forelimb are very different. Spherical divergences of all fracture sets in the
forelimb are small (Table 4.1), and the hinge parallel fracture set striking 135 o is
166

sparse; whereas in the hinge, large spherical divergences are found and the 135 o
fracture set is intensely formed. We believe the fractures in the forelimb formed due to
some mechanism other than bedding flexure. Noting that the fracture sets developed in
the forelimb, as well as the most intensely formed set, vary from site to site, we
suggest that fracturing has been affected by some local mechanism of deformation.
The correlation between curvature and intensity of fracturing is not necessarily direct.
Conclusions
GPS collection and post-processing methods have allowed us to acquire very
precise three-dimensional surface data of pavements within the Phosphoria Formation
at Sheep Mountain. Curvature analyses of, and fracture measurements across, these
surfaces indicate that greater curvature correlates with greater variance in fracture
orientation. Greater fracture intensities may loosely correlate with curvature, however
structural position of the fold must be taken into account.
Acknowledgements
This project is funded by the Stanford Rock Fracture Project and the National
Science Foundation Collaboration in Mathematical Geosciences Program Grant No.
EAR-04177521. We thank Ashley Griffith, Ole Kaven, Ian Mynatt, and Chris Wilson
for help in collecting field data. Trevor Hebert from Jasper Ridge Biological Preserve
provided crucial GPS support.
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170

Appendix 1
Tectonic Shortening Style in the Southern San Joaquin Valley,
Revisited
Abstract
Pure shear and simple shear kinematic analyses are used to determine and assess
the geological and geophysical implications of a suggested 32° − 48° Quaternary
(since 0.78 Ma) rotation of the Elk Hills anticline within a zone that is 40 km wide and
bounded to the west by the San Andreas Fault. Pure shear analysis reveals that a 32°
rotation of the Elk Hills anticline would have involved a 45% fault perpendicular
shortening of the shear zone. Simple shear analysis reveals that the Elk Hills anticline
would have evolved from a domal structure. No geological evidence in support of
either of these phenomena exists at Elk Hills. Further calculations indicate that the
suggested magnitude of rotation within a simple shear zone would account for 6.2
cm/yr of relative plate motion between the Pacific and North American plates. When
this value is added to the measured long term San Andreas slip rate, a relative plate
motion is calculated that is, at a minimum, 70% more than the value derived from
Euler pole angular velocities. In light of these inconsistencies, we find the suggested
rotation of Elk Hills is unlikely.
Mechanical models consider the end member cases of thrusting and strike-slip
related wrenching for the development of the Elk Hills anticline. Model results
highlight the inconsistency between suggested wrench evolution of Elk Hills and
existing geological evidence. Forward elastic models driven by strike-slip along the
San Andreas Fault alone cannot reproduce the vertical displacements mapped within
seismic data and visualized within structure contour maps. Additional consideration of
the shapes of the faults imaged within the seismic reflection volume at Elk Hills
indicates that the shortening within the southwestern San Joaquin Valley has been
more consistent with thrust rather than wrench tectonics during the growth of the
anticline.
171

Introduction
Literature published over the latter half of the past century chronicles the debate
over the mechanism by which folds lining the western side of the southern San
Joaquin Valley (Fig. A1.1) have developed. At the introduction of wrench tectonics in
1956, the southwestern San Joaquin Valley was noted as a location in which the
average orientation of anticlines is compatible with one of several orientations at
which wrench related anticlines were hypothesized to develop (Moody and Hill,
1956). This wrench faulting mechanism of formation for the San Joaquin Valley
anticlines gained momentum in the 1970s (Wilcox et al., 1973; Harding, 1974, 1976).
Seismic activity in the following decade at New Idria in 1982 (M=5.5), Coalinga in
1983 (M=6.5) and Kettleman Hills North Dome in 1985 (M=6.1), led to the revelation
that present day slip occurs on thrust faults that strike subparallel to the San Andreas
Fault (Wentworth et al., 1984; Namson and Davis, 1988); and to the reclassification of
these structures as thrust related (Mount and Suppe, 1987; Zoback et al., 1987). A later
study focused on Elk Hills attempted to reconcile the previous wrench and thrust
interpretations for the San Joaquin Valley anticlines, suggesting that anticlines farther
from the San Andreas Fault, such as Coalinga, Kettleman Hills, and Lost Hills
deformed according to thrust tectonics, while those closer to the San Andreas Fault,
such as Elk Hills deformed according to wrench tectonics (Nicholson, 1990). This
structural study adopted the positive flower structure model described by Lowell
(1972; Fig. A1.2) to explain the existence of two echelon anticlines at Elk Hills. Five
years later, a study investigating the structure, stratigraphy, and tectonics of the Great
Valley based on well log correlations and gravity anomalies provided further support
for the thrust formation interpretation for the anticlines in the San Joaquin Valley
including Elk Hills (Imperato, 1995). Additional investigation of the structures
including analysis of paleomagnetic data (White, 1987) led to the suggestion that the
opposing theories of wrench and thrust deformation may be compatible within the San
Joaquin Valley if viewed as temporally distinct processes (Miller, 1998). The
proposition resulting from this investigation was that the folds within the southwestern
San Joaquin Valley formed initially with trends oblique to the San Andreas Fault and
subsequently were rotated to their subparallel orientations, with deformation style
172

36 0 00’
Diablo Range
New Idria
Coalinga
Coalinga
120 0 00’
San Andreas Fault
N
Kettleman Hills
Temblor Range
0 mile 20
0 km 30
120 0 00’
San Joaquin
Valley
Lost Hills
Elk Hills
Buena Vista
119 0 00’
Taft
Midway Sunset
Sierra Nevada Range
Bakersfield
San Emigdio Mtns
119 0 00’
Figure A1.1. Location of the Elk Hills, Lost Hills, Kettleman Dome, Coalinga, and
New Idria anticlines within the southwestern San Joaquin Valley.
173
36 0 00’
35 0 00’

29R
NWS
31S
Figure A1.2. Schematic model of a compressional flower structure applied to Elk
Hills. Anticlines 29R, 31S, and the Northwest Stevens (NWS) are labeled in red.
Modified from Lowell (1972) according to the explanation of Nicholson (1990).
174

transitioning from wrench-related shearing to fault-perpendicular shortening (Miller,
1998).
This hypothesis introduced by Miller (1998) resulted from an attempt to
reconcile: (1) the obliquity of San Joaquin Valley anticlines to the San Andreas Fault
and their en echelon formation; (2) the existence of paleomagnetic data from the
flanks of anticlines in the San Joaquin Valley (White, 1987) and unpublished isochore
maps over Lost Hills (Julander, 1992), both of which suggest a clockwise rotation of
the structures; and (3) recent earthquakes suggesting present day slip in a direction
perpendicular to the San Andreas Fault (Eaton et al., 1983; Wentworth et al., 1984;
Namson and Davis, 1988; Ekstrom et al., 1992). Although the paleomagnetic data
appear to be robust (McWilliams, 2004, pers. comm.), we are cautious in accepting
these data. For non-cylindrical folds such as Elk Hills, apparent rotations are often
introduced into paleomagnetic data because a simple bedding correction does not
correctly restore the geometry (Stewart, 1995; Pueyo et al., 2003). We look to shearing
calculations to determine if the suggested magnitude of rotation is consistent with
existing geological and geophysical data for the San Joaquin Valley.
In this paper, we first review White’s study (1987), describing the existing Elk
Hills paleomagnetic data. We then introduce Miller’s shear zone hypothesis (1998) in
further detail. Using kinematic equations, we quantify the amount of deformation
accompanying the suggested 32° of rotation at Elk Hills through both pure and simple
shearing. Finally, we discuss the implications of the calculated shearing related
deformation, and we assess the likelihood of the faults and folds at Elk Hills initiating
within a wrench tectonic environment in the absence of a rotation.
Previous Work
White gathered twenty one samples from surface outcrops of the Pleistocene
Tulare formation (3.4 Ma) on the northern flank of the 31S anticline at Elk Hills and
analyzed them for remanent magnetism. The resulting data indicated that a secondary
normal magnetic field overprinted a primary reversed magnetic field. Based on the
magnetic reversal chart (Harland et al., 1990), this secondary normal remanence was
inferred to have been acquired during the Bruhnes chron, (0.78 Ma to the present). The
orientation of the secondary remanent field was expected to mimic the orientation of
175

the present axial dipole field (PADF). The mean inclination of the Elk Hills samples
was measured at 52.3°, only a few degrees from the PADF inclination of 55°. The
mean declination of the Elk Hills samples was measured at 48° +/− 11°, far from the
PADF declination of 0°. Due to this disparity, White (1987) suggested that a
clockwise rotation of 48° of the Elk Hills anticline occurred sometime after the
secondary remanent field was locked in. If the secondary field had been acquired more
recently, during the present-day field that has a declination of 16°, then the rotation of
Elk Hills would have been only 32°. This study, later cited as evidence for the
shearing related rotation of anticlines along the western margin of the southern San
Joaquin Valley (Miller, 1998), indicates that sometime over the past 0.78 Ma, Elk
Hills has rotated at least 32° clockwise.
Although Miller (1998) developed his rotation hypothesis based on
paleomagnetic data and other geological and geophysical data collected at the
Kettleman Hills and Lost Hills anticlines that are northwest of Elk Hills, he
acknowledges that a clockwise rotation of 35° at Elk Hills (based on the findings of
White, 1987) is also consistent with his hypothesis. Miller (1998) suggests that the
anticlines of the southwestern San Joaquin Valley have rotated within a broad shear
zone that is bounded to the west by the San Andreas Fault. The rotation of the
anticlines was driven by early right-lateral simple shearing and later shortening
perpendicular to the shear zone, which is characterized as pure shear. Miller states that
the relative importance of simple shear versus pure shear cannot be defined due to the
lack of quantification of extension parallel to the fold hinges along the shear zone. He
acknowledges that if the suggested rotations were produced by simple shear alone, the
associated hinge parallel extension would far exceed that inferred from the folds
themselves, and concludes that pure shear is likely the dominant mechanism for
rotation. Application of Miller’s hypothesis to Elk Hills would suggest that the
anticline has undergone 32° - 48° of clockwise rotation from an initial orientation of
(at least) 62° to the San Andreas Fault.
176

Shearing Calculations
The application of either a pure shear or simple shear model to a crustal scale
zone at shallow depths requires idealizations that may not be justified. These
kinematic models are used to describe the distributed deformation of ductile materials
that flow in response to deviatoric stress (Ramsay and Graham, 1970; Ramsay, 1980;
Robin and Cruden, 1994; Treagus and Lan, 2003). Seismic data (e.g. Medwedeff and
Suppe, 1986; Namson and Davis, 1988; Bloch et al., 1993; Guzofski and Shaw, 2004)
and field studies carried out both east of the San Andreas Fault (e.g. Dholakia et al.,
1998; Woodring et al., 1940) and along the coast of California (e.g. Belfield et al.,
1983; Hickman and Dunham, 1992; Gross, 1993) portray a shallow crust that is
riddled with faults and fractures, characteristic of a brittle response to the applied
stress. Additionally, strength of the crust versus depth plots indicate that the brittle-
ductile transition is at approximately 12 km depth (Sibson, 1983). For reference, the
deepest unit considered in the present study is at an average depth of 4 km, above
which ductile flow would not be expected. A second questionable idealization is that
the deformation within the broad shear zone is homogeneous. The presence of the
prominent folds themselves within the zone east of the San Andreas Fault
demonstrates that the deformation is heterogeneous. This has been pointed out and
modeled for other transpressional regimes throughout the world (e.g. Robin and
Cruden, 1994). Plate boundaries, such as the San Andreas Fault in California, the Najd
Fault System in Saudi Arabia, and the North Anatolian Fault in Turkey, are systems of
subparallel vertical strike-slip faults formed in response to shearing motion of one
plate with respect to the other. Neither existing seismic data nor digital elevation maps
indicate the presence of large scale vertical strike-slip faults in the zone containing Elk
Hills, Lost Hills, Kettleman Hills, Coalinga, and New Idria.
Acknowledging the oversimplifications of the combined pure shear and simple
shear model presented by Miller (1998), we evaluate this model using data from Elk
Hills. We consider the present day geometry of Elk Hills and work backwards in time,
calculating how many degrees of clockwise rotation may have occurred over the past
0.78 Ma through pure shear alone. We then attribute the remaining rotation to simple
shearing and assess the amount of hinge parallel elongation and hinge perpendicular
177

shortening. We also consider the implications that this amount of rotation has for the
relative plate motion of the North American plate with respect to the Pacific plate. The
western extent of the proposed shear zone is taken as the San Andreas Fault (Miller,
1998), and the eastern extent is postulated to lie just beyond the northeastern flanks of
the New Idria, Coalinga, Kettleman Hills, Lost Hills, and Elk Hills anticlines. The
minimum width of a zone that just encompasses these structures is 40 km.
Pure Shear
Bloch et al. (1993) have estimated a 16% contraction in the western San Joaquin
Valley in an orientation perpendicular to the San Andreas Fault since 2.5 Ma.
Assuming a constant strain rate, this indicates that a shortening perpendicular to the
zone of approximately 5% has occurred over the past 0.78 Ma. We take this as a
maximum value of shortening, as Miller suggests that a period of simple shear
occurred, initiating the rotation of the anticlines, prior to the current regime of pure
shear. We consider two-dimensional pure shear (Ramsay, 1967) in the horizontal
plane (no extension in the vertical direction) to determine the amount of rotation of a
material line that is presently oriented at 30° to the San Andreas Fault, the orientation
of the hinge of the Elk Hills anticline. For a 5% shortening across the zone, we have
the squares of principal stretches λ 1 = 0.908 and λ 2 = 1.103. The angle of rotation
(θrot) is found from (Ramsay 1967, p.67):
⎛ λ ⎞
2
1
tanθ i tanθ
f
λ ⎟
2
⎟ =
⎜
⎝
Using a θf of 60° and a θi of 57.5°, we calculate a θrot of 2.5°. Given the estimate of
shortening across the zone, less than 10% of the rotation can be accounted for by pure
shear: a shortening of 45% would be necessary to rotate Elk Hills 32°. This shortening
would reduce the width of the zone from 73 km initially to 40 km post rotation.
Simple Shear
We calculate the simple shear strain, principal stretches, and orientations of the
principal stretches for a rotation of both 32° and 48° to assess the range of rotation
178
⎠
1
() 1

suggested by White (1987). The value of the homogeneous simple shear strain (γ)
involved in the rotation can be calculated by exploiting the relationship (Ramsay 1967,
p.88) between the initial angle (α = 62° to 78°) and the final angle (α’ = 30°) that the
Elk Hills anticline makes with the San Andreas Fault:
γ = cot α’ – cot α (2)
For a 32° rotation, we calculate a simple shear strain value of 1.20. For a 48° rotation,
this value is 1.52. With these estimates of shear strain, the magnitudes of the squares
of the principal stretches of the strain ellipses for the two end member cases are 3.12
(λ1) and 0.32 (λ2) for the low end and 4.04 (λ1) and 0.25 (λ2) for the high end, as given
by (Ramsay 1967, p.85):
2 ( γ + 4)
1 2
2
γ + 2 ± γ
λ 1 , λ2
=
(3)
2
The range of maximum principal stretches (Smax) is thus 1.77 – 2.02. The orientation
of the line of maximum stretch for each of the end member cases is (Ramsay, 1967):
−1
⎛ γ ⎞
θ = tan ⎜
⎟
⎜
⎟
(4)
2
⎝ 1+
γ − 1 λ1
⎠
For a 32° rotation, we calculate an orientation of 29.5°, for a 48° rotation, an
orientation of 26.4°.
The respective elongation and shortening of material lines parallel to and
perpendicular to the fold hinge may be deduced from the value of shearing. For
example, a material line originally oriented at 62° is elongated by a factor of 1.77
when rotated to 30° with a value of γ = 1.20, and a material line oriented at 152° is
shortened by a factor of 0.57. The entire Elk Hills field today has a dimension of 25
km in the hinge parallel direction and 8 km in the hinge perpendicular direction. The
values of lengthening and shortening indicate that the pre-rotational structure would
have ranged from 14 km long by 14 km wide to 14 km long by 16 km wide,
approximating a domal shape.
Implication of Shearing-Related Rotation on Relative Plate Velocities
We calculate the relative motion between the North American and Pacific plates
associated with the proposed shearing from the following calculation incorporating the
179

shear zone width (w), the value of the homogeneous simple shear strain (γ), and the
time period of interest (t) (Ramsay, 1967):
w⋅
γ
slip rate = (5)
t
Using a shear zone width of 40 km, and the suggested time period of rotation, 0.78
Ma, we calculate a velocity ranging from 6.2 cm/yr to 7.8 cm/yr. The current long
term slip rate on the San Andreas Fault in this area is approximately 2.3 cm/yr (Toda
and Stein, 2002). Adding these estimates, we have a relative plate velocity ranging
from 8.5 cm/yr to 10.1 cm/yr for the range of rotations suggested by White (1987).
Discussion
Analysis of shearing calculations
The two-dimensional pure shear analysis of the zone east of the San Andreas
Fault is an approximation at best, as there was vertical motion as evidenced by the
anticlines. For homogeneous three-dimensional pure shear, uplift would be uniform
across the zone and would not alter the orientation of material lines in the horizontal
plane. Because volume is conserved, vertical extension would decrease the magnitude
of the horizontal extension calculated for the two-dimensional plane strain case so the
rotation would be less than that calculated above. The existence of the anticlines
indicates that the uplift was not uniform. Structure contour maps of horizons of mid
Miocene (10 Ma) age at Elk Hills and younger indicate that the maximum uplift since
this time is about 2 km (Fig. A1.3a). For a constant deformation rate, we calculate an
uplift of 0.16 km over the past 0.78 Ma. This value is 8% of the horizontal
displacement, and is a maximum value of uplift because we took a constant vertical
uplift rate yet most deformation occurred from mid Miocene through early Pliocene
time (Chapter 1; Imperato, 1995). We conclude that the rotation of Elk Hills due
Figure A1.3 (opposite page). (a) Structure contour map of a Middle Miocene (top
McDonald) stratigraphic unit. (b) A cross section through the western part of the field
running along the line A to A’ in (a). (c) A cross section through the eastern part of the
field running along the line B to B’ in (a). Anticlinal crests, faults, and marker horizons
are labeled.
180

(b)
1
2
3
4
5
depth (km) 0
6
7
8
(a)
35 0 16’00” 35 0 20’00”
N
0mile1 0 km 2
0 mile 1
0 km 2
(c)
2R
29R anticline
A
NWS anticline
5R
A’
3R
31S anticline
1R
C.I. = 152 m (500 ft)
B’
B
7
6R
depth (m)
SW NE
1
2
3
4
5
depth (km) 0
6
7
8
119 0 32’00”
119 0 32’00”
0 mile 1
0 km 2
1R
29R
anticline
5R
6R
119 0 26’00”
119 0 26’00”
A A’
31S
anticline
3R
7
31S
anticline
2R
NWS
anticline
B B’
S N
181
119 0 20’00”
119 0 20’00”
35 0 20’00”
4877
4267
3658
3048
2438
1829
NE
MYA4-A
WILHELM
CALITROLEUM
BASE REEF RIDGE
MYA4-A
WILHELM
CALITROLEUM
BASEREEFRIDGE
McDONALD
McDONALD

to pure shearing deformation was negligible and disregard it. If the shear zone
hypothesis is correct, then the majority of the rotation at Elk Hills must be attributed to
simple shear.
If the simple shear kinematic model is a valid analog for the structural history of
Elk Hills, we would expect to see some signature of stretching (e.g. normal faults
perpendicular to the hinge) and shortening (thrust faults parallel to the hinge). Hinge
perpendicular normal faults can be seen in the seismic data, but they terminate at depth
within a shale unit that separates the Miocene and older sediments from the Pliocene
and younger sediments (Maher et al., 1975; unpublished seismic data, Occidental Oil
and Gas). Because Miocene units are involved in the folding at Elk Hills, we would
expect to see extension accommodated by normal faulting of these layers. Similarly,
thrust faults parallel to the fold hinge are evident within the seismic data. However,
sedimentary signatures within the seismic data show that the majority of uplift related
thrusting occurred prior to Pleistocene time and therefore is not consistent with the
rotation and shortening occurring in the last 0.78 my. Furthermore, mechanical models
show that to generate a thrust fault related anticline with equal axes, the down dip fault
dimension must be approximately twice the along strike dimension (Savage and
Cooke, 2004). In the literature, field and subsurface studies documenting faults with a
greater down dip dimension are noticeably lacking (e.g. Schultz and Fossen, 2002;
Maerten et al., 2002; Billi et al., 2003).
Next, we assess the shearing related rotation hypothesis by comparing the
relative plate velocities calculated above with those derived from published values of
Euler pole angular velocities (DeMets et al., 1990). Following the method presented
by Fowler (1990), the present day relative velocity between the North American and
Pacific plates is approximately 5 cm/yr in an orientation of 139°, only a few degrees
from the orientation of the San Andreas Fault, near Elk Hills. This is a high value, as
recent geodetic results indicate that the Coast Ranges and the San Andreas Fault
accommodate 39 ± 2 mm/yr of relative plate motion, primarily by strike-slip faulting
(Argus and Gordon, 2001). Still, the estimated values of 8.5 cm/yr to 10.1 cm/yr are
70% and 100% more than this maximum relative plate motion. The 2.7 cm/yr
discrepancy between the relative plate motion and the long term slip rate of 2.3 cm/yr
182

(a)
35 0 16’00” 35 0 20’00”
(b)
35 0 16’00” 35 0 20’00”
N
0mile 1
0 km 2
N
0mile 1
0 km 2
119 0 32’00”
2R
2R
119 0 32’00”
5R
5R
3R
1R
119 0 26’00”
3R
1R
119 0 26’00”
C.I. = 76 m (250 ft)
7
6R
C.I. = 15 m (50 ft)
7
119 0 20’00”
6R
119 0 20’00”
35 0 20’00”
thickness
(m)
35 0 20’00”
1524
1219
914
610
305
thickness
(m)
Figure A1.4. Isochore maps of the intervals (a) McDonald to Base Reef Ridge and
(b) Wilhelm to Mya 4-A, as interpreted within a three-dimensional volume of seismic
reflection data. Fault traces are plotted and labeled with solid lines representing
active faults, dashed lines representing faults along which activity has ceased, and
dotted lines representing faults that have not yet begun to slip during the deposition of
the contoured interval.
183
366
305
244
183
122

(Toda, 2002) must be accounted for by deformation near the plate boundaries. If we
attribute all of this deformation to the shear zone, by using equation (5) followed by
equation (2), we back calculate a rotation of 9.7° over the past 0.78 Ma. The non San
Andreas Fault related relative plate motion is not enough to account for the suggested
rotation, thus rendering the proposed Pleistocene through Holocene rotation suggested
for the Elk Hills anticline unlikely.
Variation in isochore trends at Elk Hills
We posit that the change in orientation of stratigraphic thinning at Elk Hills that
is apparent in isochore maps can be explained based on changes in the activity of
faults that have been interpreted from seismic reflection data. In figure A1.4, we
present an isochore map for the oldest (Fig. A1.4a) and youngest (Fig. A1.4b)
stratigraphic intervals included in the Elk Hills study (Chapter 1). For the older
interval, the activity of the 7 fault has a distinct east-west trending influence on the
isochore map in the eastern part of the field (Fig. A1.4a). At the time of deposition of
the younger interval, activity along the 7 fault had ceased, and the east-west trend
became diffuse, giving way to the more northwest-southeast directed trend (Fig.
A1.4b). One may imagine that Lost Hills, an anticline located less than 50 km
northwest of Elk Hills, evolved in response to a similarly complex four-dimensional
fault geometry. Thus, the reported change in the orientation of thinning over the fold
(Julander, 1992) does not necessarily implicate a rotation of the fold axis; it could also
be a result of changes in fault activity.
Analysis of a wrenching growth mechanism at Elk Hills
Having determined that large rotations of anticlines within the San Joaquin
Valley are unlikely, we investigate a slightly different wrench faulting mechanism for
the formation of Elk Hills wherein the majority of the Elk Hills faults formed
subparallel to a master strike-slip fault driving the deformation, and thus would not
rotate appreciably with slip along the master fault. In the literature, faults in this
geometry have been classified as a “flower structure” (Lowell, 1972). We assess the
validity of this wrench faulting model as applied to Elk Hills in light of the available
184

geological and geophysical data as well as mechanical considerations. The classic
model of a compressional flower structure, presented by Lowell (1972, Fig. A1.2),
consists of subparallel concave downward thrust faults that converge at depth into a
deep-seated strike slip fault trending in the same orientation. Anticlines develop above
the fault system at an oblique angle to the strike of the faults. In this model, the
initiation of thrust faults and the subsequent anticlines is attributed to a component of
compression acting in a direction perpendicular to the faults. The maximum horizontal
compression for this model is assumed to be essentially parallel to the strike of the
deep strike-slip fault, however, driving predominantly horizontal motion.
Some inconsistencies arise when applying this flower structure model to Elk
Hills. The concave downward geometry of the thrust faults is not supported by the
seismic reflection data. All interpretations of the western part of the volume suggest
that the major faults are concave upward, steep in the shallow section and soling out
with depth (Fig. A1.3b, A1.3c). Additionally, 3D representations of interpretations of
the faults and deformed stratigraphic horizons reveal that the faults (1R, 2R, 3R, and
5R) and anticlines (29R and 31S) at Elk Hills are subparallel features (Fig. A1.3a). A
final inconsistency lays in the suggested direction of slip along the deep seated fault.
The model is suspect as it suggests the development of left-lateral slip within and at a
very low angle (25°) to the broader right-lateral domain of the San Andreas Fault
system. Thus, the data cast doubt on the interpretation of Elk Hills as a flower
structure.
Carrying this investigation one step further, we test the mechanical consequences
of applying a flower structure model to Elk Hills. We import a fault geometry
developed with the flower structure model as a basis for interpretation into an elastic
boundary element code. In the shallow layers of the seismic volume, this fault
geometry is similar to the fault geometry used in the previously described models. At
depth, however, where the seismic data are obscure, we take the liberty of interpreting
a different fault geometry. In this flower structure model, the faults, although still
concave upward, converge at depth into a deep strike slip fault. A left-lateral
displacement discontinuity is applied along the deep-seated fault as a driving
mechanism for slip along the shallower Elk Hills faults. These shallower faults are
185

designated as shear traction free surfaces, which permits them to slip freely in both
dip-slip and strike-slip motion, and they are restricted to only in-plane motion. The
objective of this model is to apply the suggested strike-slip motion to the deep-seated
fault and to assess if such motion is capable of generating the slip along the more
shallow thrust faults and generating the deformation of stratigraphic horizons as
imaged within the seismic data. The results of this model are shown in figure A1.5, a
map view representation of the vertical displacement field resulting from a single
increment of deformation at a stratigraphic level comparable to the level of a Late
Pliocene horizon. Uplift does occur at the central part of Elk Hills. The general trends
of the 29R and 31S anticlines are not apparent. The flower structure model thus proves
to be inconsistent with both the interpretation of the shallow seismic data and the
mechanical models.
Conversely, the thrust fault related model is supported by the mechanical models
(Chapter 1) and the seismic data as well as the regional geology. Most significantly,
the ability of the mechanical models to approximately reproduce the deformation
observed within the seismic data set (Chapter 1) supports the idea that the western part
of the Elk Hills is a thrust related structure. Additional support is garnered from the
fact that evidence exists within the seismic data set for the presence of concave
upward faults with dips that shallow at depth. Consideration of the regional geology
also supports the model of Elk Hills as a thrust related feature. The world stress map
(Zoback, 1992) compiled from a collection of earthquake focal mechanisms, wellbore
breakout and drilling induced fracture analyses, in-situ stress measurements, and fault
slip analyses, indicates that the regional maximum horizontal compressional stress is
oriented northeast – southwest. This orientation is consistent with faults and anticlines
oriented perpendicular to this orientation, with strikes trending northwest – southeast,
and is indeed the orientation of the maximum strain direction that was applied as a
remote boundary condition in our modeling efforts.
Conclusions
The absence of geological and geophysical evidence for features that would
develop in response to large amounts of pure shear or simple shear deformation in the
186

35 0 16’00” 35 0 20’00”
0
N
km 2
119 0 32’00”
119 0 26’00”
normalized displacement
119 0 20’00”
Figure A1.5. Model results of a mechanical test of a suggested strike-slip driven
deformation at Elk Hills wherein the shallow Elk Hills faults and two deep seated leftlateral
strike-slip faults form a compressional flower structure. The inset is a threedimensional
view with the geometry of the hypothetical deep vertical strike-slip faults
drawn in dashed lines. Model results are shown as a normalized vertical
displacement field with a contour interval of 0.1.
187
35 0 20’00”
35 0 16’00”

southwestern San Joaquin Valley indicates that a suggested 32° − 48° rotation of the
Elk Hills anticline cannot be accounted for. Geometrical and mechanical investigation
of a wrench faulting scenario for Elk Hills in the absence of any rotation also proves to
be incompatible with available data. In light of these inconsistencies, we find that the
shortening within the southwestern San Joaquin Valley has been more consistent with
compressional rather than wrench tectonics during the growth of the Elk Hills
anticline.
Acknowledgements
This project was supported by funds from the Stanford Rock Fracture Project.
The ideas presented in this manuscript benefited from discussions with Don Miller and
Mike McWilliams.
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191

192

Appendix 2
THE ROCK FRACTURE PROJECT FIELD TRIP
Sheep Mountain Anticline, WY
by
Patricia E. Fiore
Nicolas Bellahsen
David D. Pollard
2006
June 15 - 16, 2006
193

Introduction
Sheep Mountain anticline (SMA) is a Laramide, basement cored fold located
along the eastern flank of the Bighorn basin, which trends NW/SE and is bounded to
the east by the Bighorn Mountains, to the south by the Owl Creek Mountains, and to
the west by the Absaroka and Beartooth Mountains (Figure A2.1).
Sheep
Mountain
anticline
44°
43°
45°
110°
Absaroka Mnts
WIND RIVER
RANGE
109°
BIG
HORN
WIND RIVER
BASIN
BASIN
Owl Creek Mnts
108°
Big Horn Mnts
107°
100 km
POWDER
Casper Arch
RIVER
BASIN
Figure A2.1. Tectonic map of Wyoming showing the location of Sheep Mountain
anticline. From Bellahsen et al., 2006a.
Themes:
Fracture characterization at the outcrop
This field trip emphasizes the importance of a full fracture characterization
which begins at the outcrop. A well constrained fracture history combines fracture
orientations (strike and dip relative to bedding) with all other fracture characteristics
observable in outcrop, including surface textures, filling, geometry, displacement
discontinuity, and abutting relations. An understanding of the mode of deformation of
a tectonic fracture set (opening, closing, shearing), along with its time of formation
relative to other fracture sets, greatly enhances the ability to determine the causal
mechanism.
194

Fracture characterization over the fold
During this field trip we will consider different scales of deformation. Although
most of the field trip stops focus on outcrop observations of fractures, the outcrop
stops are in different structural locations on the fold and therefore can be combined to
understand the larger scale structure. Variations in three fracture sets, the spatial
density of fractures in a given set, the type of fillings, and the reactivation by shearing
of originally opening fractures all contribute to the interpretation of the folding.
Fold-thrust fault relationships based on fracture patterns
Field work on the fractures has helped constrain the kinematics of folding at
Sheep Mountain and relationships to the underlying thrust fault. We will investigate
how the location and geometry of a blind thrust fault can be deduced, with respect to
the position of the fold limbs, based on spatial variations in fracture patterns.
Tectonic history revealed by fracture patterns
Systematic fracture sets may form in response to either remote regional stresses
or local deformation events, such as folding and faulting. The fracture pattern at a
specific field location will reflect the tectonic history of the site but may not record all
such events. Interpretation of the fracture pattern at Sheep Mountain will be put in the
context of regional orogenic events, their maximum compression direction, and their
timing. This study helps to determine the causal mechanisms of some fracture sets.
195

Field Trip Stops:
First Day
Stop 1: Geology of the greater region
Stop 2: Fold shape
Stop 3: Fracture introduction, nose fractures
Second Day
Stop 4: Backlimb fractures
Stop 5: Backlimb fractures and shearing
Stop 6a & 6b: Backlimb fractures and shearing, influence of thumb
Stop 7: Forelimb and hinge fractures
Stop 8: Fracturing synthesis
N
108°10'
1
2
BACKLIMB
HINGE
4
5b
44°39'
FORELIMB
5a
3a
3b
108°10'
44°38'
1 km
Figure A2.2. Digital Orthophoto Quarter Quadrangles of the NW part of SMA.
Locations of stops in the Tensleep sandstone are shown in red; stops in the
Phosphoria limestone are shown in yellow.
196
108°08'
44°37

N
108°12'
Quaternary
Cretaceous
Jurassic
Triassic
108°10'
Permian (Phosphoria Fm)
Carboniferous (Pennsylvanian, Tensleep Fm)
Carboniferous (Pennsylvanian, Amsden Fm)
Carboniferous (Mississipian, Madison Fm)
Anticlinal axis Synclinal axis
108°08'
44°38'
108°06'
1 km
108°04'
44°36'
Figure A2.3. Geological map of Sheep Mountain anticline after Rioux, 1994. Fracture
measurements discussed during this field trip have been made in the Phosphoria,
Tensleep, Amsden, and Madison formations. Additional measurements have been
made in the Jurassic Gypsum Springs and Sundance Formations (Savage, 2003).
Due to outcrop quality and access considerations, work to date has been focused on
the part of the anticline that lies to the NW of the river cut.
197

44°39’0”N
44°36’0”N
108°12’0”W 108°9’0”W
108°12’0”W 108°9’0”W
Figure A2.4. Structural map of the NW part of Sheep Mountain anticline. Black
symbols are data from Hennier (1984), white symbols and formation contacts (slightly
modified from previous interpretations) are interpreted from remote surface mapping.
From Banerjee and Mitra, [AAPG Bulletin. AAPG@2004. Reprinted by permission of
the AAPG whose permission is required for further use.]
198
44°39’0”N 44°36’0”N

DAY 1
Thursday, June 15 th
Arrive in Billings, MT and leave via rental SUVs at 1:00 PM. Drive to Sheep
Mountain anticline via 212S to 310S.
Just before mile marker 223 on 310S, take 1 st left past Lane 16 ½, cut through Alkali
anticline (Fig. A2.5). At 1 st intersection, take a left to head to the NE. At second
intersection, stay straight, driving toward the SE (do not take a left). Cut across the
plunging nose of Sheep Mountain anticline and park to the NW of where the structure
rises.
Figure A2.5. Road map (yellow line) to the nose of Sheep Mt. anticline from highway
310 through Alkali anticline (trend drawn in black on map).
Figure A2.6. Day 1 stops at the nose of Sheep Mt. anticline. Park on the NW side of
the fold near the nose, just north of the fence. Walk (dotted yellow line) through the
Chugwater up the nose of the fold.
199

Stop 1: Geology of the greater region
NW nose
30 minutes walking (Fig. A2.6)
3:30 PM – 4:30 PM
Waypoint (UTM zone 12N): 4947765 N
0722336 E
elev. = 1370 m
Objectives
Discuss the tectonic setting of the Laramide orogeny
Discuss the structural style of the Laramide orogeny
Introduce stratigraphy of the Bighorn Basin
Point out the surrounding structures
Discuss previous structural interpretations of Sheep Mountain
Key Points
SMA is a Laramide fault related fold that exposes Paleozoic sediments within
its core.
The Sheep Mountain fault is a 3 rd order structure: Bighorn Mts. eastern frontal
thrust, Rio thrust, SMA thrust.
A secondary fold exists on the backlimb of SMA.
Tectonic setting of Laramide Orogeny
Sheep Mountain formed during the Laramide orogeny, which occurred during
late Cretaceous through early Tertiary time, from about 80 Ma to 40 Ma, and produced
folds trending both NW-SE and east-west. These varying structural orientations have
sparked debate about the orientation and possible temporal variation of the tectonic
stresses of the orogeny. A common interpretation is of a constant NE-trending
compression throughout Laramide time (Dickinson and Snyder, 1978; Engebretson et
al., 1985; Bird, 1998; Bird, 2002).
Laramide tectonism is attributed to subduction of the Farallon plate beneath the
North American plate at an abnormally shallow angle (Fig. A2.7). One line of
evidence for shallow subduction is the lack of Laramide age volcanism in the Rocky
Mountain foreland. A younger analog has been identified in the Andean foreland
Sierras Pampeanas (Sales, 1968; Coney, 1976; Jordan et al., 1983; Fielding and
Jordan, 1988).
200

(a)
(b)
Figure A2.7. Two types of arc orogens displaying two modes of subduction: (a)
steep and (b) shallow plate descent. Modified after Barazangi and Isacks (1976) and
Megard and Philip (1976). From Dickinson and Snyder (1978).
201

Structural styles of Laramide folds and thrust faults
Laramide folds are classified as “thick-skinned” structures, indicating the role of
basement blocks in the deformation. Various theories presented since the 1940s as to
how basement involved structures develop have generated controversy over the
relative importance of vertical uplift (forced folds/drape folds) versus horizontal
contraction (thrust-fault related folds). Blackstone (1940) and Berg (1962) were the
first proponents of the thrust-fault related Laramide deformation with their structural
interpretations of specific Rocky Mountain folds (Fig. A2.8). In the 1970s,
interpretations shifted toward vertical deformation with interpretations of steep to
subvertical fault zones and unfolded basement that deformed by brittle fracture only
(Fig. A2.9; Stearns, 1971, 1978; Stearns and Weinberg, 1975; Stearns and Stearns,
1978), a concept that had been introduced earlier by Thom (1923, 1952) and Prucha et
al. (1965). In the late 1970s, high quality seismic reflection profiles across the Rocky
Mountain foreland provided ground truth for the controversy. These data, revealing
thrust fault geometries that place PreCambrian basement over Paleozoic sediments,
emphasized the importance of horizontal contraction (Smithson et al., 1978, 1979).
Figure A2.8. Thrust fault interpretation of the Golden Thrust in Jefferson County,
Colorado. From Berg, 1962. [AAPG Bulletin. AAPG@1962. Reprinted by permission
of the AAPG whose permission is required for further use.]
202

Figure A2.9. Drape fold interpretation of Rattlesnake Mountain near Cody, Wyoming.
From Stearns, 1971.
Although modern data have cast doubt on the vertical uplift theory for Laramide
deformation, the issue of how basement deforms remains controversial. Some studies
have suggested how cover rocks may fold in the absence of folded basement (Erslev,
1986; Spang and Evans, 1988; Narr and Suppe, 1994), while other studies have
suggested mechanisms by which basement may fold due to slip along foliation planes
(Schmidt and Garihan, 1983; Miller and Lageson, 1990; Schmidt et al., 1993), or slip
along closely spaced fractures (Spang et al., 1985; Spang and Evans 1988; Garcia and
Davis, 2004). Although the exact mechanism for basement folding at Sheep Mountain
has not been identified, during this field trip, we will make the case for folding of the
basement beneath the anticline.
203

Stratigraphy of the Bighorn Basin
During the Paleozoic and Mesozoic, the Bighorn basin filled with approximately
3000 m of interbedded shales, sandstones, and limestones (Fig. A2.10; Thomas, 1965;
Ladd, 1979). These sediments lie on top of PreCambrian basement.
At Sheep Mountain, the oldest exposed formation is the Lower Carboniferous
Madison Limestone, which is about 200m thick and is topped by a paleokarst surface.
The Madison Formation is unconformably overlain by the Upper Carboniferous
Amsden Formation. The base of the Amsden Formation is marked by a crossbedded,
light gray fine-grained quartz arenite (Ladd, 1979). The remainder of the Formation
consists of thick siltstones, sandstones, shales and carbonates (Fig. A2.11, Fig. A2.12).
Above the Amsden Formation, the Tensleep Formation (also Upper Carboniferous in
age) is composed of interbedded thin sandstones, shales, and carbonates in its lower
part and thicker beds of crossbedded quartz arenite in its upper part. Above the
Carboniferous section is the Phosphoria Formation, Permian in age. The lower beds of
the Phosphoria Fm. are predominantly siltstones and shales, with a thin interbedded
gypsum layer (Ladd, 1979). Higher in section, the Phosphoria Formation is composed
of thick carbonates (biolithite, micrite and biosparite). Due to minor Ancestral Rocky
Mountains uplift, the Tensleep and Phosphoria Formations are thinned at Sheep
Mountain (Simmons and Scholle, 1990). Above these units, the base of the Mesozoic
rocks is defined by the Triassic Chugwater Formation, distinctive due to its red color.
The overlying sediments are composed of sandstones and shales that have been eroded
from the Sheep Mountain ediface.
Our studies at Sheep Mountain have focused on fracturing of the Madison,
Tensleep, Amsden and Phosphoria Formations. These formations range from
Mississippian to Permian in age and were deposited approximately 330 Ma – 250 Ma
(Fig. A2.12). During the field trip, we will investigate the role that lithology plays in
fracturing.
204

K
J
TR
P
P
M
D
O
C
pC
Mesa Verde
Cody
Frontier
Mowry
Thermopolis
Cloverly
Morrison
Sundance
Gypsum Springs
Chugwater
Phosphoria
Tensleep
Amsden
Madison
Jefferson -
Three Forks
Bighorn
Gallatin
Gros Ventre
Flathead
Granite
Shale
Sandstone
Limestone
Dolomite
Gypsum
Granite
Figure A2.10. Stratigraphic column for the Bighorn Basin. After Hennier, 1984.
205

Amsden
Tensleep
Phosphoria
Chugwater
Gypsum Springs
Sundance
Morrison
Thermopolis
Cloverly
Figure A2.11. Photograph of the NW nose of Sheep Mountain. The stratigraphic
layers that we will drive through, walk over, and investigate in outcrop on this field trip
are labeled.
Perimian Trias
Carb.
(Penn.)
Carboniferous (Miss.)
250 Ma
292 Ma
320 Ma
Chugwater
174m
Phosphoria
68m
Tens
29m
Ams
35m
Madison
230m
Frontier
Mowry
Figure A2.12. Stratigraphic column for Sheep Mountain. The formations in which
fracture measurements were made are shown in this column. From Bellahsen et al.,
2006a.
206

Structures surrounding Sheep Mountain
The view from the NW nose of Sheep Mountain reveals a complicated
geometrical pattern of folds (Fig. A2.13; Fig. A2.14). To the east-southeast, Crystal
Creek Anticline has a meandering fold trend. To the northeast, a small syncline flanks
the forelimb of Sheep Mountain. Beyond this syncline, Spence Dome, an actively
producing oil field, has a domal shape that is oblong in the NNW-SSE direction.
Further to the northeast, Little Sheep Mountain Anticline trends subparallel to Sheep
Mountain. Along the trend of Sheep Mountain, to the NW, Rose Dome is oblong in
the NW-SE direction. The intersection of this Rose Dome trend with the Spence Dome
and Sheep Mountain trends produces a complicated geometry just northeast of the
plunging nose of Sheep Mountain. To the northwest, Goose Egg Anticline and Alkali
Anticline lie along a NW-SE trend, subparallel to Sheep Mountain. It has been
proposed that these anticlines initiated as distinct folds and grew together (Savage,
2003).
Figure A2.13. Geological map for the area surrounding Sheep Mountain. Fold hinge
lines are plotted and labeled. Modified from Rioux, 1994. From Savage, 2003.
207

¹
0 2.5 5 10 15 20
Km
Figure A2.14. Color Infra Red digital orthoquad quadrangle photos (CIR DOQQs) of the Bighorn area with the hinge
lines of major folds shown in white. DOQQs downloaded from http://wgiac.state.wy.us/.
Sheep Mt.
Anticline
Alkali
Anticline
Crystal Creek
Anticline
208
Spence
Dome
GooseEgg
Anticline
Rose
Dome
Little
Sheep Mt.
Anticline
Big Horn Mountains

In a recent study investigating fold and fault interactions in three dimensions,
Savage (2003) inferred the geometry of the blind thrust faults that formed these
Laramide features from the shapes of the folds as mapped in the field. Incorporating
the faults into elastic boundary element models and simulating the deformation of the
area (Fig. A2.15), Savage concluded that slip along faults oriented obliquely to one
another could have produced the pattern of folds seen in the Sheep Mountain area with
one direction of tectonic contraction.
Figure A2.15. Synthetic structure contour map for the region surrounding Sheep
Mountain with a 2 m contour interval (From Savage, 2003). Orientations of faults
included in the model are plotted. The shape of the folds represented in this structure
contour map are similar to those seen in figures A2.13 and A2.14.
209

The same study investigated strain energy density (Fig. A2.16a; Fig. A2.16b)
and Navier-Coulomb stress (Fig. A2.16c; Fig. A2.16d) to determine whether the NW-
SE trending faults could have caused stress perturbations on faults oblique to the
direction of Laramide contraction that brought them closer to failure. An interesting
result, having implications for the structural interpretation of Sheep Mountain, is that
both the strain energy density and the Navier-Coulomb stress plots show highs in the
area to the southwest of Sheep Mountain Anticline (Fig. A2.16). This is the suggested
location of the blind Rio thrust fault (Stone, 1993).
The Rio thrust fault is a backthrust of the major southwest dipping thrust fault
that bounds the eastern edge of the Bighorn Mountains and is responsible for their
uplift (Fig. A2.17; Stone, 1993). Sheep Mountain Anticline lies in the hanging wall of
the Rio thrust fault, and although current interpretations of the relationship between
the Rio thrust fault and the SMA thrust fault conflict (Fig. A2.21-A2.23), the Sheep
Mountain fault is most likely a backthrust of the Rio thrust fault.
210

(a) (b)
0.0 1.2 2.5 3.8 5.0
MPa
(c) (d)
-40 0 40
MPa
Figure A2.16. (a) Strain energy density for a four fault model; (b) strain energy
density for a seven fault model; (c) Navier-Coulomb stress for a four fault model; (d)
Navier-Coulomb stress for a seven fault model. Areas of high strain energy density
and high Navier-Coulomb stress suggest the presence of faults missing from the
models and/or fault propagation tendency. From Savage, 2003.
211

(a)
(b)
Bighorn Basin
Sheep Mt.
Rio
Thrust
SMA
Thrust
Bighorn Mts.
Western Thrust
Bighorn
Mountains
Bighorn Mts.
Eastern Thrust
N
10km
Figure A2.17. (a) Color infra-red DOQQs of the Bighorn Mt. and Bighorn Basin area.
Quadrangles downloaded from http://wgiac.state.wy.us/. Dashed red lines trace the
surface projections of major thrust faults. Yellow line shows the location of the crosssection
in (b). (b) Schematic cross section through the Bighorn Basin and Bighorn
Mountains. The SMA thrust can be considered a 3 rd order structure. It is a backthrust
of the Rio thrust fault, which is in turn a backthrust of the Bighorn Mts. Eastern Thrust.
212

Structural interpretations for Sheep Mountain anticline
The first structural interpretations of Sheep Mountain anticline to consider the
geometry of faults in the subsurface (Fig. A2.18; Fig. A2.19; Fig. A2.20; Hennier and
Spang, 1983; Forster et al., 1996; Brown 1984) were based primarily on surficial
mapping of bedding contacts and attitudes (Rioux, 1958; Hennier and Spang, 1983),
along with stratigraphic picks from exploration wells. The studies conclude that the
steep forelimb of the anticline is due to a southwest dipping thrust fault. To reconcile
this northeast thrusting direction with the southwest thrusting direction of a deeper
fault, suggested by Gries (1983) in light of unpublished seismic data and later named
the Rio thrust fault by Stone (1993), these studies proposed that the fault causing the
uplift of Sheep Mountain is a backthrust of the Rio thrust (Fig. A2.17; Fig. A2.21).
Figure A2.18. SW–NE trending cross section through Sheep Mountain anticline from
Hennier and Spang, 1983. Bedding dips and formation contacts are constrained by
surface mapping and geologic markers from exploration wells. Hennier and Spang
postulate a relatively undeformed basement with multiple thrust planes in an overall
wedge shaped geometry to generate folding in the overlying sediments.
213

Figure A2.19. SW-NE trending cross-section through Sheep Mountain anticline from
Forster et al., 1996. Bedding dips and formation contacts are constrained by surface
mapping and geologic markers from exploration wells. A wedge shaped fault zone is
hypothesized as the mechanism by which overlying strata fold.
Figure A2.20. SW-NE trending cross-section through Sheep Mountain anticline from
Brown, 1984. Geological constraints are not given, but are most likely surface dips
and formation markers from wells. Brown (1984) proposes substantial basement
folding and a wedge shaped fault zone beneath the forelimb of Sheep Mountain.
[AAPG Continuing Education Courses. AAPG@1984. Reprinted by permission of the
AAPG whose permission is required for further use.]
214

Figure A2.21. SW-NE trending cross-section from the Bighorn Basin through the
Bighorn Mountains from Forster et al., 1996 showing the fault beneath Sheep
Mountain as a backthrust of the Rio Fault. Bedding dips and formation contacts are
constrained by surface mapping and geologic markers from exploration wells.
Basement is slightly folded in the cross-section, but there is still a wedge shaped fault
zone hypothesized as the mechanism by which overlying strata fold.
Figure A2.22. SW-NE trending cross-section through Sheep Mountain anticline from
Stanton and Erslev, 2002. Geological constraints are surface dips, formation markers
from wells, and three 2D seismic profiles. Stanton and Erslev propose a moderately
folded basement. Their kinematic modeling suggests that the Rio thrust fault slipped
after slip along the fault beneath Sheep Mountain Anticline had already uplifted the
fold.
215

A later study reinvestigated the fault geometry (Stanton and Erslev, 2004) with
the aid of additional subsurface data in the form of two seismic reflection profiles
perpendicular to, and one profile parallel to, the trend of Sheep Mountain. Stanton and
Erslev (2004) built a 3D geometric model of the structure at Sheep Mountain and then
kinematically restored 2D cross sections and 3D stratigraphic surfaces taken from the
geometric model, using line length balancing and inclined shear unfolding techniques.
Based on these restorations, they suggest that the southwest dipping fault formed prior
to the Rio thrust, being cut and offset as the Rio thrust began to slip (Fig. A2.22).
These restorations suggest the existence of a fault surface (the lower part of the
southwest dipping fault) that is not supported by any currently available subsurface
data (Don Stone, pers. communication).
An additional structural geometry has been suggested for Sheep Mountain based
on geologic interpretations further to the south, at the Torchlight Field (Don Stone,
pers. commun.; Fig. A2.23; Fig. A2.24; Stone, 2004). At the Torchlight Field, the
geochemistry of oil pools at various depths within the fold suggests that these pools
were segmented during fold growth (Stone, 2004). As a result, Stone has proposed a
structural growth history whereby the Rio thrust and the Torchlight thrust, which can
be likened to the southwest dipping fault beneath Sheep Mountain, propagated
simultaneously. In this structural interpretation, the two faults do not intersect or abut
one another (Fig. A2.23).
216

Figure A2.23 (opposite page). SW-NE trending cross-section through the Torchlight
Field showing the coeval Rio and Torchlight thrust faults. From Stone, 2004. [The
Mountain Geologist. RMAG@2004. Reprinted by permission of the RMAG whose
permission is required for further use.]
T
56
N
T
55
N
T
54
N
T
53
N
T
52
N
43°
45°
44°
110°
Absaroka Mnts
WIND RIVER
RANGE
R95W
RIO
N
BIG
HORN
WIND RIVER
BASIN
108°15’
BASIN
Owl Creek Mnts
109°
108°
100 km
THRUST
Big Horn Mnts
R94W R93W R92W
Sheep MountainAnticline
POWDER
Casper Arch
107°
RIVER
BASIN
RIO
THRUST
A
BighornRiver
BASIN
BIGHORN
MOUNTAINS
A‘
basement
involved
thrusts
Paleozoic
anticlines
5 mi
8km
SCALE
Torchlight Field
MANDERSON
Figure A2.24. Tectonic map of the northeastern edge of the Bighorn Basin showing
the location of Sheep Mountain anticline in red. The inset shows the location, within
Wyoming, of the area shown in the figure. Solid black lines represent the axes of
Paleozoic anticlines, and dashed black lines represent the related thrust faults. The
curvilinear, segmented thick dashed black line represents the projected trace of the
Rio thrust fault. Green dashed line A-A’ shows the location of the seismic profile
through the Torchlight Field. Modified from Stone, 2004.
217
44°45’
44°30’

A recently published geomechanical study (Savage and Cooke, 2004) used a
heuristic approach to infer the fault geometry responsible for generating the splay fold,
termed “the thumb” (Savage and Cooke, 2004), along the southwestern backlimb of
SMA (Fig. A2.25). Following Hennier and Spang (1984), Savage and Cooke (2004)
assumed that the main Sheep Mountain fold is underlain by a primary fault and that a
secondary fault underlies the thumb. They used a boundary element code to forward
model for the vertical displacement fields resulting from a series of models within
which the primary fault was held constant in length, depth, dip, and aspect ratio and
the secondary fault varied systematically in these parameters, as well as in distance
from the main fault (Fig. A2.26). The study also considered the influence of fault
interaction and differing principal contraction directions on fold shape. Model results,
some of which are presented in Figure A2.27, indicate that best estimates for the
geometry of the secondary fault are: 30% of the length of the main fault; shallower
depth than the main fault; 20° clockwise from the main fault, 45° dip; not connected to
the main fault.
Figure A2. 25. Structure contour map of SMA (from Andrews et al., 1944) with gray
arrow showing the location of the thumb structure that has been interpreted by
Hennier and Spang (1984) to overly a splay fault that branches from the major fault
underlying SMA. [Reprinted from Journal of Structural Geology, v. 26., Savage, H.
and M. L. Cooke, The effect of non-parallel fault interaction on fold patterns, p. 905-
917, Copyright 2004, with permission from Elsevier].
218

Figure A2.26. Model set-up. The geometry of the primary fault is held constant in
length, depth, dip, and aspect ratio. The secondary fault varies in (A) size, distance
from the primary fault, orientation, and (B) depth. [Reprinted from Journal of Structural
Geology, v. 26., Savage, H. and M. L. Cooke, The effect of non-parallel fault
interaction on fold patterns, p. 905-917, Copyright 2004, with permission from
Elsevier].
219

Figure A2.27. Surface fold patterns for models within which secondary fold size and
depth were varied. Thick gray lines show traces of the upper tip of the faults. Contour
interval is 2 m. The dip and orientation of the secondary fault is held constant at 60°
and 20° respectively. The gray polygon outlines the synthetic structure contour maps
that depict multiple fold patterns whereas synthetic structure contour maps outside
the gray polygon depict isolated folds. From Savage and Cooke, 2004. [Reprinted
from Journal of Structural Geology, v. 26., Savage, H. and M. L. Cooke, The effect of
non-parallel fault interaction on fold patterns, p. 905-917, Copyright 2004, with
permission from Elsevier].
220

44°30’
44°45’
Reprocessing of ten seismic lines acquired in the early 1980s is underway.
Figure A2.28 shows the locations of these lines. We hope to better understand the
geometry of the Sheep Mountain fault and the Rio thrust fault. Initial results place
constraints on the depth to the Sheep Mountain fault and its angle of dip. The Rio
thrust fault is more difficult to constrain, but specific unfaulted sedimentary layers
provide a minimum constraint on the depth to the Rio thrust fault.
108°22’30”
BH-6
108°22’30”
41-82
2 km
17-81
19-81
12-81
11-81
44-82
108°00’
108°00’
Figure A2.28. DEM of the western Bighorn Basin showing the location of 10 seismic
lines that are being investigated for thrust fault geometry.
14-81
221
TE-103
13-81
44°45’
44°30’

Stop 2: Fold shape
5 minutes walking (Fig. A2.6)
4:35 PM – 4:45 PM
Waypoint (UTM zone 12N): 4947765 N
0722336 E
elev. = 1370 m
Objectives
Discuss fold shape
Discuss location of hinge
Key Points
The fold shape changes from being tight and kink-like in the NW to being
more rounded toward the SE.
The hinge is not coincident with the topographic high, but instead lies to the
NE.
The shape of Sheep Mountain anticline changes along the fold axis. Near the
northern termination, the fold profile is very tight (Twiss and Moores, 1992, p.228;
Fig. A2.29a). Toward the south, the asymmetry increases while the fold hinge
becomes rounder (Fig. A2.29b).
(a) (b)
Figure A2.29. The hinge of SMA changes along strike from being tighter in the NW
(a) to rounder in the SE (b). (a) View to the southeast. (b) View to the west.
222

The hinge of Sheep Mountain anticline lies to the northeast side of the
topographic high (Fig. A2.30). The highest parts of SMA are within the backlimb of
the fold.
Figure A2.30. The hinge of SMA is not coincident with the topographic high.
Resistant beds within the Phosphoria (yellow) and Tensleep (red) are correlated from
the backlimb through the hinge (where they are eroded) and to the forelimb with
dotted lines. View to the SE.
223

Stop 3: Fracture introduction; nose fractures
NW nose – site 2
5 minutes walking (Fig. A2.6)
4:45 PM – 5:45 PM
Waypoint (UTM zone 12N): 4947359 N
0722823 E
elev. = 1423 m
Objectives
Review previous fracture studies for Sheep Mountain
Discuss methods of fracture characterization
Present fracture interpretation for the site and the nose introducing the two
main systematic fracture sets
Key Points
Previous fracture studies date back to the 1960s and are archaic.
Current SMA fracture studies include a complete outcrop characterization:
fracture orientations (strike and dip relative to bedding), surface
textures, filling, displacement discontinuity, and abutting relations.
Two systematic fracture sets are observable in the nose of SMA. The strike of
the fractures within these sets rotates clockwise toward the NW
termination of the fold.
Previous fracture studies at Sheep Mountain
Two fracture studies at Sheep Mountain were conducted during the 1960s:
Harris et al. (1960) and Johnson et al. (1965). Both studies relied primarily on field
observations of fracture orientations and measures of spacing or frequency.
Recognizing that many factors influence the occurrence and concentration of
fractures on a fold, Harris et al. (1960) developed a method to correct for variations in
lithology and bed thickness. After documenting the number of fractures per square
yard at various stations, the researchers calculated proportionality constants to
normalize measurements made within beds of different lithologic units and
thicknesses to a datum bed and thus better understand how structural position
influences fracturing. The collected data are displayed on (a) a fracture pattern map
(Fig. A2.31) that shows the trends of the deformational fracture sets and their field
intensities at locations on a structure contour map and (b) an iso-fracture map that
shows the concentration of fractures relative to a datum bed (Fig. A2.32).
224

Harris et al. (1960) found that thinner beds are more susceptible to fracturing
than thicker beds and ductile units have poorer developed and more widely spaced
fractures than brittle units. Based on strike directions, they determined that one main
fracture set is present on each flank of Sheep Mountain and that these fracture sets are
both present at the plunging noses of the fold. These two systematic (planar, parallel,
repetitious) fracture sets were interpreted to be conjugate sets “of compressional
deformational origin” and “related to shear stresses”.
Figure A2.31. Fracture pattern map from Harris et al., 1960 showing the strike
directions and observed densities of the major fracture sets at Sheep Mountain
superposed on a structure contour map. [AAPG Bulletin. AAPG@1960. Reprinted by
permission of the AAPG whose permission is required for further use.]
225

A critique of this study in light of present day characterization techniques
presents points for improvement. (1) In correcting fracture measurements to a datum
bed, fracture saturation (Bai and Pollard, 1999; Wu and Pollard, 1995) is assumed. (2)
Diagnostic evidence for the interpretation of the main fractures sets as being related to
shear stresses (see Pollard and Aydin, 1988) was not published. (3) Fracture
orientations were not rotated to remove the effect of bedding orientation. (4) The
relative age relationships of the fracture sets, which could have strengthened or
invalidated the interpretation that the two sets at SMA formed during the same
deformational event, were not deduced from field observations.
Figure A2.32. Iso-fracture map from Harris et al., 1960 showing the relative intensity
of fracturing in the Sheep Mountain area as corrected to a datum bed. [AAPG
Bulletin. AAPG@1960. Reprinted by permission of the AAPG whose permission is
required for further use.]
226

Johnson et al. (1965) studied fracture geometries within two formations of
significantly different ages, the Pennsylvanian Tensleep Fm. and the Lower
Cretaceous Cloverly Fm., in the Bighorn Basin. The study was designed to test the
hypothesis that differences between the fracture patterns within the two lithologies
would suggest that a Permo-Triassic orogeny had occurred in the Bighorn Basin.
Fracture strike, dip, length and frequency were noted at several study sites.
Four fracture sets were documented (Fig. A2.33) in both lithologies, prompting
the conclusion that pre-existing heterogeneities are an important factor during the
development of fractures, despite the age relation between the fracturing beds and the
previous orogenies. Based on orientation data, Johnson et al. (1965) suggest the
mechanism by which each fracture set formed. East-west and north-south trending sets
were suggested to be “shear-joints” developed at acute angles to the fold axes. A 105º
to 155º trending set was interpreted as tension-joints developed parallel to fold axes.
Together with a 025º to 065º trending set, this 105º to 155º trending set was also
interpreted as “release tension-joints” developed either perpendicular or parallel to the
fold axis.
Again, a critique of this study in light of present day characterization techniques
provides points for improvement. (1) Rather than being documented in the field, the
modes of deformation of these fracture sets were suggested based on angular
relationships between fracture sets and fold axes. (2) In the northeastern section of the
study area, fold axes are north-south, and the north-south and east-west fracture sets
are still observed. The interpretation of these as shear-joints formed at acute angles to
the fold axes breaks down. (3) Fracture measurements were not unfolded. (4) Regional
studies or measurements in flat lying areas were not looked at to delineate regional
fracture sets from folding related fracture sets.
227

Figure A2.33. Joint frequencies presented in rose diagrams at selected study sites.
The spatial locations of these sites are plotted with respect to structural axes. From
Johnson et al., 1965.
228

Methods of fracture characterization
At Sheep Mountain, fracture characterization of systematic fractures at the
outcrop included recording orientation relative to bedding, size, and spacing (Fig.
A2.34); and noting evidence for opening or shearing mode in the form of fillings, tail
cracks, tensile gashes, etc. (Fig. A2.35a). Fracture mode was also investigated at the
microscale (Fig. A2.35b). Chronological relationships based on abutting relations
among the fracture sets were noted and documented by mapping on field photos (Fig.
A2.36).
(a) (b)
Figure A2.34. Characterizing fracture orientations. (a) Fracture orientations and
orientation of bedding were recorded. (b) Fracture measurements were then plotted
on stereonets and rotated to derive their orientations relative to horizontal bedding.
Densities of clusters of poles to fractures, shown in shades of pink, helped to
determine the orientations of distinct fracture sets, represented by black great circles.
Figure A2.35. Characterizing mode of deformation. (a) Field evidence for sheared
fractures includes the presence of tail cracks. (b) Thin section evidence for jointing
includes the absence of the products of shearing such as crushed grains, planar
fabrics, and slickenlines.
229

Figure A2.36. Characterizing abutting relationships. (a) Field photograph of a
pavement with two fracture sets. (b) Interpretation of abutting relationships between
fracture sets.
230

Fracture interpretation
Site 2 - Tensleep sandstone
Nose Hinge
Figure A2.37. Field photograph showing the fracture pattern in a sandstone
pavement of the Tensleep Fm. at site 2 in the nose hinge.
At the site 2 sandstone pavement (Fig. A2.37), we will introduce many aspects
of the Sheep Mountain fracture characterization study. First, different sets can be
distinguished based on orientation (strike and dip) and mode of deformation (Fig.
A2.38; Fig. A2.39, Fig. A2.40). Where shearing indicators exist in the field, we will
determine if all fractures of the given orientation have slipped in the same direction.
We will look at abutting relationships to see if consistent age relationships can be
determined (Fig. A2.39, Fig. A2.40), and we will notice the spacing between fractures
of each set. These techniques will be used over the course of the field trip to
characterize fracture patterns seen in outcrop at Sheep Mountain.
The major systematic fracture sets present at site 2 are the 045º and the 135º sets
(Figure 38). Respectively, they are called Set II and Set III.
Figure A2.38. Polar stereonets left to right are present day fracture poles, pre-folding
fracture poles, and great circles for the mean orientation of each set. Poles to
bedding are gray dots.
231

N
10 cm
Figure A2.39. Field photo and line drawing from site 2 showing interpreted fracture
sets and abutting relationships. Note that the 135º fractures have a range of
orientations. Here, 135º, 010º, and 080º abut against 045º. Some geometries within
this outcrop might suggest that the 010º fracture set are tail cracks related to left
lateral shear along 045º fractures. We will determine if other kinematic evidence for
this idea is present at the outcrop.
N
10 cm
Figure A2.40. Field photo and line drawing from site 2 showing interpreted fracture
sets and abutting relationships. Here, 135º fractures abut against 080º more than
080º abut against 135º. Geometries in this photo might suggest that the 080º fracture
set is related to right lateral shear along 045º fractures. We will determine if other
kinematic evidence for this idea is present at the outcrop.
232
045º
N
10 cm
080º
135º
010º
045º
080º
135º
N
10 cm

Fracture characterization in the nose
The fold nose is defined as the area NW of the position in the backlimb where
bedding strike has rotated to 150° from the typical value of 135°. In the nose, fracture
data were collected primarily from limestones within the Phosphoria Formation
because the Tensleep Formation crops out in limited locations.
Close to the nose hinge, in the Tensleep Fm, the fractures consist of two main
joint sets trending 045° (Set II) and 135° (Set III) (Fig. A2.38). From abutting
relationships, the Set II joints predate Set III joints (Fig. A2.39; Fig. A2.40). In the
nose hinge, we also observe two main fracture sets (Figure 41) in both Tensleep (Fig.
A2.42) and Phosphoria (Fig. A2.43) outcrops. One set is NE-trending and composed
of joints. Another set is SE-trending and also composed of joints. The chronology is
difficult to determine (Fig. A2.42) as the abutting relationships are not entirely
consistent. However, based on strike and mode of deformation, we suggest that theses
two joint sets are similar to Set II and Set III described throughout the fold that we will
see later during the field trip.
Throughout the nose, as mentioned above, we observe that the NE-trending Set
II joints vary in orientation from 045° to 070° toward the northwest (Fig. A2.41).
Fractures trend 045°at sites 2, 26, 53, and 60 and 070° at all but one of the remaining
sites. The SE-trending Set III joints also vary in orientation throughout the nose, but to
the largest extent within the nose backlimb (Fig. A2.41). They trend 135° at sites 60,
61, and 62, and trend 160° at sites 64, 65, and 66. In the nose hinge, these SE-trending
joints maintain an average orientation of 140° at all sites except site 57 (Fig. A2.41).
233

Jurassic
Trias
Permian (Phospphoria Fm)
Carboniferous
(Pennsylvanien, Tensleep Fm)
Carboniferous
(Pennsylvanian, Amsden Fm)
Carboniferous
(Mississipian, Madison Fm)
Anticlinal axis
Hinge
site 66
N
site 65
N
46
50
site 57
site 64
N
N
Backlimb
N
37
250 m
site 56
site 63
N
N
site 67
site 55
57
66 56
55 67
65 68
26
64
54
63 53
62
N
N
61
60
2
site 68
site 54
Forelimb
site 26
site 53
site 02
site 62 site 61 site 60
Figure A2.41. Geologic map from Rioux (1994) of the nose of Sheep Mountain
anticline with the nose fracture measurement sites and the corresponding rose
diagrams for measurement sites in the backlimb of the nose. Red lines show the
average strike of Set II fractures and blue lines show the average strike of Set III
fractures. Note that the orientations of these fracture sets rotate clockwise as we
progress to the northwest. From Bellahsen et al., 2006a.
234
54
52
46
N
58
56
36
N
N
N
31
53
57
N
N
N
N
31
78
61
79

Figure A2.42. Fracture pattern in the hinge of the fold nose. (a) Field photograph
showing the fracture pattern in the sandstone of the Tensleep Fm. at site 2. (b) Line
drawing of the outcrop in (a) showing that Set III (135°) terminate at Set II (045°)
fractures more times than Set II fractures terminate at Set III fractures. Stereonets
show poles to fractures as measured in the field, poles to fractures relative to
horizontal bedding, and great circles representing the average orientation of each
fracture set. From Bellahsen et al., 2006a.
235

Figure A2.43. Fracture pattern in the backlimb of the fold nose. (a) Field photograph
showing the fracture pattern in the limestone of the Phosphoria Fm. at site 2. (b) Line
drawing of the outcrop in (a) showing that the chronology of fracture Set II (045°) and
Set III (135°) is hard to determine from abutting relationships at this location.
Stereonets show poles to fractures as measured in the field, poles to fractures
relative to horizontal bedding, and great circles representing the average orientation
of each fracture set, respectively. From Bellahsen et al., in press.
236

DAY 2
Friday, June 16 th
310
Spence Oilfield Rd
Stop 4
Stop 7
Stop 5
Stop 6
Stop 8
Ribbon Canyon Rd
WyoBen
Lunch
CR 26
From Greybull
Figure A2.44. Google Earth image showing roads near Sheep Mountain and
directions to Day 2 stops. Light blue dashed line marks the driving route to stop 4.
Yellow dashed line marks the driving route to stops 5 - 8. Red hachured lines mark
walking routes to field trip stops.
237

Stop 4: Backlimb fractures
Site 8 – Tensleep sandstone
Backlimb
30 minutes driving from Greybull
walk up Gypsum Springs mound to the west of the road (5 min.), view site 8
8:30 AM – 9:15 AM
Waypoint (UTM zone 12N): 4947765 N
0722336 E
elev. = 1370 m
Objectives
Discuss fracture characterization at site
Discuss kinematic indicators at site
Discuss fracture characterization in the backlimb
Key Points
In the backlimb, four systematic fracture sets are observed: 110°, 045°,
135°, and 110°V.
At site 8, hackle marks and tail cracks are observed along Set II fractures
indicating both opening and shearing modes of deformation.
Figure A2.45. Photo showing location of vantage point for stop 4. Note the Tensleep
pavement on the fold at the horizon.
238

Overview
At stop 3, we will walk up onto the Gypsum Springs mound to the west of the
fold to discuss fracturing in a backlimb pavement of Tensleep sandstone that is visible
from the road (Fig. A2.45). The noticeable lineaments are due to weathering along the
two main fracture sets that are orthogonal to one another. The weathering gives the
surface a pronounced hummocky nature (Fig. A2.46, Fig. A2.47). Strike and dip
measurements relative to horizontal bedding (Fig. A2.47c) indicate that there are four
major fracture sets at this site. Three are perpendicular to bedding and trend 110° (Set
I), 045° (Set II), and 135° (Set III). A fourth set is oblique to bedding and trends 110°
(Set IV). Two minor fracture sets are also present at this site.
Set I
Set II
Figure A2.46. Photo showing the hummocky nature of site 8 pavement. The two
noticeable fracture sets trend 110° (Set I) and 045° (Set II).
239

Figure A2.47. (a) Field photo of Tensleep sandstone pavement
of site 8. (b) Line drawing of outcrop in (a) that shows Set II fractures
(strike of 045°) terminating at Set I fractures (strike of
110°). (c) Stereonets for fractures measured at pavement in (a).
From left to right, the stereonets show the poles to fractures as
oriented in the field today, poles as oriented when bedding is
restored to horizontal, and great circles representing the major
fracture sets at the outcrop as oriented when bedding is
restored to horizontal. From Bellahsen et al., 2006a.
Nb planes 116
(c)
N
N
N
3 m
Set I
Set II
240
(b)
(a)
NW SE

Kinematic Indicators
Investigation of Set II fractures (trending 045°) at site 8 provides evidence for
the kinematic history of the fractures. Hackle visible in outcrop (Fig. A2.48) indicate
that Set II fractures formed as joints, with an opening mode of deformation. Shearing
indicators (Fig. A2.49) suggest that some Set II fractures have sheared in a left-lateral
sense.
1 m
Figure A2.48. Concentric rib marks and hackle on the surface of a fracture a few
meters in size trending at 045°. Hackle such as these provide field evidence
supporting an opening mode of formation for the 045° fracture set (Pollard and Aydin,
1988).
Figure A2.49. Splay cracks suggest left-lateral shearing has occurred along this
submeter scale Set II fracture.
241

Fracture characterization in the backlimb
Figure A2.50. Aerial photo of the backlimb of SMA. View to the North.
Four systematic fracture sets are found at locations in the backlimb. Three are
bed perpendicular and trend 110° (Set I), 045° (Set II), and 135° (Set III). A fourth set
is oblique to bedding and trends 110° (Set IV) (Fig. A2.51; Fig. A2.52). A description
of each set, as observed both in outcrop and in thin section, follows.
Bed perpendicular fractures trending 110° are 10-20 m long as compared to a
height of a few meters (equivalent to mechanical layer thickness). The fracture traces
are linear and their spacing varies from 1 to 3 m (Fig. A2.47). Their deformation mode
is difficult to determine in the field. They resemble joints at some sites and at other
sites they resemble deformation bands or display evidence of left lateral shear.
Microscopically, the fillings of Set I fractures are characterized by a decrease of grain
size, a decrease of porosity, and an increase in amount of calcite cement as compared
to the host rock (Fig. A2.53).
Set II fractures trend 045° and are bed perpendicular. Set II fractures terminate
against Set I fractures (Fig. A2.47) and, as a result, are only 2 to 5 m in length. Their
traces are linear and their spacing is approximately 1 meter. In most locations, they are
interpreted as opening mode. As seen in thin section, the fillings typically consist of
large calcite crystals without evidence of grain fracturing or crushing, which supports
242

a dilational origin (Fig. A2.54). Some instances where left-lateral shearing occurred
along Set II fractures has been documented (Fig. A2.49).
Set III fractures have a more restricted occurrence than Sets I and II (Fig.
A2.52). They trend 135°, are bed perpendicular, and contain a coarse calcite mineral
filling (Fig. A2.55) that is indicative of opening mode. The length of these fractures is
on the order of a few meters. Set III fractures terminate against both Set I and Set II
fractures.
Set IV fractures trend 110° and are parallel to Set I fractures, but are vertical and
therefore oblique rather than perpendicular to bedding (Fig. A2.57). Abutting
relationships are difficult to establish because these fractures have been observed
mainly in cross-section. These fractures are several meters long with an approximate
spacing of one meter. Most Set IV fractures are open, and lack evidence of shearing.
Microstructural examination shows that the preserved calcite filling is distinct from
that in Set II and Set III fractures (Fig. A2.56). Matrix grains at the walls of Set IV
fractures are crushed and display a preferred elongation direction, suggesting a two
phase deformation: a shearing event followed by an opening vein-filling event.
Figure A2.51. A typical backlimb stereonet showing the orientations of the four main
fracture sets found in this structural location at SMA. Set I fractures (110°) are in
green, Set II fractures (045°) are in blue, Set III fractures (135°) are in yellow, and Set
IV fractures (110°V) are in purple.
243

Site 7-8
N
Site 18
N
40
N
20
108°10'
Site 25
N
Site 72
N
Site 77a
N
38
15
40
7-8
Site 71
N
Site 80
N
Site 84
N
26
24
07
37
25
Site 78
N
Site 22
N
08
26
Site 07
N
25
23
36
44°39'
18 18
Site 08
N
71 17
72
Site 81
N
Site 76
N
35
16
116
Site 23
N
108°09'
01
80 78
15
81
22
22
Site 77b
N
32
77
76
30
Site 85
N
19
84
25
86
85
20
Site 18
N
51
Site 17
N
83
Site 83
N
21
29
42
59
Site 16
N
Site 01
N
44
Site 15
N
74
1 km
Site 59
N
48
37
Site 22
N
139
73
52
Fracture Sets
Site 74
N
Site 19
N
36
44
Set I
Set II
Set III
Set IV
minor set
47
Site 20
N
108°08'
Site 21
N
44
Site 73
N
63
Site 52
N
Figure A2.52. Backlimb fracture measurements. Phosphoria sites are labeled with
yellow numbers and dots with the corresponding stereonets to the lower left of the
DOQQ. Tensleep sites are labeled in red numbers and dots with the corresponding
stereonets to the upper right of the DOQQ. Great circles are color coded: Set I is
green, Set II is blue, Set III is yellow, and Set IV is purple. Other sets present at
measurement sites that are not one of the four main fracture sets are shown in gray.
244
44°37'
35
35

0.5 mm
Figure A2.53. Microscopic detail of a Set I (110°) fracture in the Tensleep Fm.
sandstone of the backlimb. The fracture is characterized by a zone with less porosity,
smaller quartz grains and a greater amount of calcite cement as compared to the host
rock. These fractures are suggestive of shearing as in a deformation band. From
Bellahsen et al., 2006a.
Figure A2.54. Microscopic detail of a Set II (045°) fracture in the Tensleep Fm.
sandstone of the backlimb. The fracture is characterized by distinct fracture walls and
a large-crystal calcite filling, suggestive of opening. From Bellahsen et al., 2006a.
245

Figure A2.55. Microscopic detail of a Set III (135°) fracture in the Tensleep Fm.
sandstone of the backlimb. The fracture is characterized by distinct fracture walls and
a large-crystal calcite filling, suggestive of opening. From Bellahsen et al., 2006a.
Figure A2.56. Microscopic detail of a Set IV (110°, vertical) fracture in the Tensleep
Fm. sandstone of the backlimb. The fracture is characterized by distinct fracture walls
and a large-crystal calcite filling and also has very fine grains along the fracture walls,
suggestive of shearing followed by opening. From Bellahsen et al., 2006a.
246

NE SW
1 m
Figure A2.57. Vertical Set IV fractures in the backlimb to the NW of stop 5 at site 23
in the Tensleep Fm. From Bellahsen et al., 2006a.
247

Stop 5: Backlimb fractures and shearing of Set I
Site 72 – Phosphoria limestone
Backlimb
5 minutes driving from previous stop; 10 minutes walking
9:30 – 10:00
Waypoint (UTM zone 12N): 4945401 N
0724268 E
elev. = 1310 m
Objectives
Observe and discuss shearing indicators at the outcrop.
Key Points
Field evidence for shearing of fractures exists in the form of tail cracks.
Tail cracks indicate a left-lateral sense of shear along Set I fractures.
045°
020°
090°
Figure A2.58. Site 72 pavement at stop 5. Five systematic fracture sets are found at
this outcrop. The nominal strike direction of each set is labeled in the photo: 020°,
045°, 090°, 110°, and 170°
170°
248
110°

Shearing of Set I fractures in the backlimb
Shearing along Set I fractures has been noted in the backlimb. Tail cracks along
isolated small fractures provide the most convincing evidence for shear (Figures 59 –
62). At site 72, we also see shear along fractures that measure several meters long or
more (Figure 63). These tail cracks have an average strike of 080°. All recorded tail
cracks indicate a left-lateral sense of shearing.
N
Figure A2.59. Set I fractures in the backlimb at site 72 that have sheared in a leftlateral
sense.
249
N

N
10 cm
N
10 cm
Figure A2.60. Set I fracture in the backlimb at site 72 that has sheared in a leftlateral
sense.
N
10 cm
Figure A2.61. Set I fracture in the backlimb at site 72 that has sheared in a leftlateral
sense.
250
N
10 cm

W E
Figure A2.62. Set I fractures in the backlimb at site 74 that have sheared in a leftlateral
sense. As in this photo, set I fractures that have sheared are often found in
close proximity to set I fractures that have not sheared.
251

080°
110°
Figure A2.63. Set I fractures on the order of several meters in the backlimb at site 72
that have sheared in a left-lateral sense.
252

Stop 6: Backlimb fractures
Site 81 – Phosphoria limestone; Site 22 – Tensleep sandstone (same wash)
Backlimb
10 minutes driving from previous stop
15 minutes walking
10:30 AM – 11:30 AM
Waypoint (UTM zone 12N): 4944638 N
0724648 E
elev. = 1293 m
Objectives
Discuss fracture characterization at site
Point out shearing seen in outcrop
Discuss the role of the thumb in local variation of fracture pattern
Key Points
110° vertical fractures are present in the Phosphoria pavement at this site.
Conjugate shearing along fractures striking 045° and 080° in the Tensleep
pavement constrains the stress field during shearing.
a
Figure A2.64. Photograph of stop 6 sites. We will investigate fracturing in the
Phosphoria limestone, the pavements marked in yellow in the foreground of this
photo, as well as in the Tensleep sandstone, the pavement marked in red visible at
the back of the wash seen in this photo.
253
b
a

Fracture characterization
This stop is a drainage wash where we will walk through a cross section of
Phosphoria limestone outcrop and visit a Tensleep sandstone pavement that is exposed
in the wash (Figure 64). The four typical backlimb fracture sets are observed at this
stop (Figure 65, 66, 67). After removal of bedding dips, three of these sets strike 110°,
045°, 135° respectively and are perpendicular to bedding, whereas one set strikes 110°
and is nearly vertical (not perpendicular to bedding). An additional set, striking 070°
and dipping perpendicular to bedding is also observed at this site (Figure 67).
An 070° fracture set is observed at this site and is interpreted as being similar to
Set II. As seen in Figure 38, stop 6 is located on the thumb structure. The trend of the
thumb is rotated 20° clockwise from the trend of the main fold, and we believe this
change in fold orientation affects the secondary structures that form. This will be
discussed with reference to mechanical models.
Phosphoria
Site 81
(a) (b)
N
32
Fracture Sets
Set I
Set II
Set III
Set IV
075°
Tensleep
Site 22
Figure A2.65. Stereonets for the (a) Phosphoria and (b) Tensleep pavements. Set II
(045°) fractures are relatively sparse at the outcrops (Fig. A2.66; Figs. A2.68-A2.71).
A set striking 070° to 080° is also present. In both pavements, set I (110°) fractures
are sparse (Fig. A2.66; Figs. A2.68- A2.72).
254
N
80

Phosphoria characterization:
N
1 m
135°
045°
070°
Figure A2.66. Photograph and line interpretation of fracturing of the Phosphoria
pavement at stop 6.
110°
(a) (b)
110°V
110°
110°V
110°V
Figure A2.67. Vertical set IV fractures in the backlimb at site 81 in the Phosphoria
Fm. (a) Field photograph of a cross-sectional view of the pavement. (b) Line drawing
interpretation of fractures of set I and set IV. (c) Set I and set IV fractures together in
a tilted pavement. Set IV fractures have formed with the same strike as set I, but they
are vertical in tilted bedding, dipping obliquely to the bedding interfaces, whereas Set
I fractures are bed perpendicular. (a), (b), and (c) show set IV fractures nucleating at
the terminations of set I fractures, providing evidence for the influence of set I
fractures on the formation of set IV fractures.
255
110°
110°V
110°
110°
110°V
(c)

Tensleep characterization:
N S
1 m
N S
1 m
Figures: A2.69
A2.70
Figure A2.74
Figure A2.71
Figure A2.68. (a) Photo of the majority of the stop 6 Tensleep pavement. (b) Line
interpretation of fractures. Boxes show the locations of following smaller scale
interpretations.
256

(a) (b)
080°
Figure A2.69. (a) Field photo of pavement at site 22 in the Tensleep sandstone. (b)
Line drawing of fractures in (a) which, based on abutting relations, is broken down
into stages of formation in figure A2.70.
(a) (b)
(c)
140°
N
140°
080°
Figure A2.70. Interpretation of stages of fracture growth for pavement in figure
A2.69 based on abutting relations. (a) Development of 140° fracture. (b) 080°
fractures form, in some places stopping against 140° fractures. (c) 020° fractures
form, abutting both 140° and 080° fractures.
257
N
140°
080°
140°
080°
020°
N
020°
N

Shearing at site
In the Tensleep sandstone, tail cracks are found on two fracture sets (Figure 71,
72, 73). The first set, with an average strike of 080°, has sheared in a left lateral sense
(Figure 72, 74, 75). The second set, composed of fractures that are less pronounced
than those of the 080° set, has an average strike of 050° and has sheared in a right
lateral sense (Figure 73; Figure 76). The conjugate shearing of these fracture sets
constrains the maximum compressive stress direction during the episode of
deformation that the shearing represents.
(a) (b)
Figure A2.71. (a) Field photograph and (b) interpretation of fracturing at site 22 in a
section of the Tensleep pavement outlined in figure A2.68. Note opposite sense of
shearing along the 075° - 095° fracture set (left lateral) and the 045° - 065° fracture
set (right lateral).
258

Figure A2.72. Field photograph of a sheared fracture at site 22. A fracture of strike
095° has been sheared in a left lateral sense.
Figure A2.73. Field photograph and line drawing of a sheared fracture at site 22. A
fracture of strike 060° has been sheared in a right lateral sense. In the field, this
fracture is within a meter of the fracture in figure A2.72.
259

(a) (b)
(c) (d) (e)
N
080°
N
080°
Figure A2.74. (a) Field photograph and (b) interpretation of a sheared 080° fracture
at site 22. (c) The fracture formed (d) and was sheared in a left lateral sense
producing low angle splays. (e) 020° fractures formed, abutting both the 080° fracture
and its related splay cracks. In some cases the 020° fractures may be secondary
higher angle splay cracks off of the primary splay cracks.
260
N
080°
N
080°
020°
020°

Figure A2.75. Field photo and interpretation of left lateral shear along a 070°
fracture. In this photo, mineralization can be seen both along the main fracture, where
it is outlined by light gray lines, and along the traces of some of the splay cracks.
261

20 cm
N
20 cm
Figure A2.76. Field photograph and interpretation of sheared 075° fractures, drawn
in red, found in the backlimb at site 15, indicating that the shearing seen at site 22
occurs at other locations on the fold. Motion along these features is right lateral.
262

An offset fracture provides evidence for bedding plane slip at site 22 (Figure 77).
The offset is on the order of centimeters, indicating that since the 168° fracture
developed, bedding plane slip has not been a huge factor in deformation of the
backlimb. The bedding plane motion, top to the northeast, is consistent with the
kinematics of folding.
NE
5 cm
Figure A2.77. Field photograph and interpretation of bedding plane slip at site 22.
Offset of this 168° fracture is on the order of centimeters and motion is top to the
northeast.
263
NE
5 cm

Role of thumb in fracture variation
In the backlimb, a fracture set trending 070° is observed in several locations
(Figure 78), one being the Tensleep pavement of site 22. Noticing that most of the
070° fractures are found near the thumb area, we hypothesize that the development of
these fractures is related to the influence of active faulting during the time of
formation of the thumb structure.
N
pole densities
28
26
24
22
20
18
16
14
12
10
8
6
4
2
E
fracture sets
110
045
135
110V
070
Site 08
Site 18
N
112, 19
44, 0
Site 23
N
Site 82
N
08
64, 0
95, 33
23
44°39'
Site 16
N
18
Site 15
N
228, 59
16
82
129, 52
15
108°09'
22
N
01
Site 01
19
37, 0
20
Site 22
N
32, 6
21
44°38'
1 km
Site 19
N
149, 33
Site 20
N
110, 32
108°08'
Site 21
N
Figure A2.78. Backlimb fracture data. Red great circles highlight a set of fractures
striking 080°. This set displays left lateral shearing in the thumb area. No consistent
sense of shearing can be determined further to the NW. Great circles are color coded
to show the main orientation of each fracture set. The densities of poles to each
fracture set are shown in shades of pink. Numbers to the lower right of each
stereonet indicate the total number of fracture measurements followed by the number
of fractures of the 080° set for that site.
264
44°37'
59, 0

We adopt a fault geometry from a previous study by Savage and Cooke (JSG,
2004), introducing a fault beneath the thumb, and run a mechanical model with the
boundary conditions shown in Figure 80. Assuming the 080° fractures initially formed
as tensile cracks, we observe the least compressive principal stress magnitude and the
maximum compressive principal stress direction (Figure 81) to consider their possible
spatial distribution.
In the area where the thumb structure joins the main fold, the formation of a
fracture set trending 080° may be explained by investigating the stress field
perturbation resulting from the interaction of the main fault with the thumb fault. The
shearing we see on these fractures may be a result of subsequent uplift and folding.
Ongoing field work is carefully documenting the presence and sense of slip along the
080° fracture set along the length of the fold. The existence of this fracture set further
to the NW cannot be explained by this stress analysis.
Figure A2.79. Field photo and interpretation of left lateral shear along 080° fractures.
At the bottom of this photo a second fracture is sheared.
265

horizontal
observation
grid
contraction
(-)
thumb
thrust
fault
main
thrust
fault
gravity
extension
(+)
Figure A2.80. Model setup. Projections of the two faults (geometry per Savage and
Cooke, 2004) are shown in dashed lines on the horizontal observation grid. The faults
are specified to be shear traction free and the fault walls are restricted from opening
or interpenetrating. A contraction is applied perpendicular to, and a small extension
parallel to, the main fault. Stress perturbations are observed across the horizontal
observation grid (Fig. A2.81).
(a)
Figure A2.81. (a) Large scale and (b) inset model results showing the least
compressive principal stress magnitude, an index for fracturing intensity, and the
most compressive principal stress direction, the direction in which tensile cracks are
expected to form. Solid black lines represent the projection of the faults to the
horizontal observation grid. Dotted yellow lines represent the location of the primary
and secondary fold hinges. Although faulting related stress perturbations in the thumb
area are compressive, the orientation of the stress trajectories are consistent with the
080° fracture set. These fractures would have required elevated pore pressure to
form under this stress state.
266
(b)

Lunch
Along highway 20 at rest stop next to Greybull Airport
30 minutes driving from previous stop
12:00 PM – 12:45 PM
Stop 7: Forelimb and hinge fractures
Site 12 – Tensleep sandstone
Forelimb
45 minutes driving from lunch stop
30 minutes walking
2:00 PM – 4:00 PM
Waypoint (UTM zone 12N): 4946412 N
0724547 E
elev. = 1327 m
Objectives
Discuss fracture characterization in the forelimb
Discuss shearing of set I fractures in the forelimb
Discuss bedding plane slip in the forelimb
Site specific observations and interpretations of orientations
REGROUP
Discuss fracture characterization in the hinge
Discuss shearing in the hinge
Key Points
In the forelimb, slickenlines indicate that set I fractures have been reactivated
in shear.
In the forelimb, set II fractures are sparse.
In the hinge, there is little evidence for shear along set I fractures. Set III
fractures have a wide range of strike directions.
Figure A2.82. Photo of the forelimb of SMA. View to the SSW. Note the near vertical
bedding dips.
267

Fracture characterization in the forelimb
In the forelimb, bedding dips are very steep, varying from 40° to 90° to the
northeast (Fig. A2.82). We observe one systematic fracture set within the Tensleep
sandstone, trending 110° (Fig. A2.83, sites 10 to 14 and 29 to 32; Fig. A2.84).
Additionally, non-systematic sets are locally developed (striking primarily 070° and
180°, Fig. A2.83) and are interpreted to reflect more local rather than fold-scale or
regional deformation.
N
Site 58
N
72
108°10'
Site 12
N
21
Site 11
N
29
15
Site 10
N
Site 29
N
58
30
14
36
35
44°39'
13
Site 33
N
Site 30
N
22
12
12
108°09'
Site 70
N
16
Site 14
N
10
11
11
Site 13
N
35
44°38'
10
10
Fracture Sets
31
33
32
Set I
Set II
Set III
Set IV
minor set
Site 69
N
Figure A2.83. Forelimb fracture measurements. Phosphoria sites are shown with
yellow dots and numbers with the corresponding stereonets to the lower left of the
DOQQ. Tensleep sites are shown with red dots and numbers with the corresponding
stereonets to the upper right of the DOQQ. Great circles are color coded: set I is
green, set II is blue, set III is yellow, and set IV is purple. Other sets present at
measurement sites that are not one of the four main fracture sets are shown in gray.
268
63
Site 11
N
24
Site 12
N
101
Site 31
N
39
Site 10
N
37
Site 32
N
56
37
108°08'
70
69
44°37

a)
S N
Nb planes 94
SE
b)
Nb planes35
N
N
N
Figure A2.84. Field photographs of fracture patterns on a tilted bedding surface
taken at forelimb sites (a) 12 and (b) 32. Note the abundance and small spacing of
set I fractures (striking 110°). Numerous fractures of different orientation can be
observed but are non-systematic. Stereonets show poles to fractures as measured in
the field, poles to fractures relative to horizontal bedding, and great circles
representing the average orientation of each fracture set, respectively. From
Bellahsen et al., 2006a.
N
269
set I
set I
N
N
1 m
1 m
NW

Set I fractures are linear and several meters long (Fig. A2.84). Their spacing is
on the order of a few tens of cm. In the forelimb, their mode of deformation is difficult
to determine, as different fractures within the set exhibit characteristics of either joint
or shear band morphology. In some cases, the fractures are open with or without
mineral fill, and in other cases, they have small positive relief. This latter attribute may
be related to either cementing (for the case of joints or dilational bands) or tighter
packing of grains within the fracture (for the case of deformation bands). At the
microscale, the fractures are defined by zones that contain smaller quartz grains with
more angular shapes, poorer sorting, less porosity, and smaller calcite cement crystals
than the surrounding rock (Fig. A2.85). These features are characteristic of
deformation bands (Aydin, 1978; Antonellini et al. 1995), and we interpret set I
fractures to be such brittle structures. Offset indicating a thrust sense of shearing was
obvious in the field.
zone of def.
0.5 mm
Figure A2.85. Microscopic detail of a set I fracture in the forelimb from site 13. This
fracture strikes 110° and dips perpendicular to bedding. In the deformed zone, there
is less porosity than in the surrounding matrix. There are also more angular quartz
grains, that are, for the most part, smaller in size than those within the matrix. There
is also a larger amount of calcite cement within the deformed zone. From Bellahsen
et al., 2006a.
270

Shearing (reactivation) of Set I fractures in the forelimb
Bed-normal reverse faults that strike 110° and dip 30° south are present along
the forelimb at sites 11, 13, 14, and 30 to 32 (Fig. A2.83). The faults are oblique to the
fold axis and the Laramide regional compression. The oblique striations noticeable
along the fault planes indicate oblique slip, consistent with the resolution of shear
stress from the NE directed compression onto these planes (Fig. A2.86).
SE NW
a)
d)
SE
c)
S 0
N
Nb planes34
1 m
N
b)
N
10 cm
N
NW
10 cm
Figure A2.86. Reactivated set I fractures in the forelimb at site 13. (a) Field
photograph of set I (110°) small reverse faults within the sandstone of the Tensleep
Fm. at site 13 that cut a bedding surface. (b) Cross sectional view of the photograph
in (a) showing offset bedding. (c) Close up of one fault. The slip decreases toward
fault tips. (d) Striation data (thin arrows on the fault planes) that indicate an oblique
reverse slip along the faults. The large arrows represent the inferred direction of
compression that is compatible with the striations. Stereonets show poles to fractures
as measured in the field, poles to fractures relative to horizontal bedding, and great
circles representing the average orientation of each fracture set, respectively. From
Bellahsen et al., 2006a.
271

Bedding plane slip in the forelimb
In the forelimb, tail cracks emanating from bedding surfaces (Fig. A2.87),
polished undersides of bedding surfaces (Fig. A2.88), and slickenlines on bedding
surfaces (Fig. A2.89) provide evidence for bedding plane slip. All recorded kinematic
indicators suggest that upper beds have sheared to the southwest, up and over lower
beds. This motion is consistent with the slip direction predicted by flexural slip folding
(Fig. A2.90). Bedding plane slip appears to be of greater significance in the forelimb
than in the backlimb, where the only direct evidence that has been found is a single
fracture offset on the order of centimeters (Fig. A2.77). Greater bed parallel slip in the
forelimb, where beds dip 40° to 90°, than in the backlimb, where beds dip 10° and
40°, is consistent with flexural folding theory, as regions of greater dip have greater
slip than areas of lesser dip (Fig. A2.90).
(a)
Figure A2.87. (a) Splay cracks between bedding surfaces at site 13 in the forelimb
provide evidence for bedding plane slip. Yellow lines highlight splay cracks; red
arrows show the interpreted direction of motion. (b) Splay cracks between bedding
surfaces at site 12 in the forelimb. Inset interpretation shows the orientation of a
bedding plane and related splays and the direction of shearing.
272
(b)

Figure A2.88. Polished undersides of bedding planes in the forelimb, as the one in
this photo from site 12, provide evidence for bedding plane slip as a mechanism of
folding at SMA.
(a)
10 cm
Figure A2.89. (a) Bed parallel slickenlines found in the canyon between the beds
marked by the yellow x in figure A2.91, but on the opposite side of the river. (b)
Closer view of the slickenlines in (a) with kinematic indicators interpreted. The rough
edges of the slickenlines indicate that the shearing motion was top up. The motion
was almost purely along the dip direction.
273
(b)
3 cm

Figure A2.90. Conceptual model of flexural slip folding in a multilayer showing
relative displacement on layer surfaces. Layers on the convex side of a surface slip
toward the hinge line relative to those on the concave side. The shear sense reverses
across the hinge line. The lines on the surface of the layer indicate the orientation of
slickenside lineations, and their lengths, along with the lengths of the arrows
representing slip between layers, indicate relative amounts of slip. Note that where
dip is greater, relative motion is greater. From Twiss and Moores, 1992, p. 246.
E W
Figure A2.91. Cross section through Sheep Mountain provided by the river cut. Red
arrows show the interpreted direction of bedding plane slip. Kinematic indicators
within the forelimb at SMA have provided evidence for upper beds shearing to the
southwest and up over lower beds. This motion is consistent with flexural slip folding
(Fig. A2.90). The yellow X marks the location across the river that corresponds to the
beds between which the slickenlines in figure A2.89 were found.
274
X

Fracture characterization at site
At site 12 in the forelimb, we will look at fracturing within three different
lithologies (Fig. A2.93): the Tensleep sandstone (Figs. A2.94 – A2.97), a limey
sandstone at the top of the Tensleep Fm. (Figure 98, 99), and the Phosphoria limestone
(Figs. A2.100, A2.101). North-south and east-west striking fracture sets are present in
all three lithologies (Fig. A2.95, A2.99, A2.101). A set striking 110° is present in the
sandstone and the limey sandstone, but it not widely seen in the Phosphoria at this site.
This lack of 110° measurements could be because the Phosphoria bed in which
fractures were measured is highly eroded and weathered at site 12. The 110° are found
elsewhere in the forelimb in the Phosphoria Fm. (Fig. A2.100).
Figure A2.92. Photo the forelimb of SMA. The red X marks the location of site 12.
275
X

Phosphoria
Tensleep
Limey
Layer
Amsden
Madison
Figure A2.93. Photograph of the southwest side of the wash at site 12. We will
investigate fracturing within the Tensleep sandstone, a limey sandstone layer, and
the Phosphoria limestone.
Tensleep characterization:
Figure A2.94. Photograph of the Tensleep pavement at site 12. A closer view is
shown in figure A2.96.
276

N
N = 136
+16S
+14S
+12S
+10S
+8S
+6S
+4S
+2S
E
N
N = 136
N
N = 136
Figure A2.95. Stereonets of fracture measurements made in the Tensleep Fm. at
site 12 showing: (a) poles and density of fractures as measured in the field, (b) poles
and density of fractures relative to horizontal bedding, and (c) great circles
representing the average orientation of each fracture set.
SE
1 m
110°
Figure A2.96. Photograph of the Tensleep Fm. at the top of the southeast side of the
wash at site 12. The dominant fracture set strikes 110°. Slickenlines indicate that the
set is comprised of small thrust faults.
277
NW

10 cm
Figure A2.97. (a) Field photograph of slickenlines along two echelon fractures in the
Tensleep sandstone trending 110°. (b) A closer view of the section outlined by the red
box in (a). The rough edges of the slickenlines indicate that the lower fault surface (no
longer present at the outcrop) slid obliquely into the photo in the down dip direction.
The fractures are thus small thrust faults.
278

Limey Layer characterization:
SE NW
Figure A2.98. Field photograph of a section of the limey layer that sits on top of the
Tensleep sandstone. The two main fracture sets are indicated in red. One set trends
110° and is most likely comprised of small thrust faults (note shadows beneath the
fractures in the photo above). Slickenlines or other kinematic indicators have not
been found in the field. The second set is a north-south trending set. The age
relationship between these fracture sets can not be deduced from field evidence.
N
N = 23
+10S
+8S
+6S
+4S
+2S
E
Figure A2.99. Stereonets of fracture measurements made in the limey sandstone
just above the Tensleep Fm. at site 12 showing: (a) poles and density of fractures as
measured in the field, (b) poles and density of fractures relative to horizontal bedding,
and (c) great circles representing the average orientation of each fracture set.
N
279
180°
110°
N = 23
1 m
N
N = 23

Phosphoria characterization:
SE
1 m
110°
Figure A2.100. Phosphoria flat-iron southeast of site 11 (Fig. A2.83) in which the
major fracture set strikes at 110°. This pavement is noticeable from the road along
which we will park to get to site 12.
N
N = 39
+24S
+22S
+20S
+18S
+16S
+14S
+12S
+10S
+8S
+6S
+4S
+2S
E
N
Figure A2.101. Stereonets of fracture measurements made in the Phosphoria Fm. at
site 12 showing: (a) poles and density of fractures as measured in the field, (b) poles
and density of fractures relative to horizontal bedding, and (c) great circles
representing the average orientation of each fracture set.
280
N = 39
N
NW
N = 39

Fracture characterization in the hinge
Figure A2.102. Photo of the hinge (dashed line) of SMA. View to the west. Dotted
line traces the line of maximum curvature. Note that the crest of SMA lies to the SW
of the hinge.
In the hinge, fracture measurements were made in the Amsden Fm. sandstone
beds. We observed three sets of fractures with orientations: 110°, 045°, 135° (Fig.
A2.103).
Set I fractures (trending 110°) are bed-normal. They are less numerous in the
hinge than in the limbs, and their spacing is greater. In thin section (Fig. A2.104a),
these fractures are marked by reduced grain size and porosity as compared to the host
rock, similar to the set I fractures in the forelimb (Fig. A2.85). The alignment of
elongate grains seen in thin section (Fig. A2.104a) may be indicative of shearing
during deformation. As can be noted from figure A2.103, this set is not visible at
many locations.
281

Site 39
N
Site 40
N
62
42
N
108°10'
Site 41
N
Site 43
N
53
12
Site 45
N
37
38
39
40 42
7 41
43
Site 44
N
49
26
Site 46
N
Site 51
N
26
19
Site 37
N
44°39'
4425
Site 50
N
Site 47
N
38
21
45
24
Site 5
N
Site 38
N
Site 42
N
Site 48
N
31
108°09'
49
35
36
Site 25
N
Site 49
N
46
43
40
51
Site 4b1
N
Site 3h
N
50
16
23
44°38'
1 km
Site 4b2
N
Site 3i
N
49
19
23
Site 4e
N
Site 3j
N
Fracture Sets
94
15
108°08'
Set I
Set II
Set III
Set IV
minor set
Site 6b
N
Site 6a
N
47, 48
3j
3h3i
5
4b
4e
6
Figure A2.103. Hinge fracture measurements. Amsden sites are shown with white
dots and numbers with the corresponding stereonets to the lower left of the DOQQ.
Madison sites are shown in red with the corresponding stereonets to the upper right
of the DOQQ. Great circles are color coded: Set I is green, set II is blue, set III is
yellow, and set IV is purple. Other sets present at measurement sites that are not one
of the four main fracture sets are shown in gray.
282
48
44°37'
26

Set II fractures trend 045°, are bed-normal, and have a coarse calcite fill (Fig.
A2.104b) similar to that seen in the backlimb (Fig. A2.54). These fractures are joints,
with lengths of a few meters and 1 meter spacing.
Set III fractures trend 135° (parallel to the fold axis), are bed-normal. Set III
fractures abut set II fractures in the hinge and thus postdate set II (Fig. A2.105). Set II
fractures abut set I fractures in the backlimb, so we infer that set III fractures also
postdate set I fractures.
a)
b)
0.5 mm
0.5 mm
Figure A2.104. (a) Microstructure of a set I (110°) fracture in the sandstone of the
Amsden Fm. in the hinge at site 44. The fracture is composed of crushed matrix
grains surrounded by quartz cement. (b) Microstructure of a set II (045°) fracture in
the sandstone of the Amsden Fm. in the hinge at site 41. The fracture has distinct
walls and is filled with large crystals of calcite cement. From Bellahsen et al., 2006a.
283

a)
Nb planes42
b)
N
N N
10 cm
Set II
N
Set III
Figure A2.105. Fracture pattern in the hinge. (a) Field photograph showing the
abutting relationships between set II (045°) and set III (135°) at site 39 in the
sandstone of the Amsden Fm. (b) Line drawing of the outcrop in (a) showing that 8 of
13 set III fractures terminate at set II fractures. Stereonets show poles to fractures as
measured in the field, poles to fractures relative to horizontal bedding, and great
circles representing the average orientation of each fracture set, respectively. From
Bellahsen et al., 2006a.
284

Shearing in the hinge
In the hinge, we find no conclusive evidence for shearing of set I fractures.
Often, the set III fractures have a wide dispersion in strike direction (Fig. A2.106). We
believe that in the hinge, the stress field is such that tensile fracturing is more
favorable than shearing of previously formed fractures (Bourne and Willemse, 2001).
In extreme cases, we see very intensive fracturing (Fig. A2.107), a phenomenon that is
seen only in the hinge. This supports our hypothesis that tensile fracturing plays a
much greater role in folding related deformation in the hinge than shearing does.
Site 53 N
Site 54 N
50° 60°
78
53
Site 55
N
60° 60°
56
Site 56
Figure A2.106. Stereonets from sites 53-56 in the hinge of the nose showing a wide
dispersion (50° to 60° spread) in the strike of joints that are subparallel to the trend of
the fold.
Figure A2.107. Field photograph taken in the Madison Fm. just southwest of the river
cut showing very intense fracturing. Pencil points northwest. The major fracture set
noticeable in the photo strikes subparallel to the hinge.
285
N
46

Stop 8: Fracture synthesis
Site 10
Backlimb
10 minutes driving from previous stop
15 minutes walking
4:30 PM – 5:30 PM
Waypoint (UTM zone 12N): 4945503 N
0726382 E
elev. = 1187 m
Objectives
Discuss stages of fracturing
Discuss constraints on kinematics of folding
Discuss spatial variations in fracture sets and how they may be understood
Discuss the role of shearing along set I fractures in folding
Key Points
Four stages of fracturing have been interpreted from the fracture pattern at
SMA.
Sheep Mountain formed with a fixed hinge style of folding.
Mechanical considerations help to explain variations in fracture sets.
During folding, the pre-existing set I fractures sheared in a left lateral sense in
the backlimb, were offset in thrust motion in the forelimb, and had
relatively little role in the deformation in the hinge.
Figure A2.108. Photograph of site 10, where we will synthesize the fracture data
observed over the past day and a half. The Madison Fm. is folded on the horizon in
this photo, while pavements of the Amsden, Tensleep, and Phosphoria are in the
foreground.
286

Site 07
N
Site 08
N
36
116
N
Site 23
N
86
Fracture Sets
108°10'
Set I
Set II
Set III
Set IV
minor set
Site 18
N
40
51
Site 40
N
62
41
07
Site 17
N
Site 15
N
Site 41
N
30
14
43
44
08
Site 43
N
12
Site 16
42 N
139
23
44°39'
Site 22
N
13
18
44
Site 30
N
45
36
Site 01
N
Site 14
22 N
Site 44
N
53
12
17
16
15
108°10'
22
37
01
Site 13
N
63
Site 45
26
N
11
46
19
Site 19
N
20
51
47
Site 12
35 N
Site 46
49 N
50
21
Site 11
N
101
Site 50
N
19
44°38'
1 km
Site 20 Site 21
N
N
44
10
Site 10
N
24
Site 51
24
N
31
32
52
63
47, 48
26
108°08'
Site 52
N
Site 31
N
37
Site 47
N
69
35
44°37'
Site 32
39 N
Site 48
38 N
Figure A2.109. DOQQ showing location of Tensleep and Amsden measurement
sites in the backlimb (green dots and numbers), hinge (yellow dots and numbers),
and forelimb (magenta dots and numbers) and the related stereonets. Backlimb
stereonets are to the lower left of the DOQQ, hinge stereonets are to the upper right
of the DOQQ, and forelimb stereonets are to the upper right of the hinge stereonets.
Great circles are color coded: set I is green, set II is blue, set III is yellow, and set IV
is purple. Other sets present at measurement sites that are not one of the four main
fracture sets are shown in gray.
287
49
37
Site 69
N
56

Stages of fracturing
Pre-existing fractures
Set I fractures are observed in most of the locations across the fold (Fig. A2.109)
and are systematically perpendicular to bedding. The exact nature of these fractures
remains uncertain because we do not know if they initiated in a shearing mode (e.g. as
deformation bands) or in an opening mode (as joints) and subsequently were sheared.
Fracture set I is oblique to the fold, striking approximately 25° counterclockwise
from the fold axis. Additionally, abutting relationships indicate that set I predates all
other fracture sets. Thus, we interpret set I as the oldest set and as having initiated
prior to the Laramide orogeny. A similar interpretation was made by Silliphant et al.
(2002) at Split Mountain in Utah and Hennings et al. (2000) at Oil Mountain in
Wyoming, where a fracture set of similar strike (WNW-trending) was present at
nearby locations where bed dips are approximately horizontal, as well as in each
position of the fold after rotation of the bedding to horizontal.
If the set I fractures formed as shear fractures, they would have formed oblique
to the direction of greatest compression. Taking an estimated 30° angle, the tectonic
compression would have been in a direction of either 080° or 140°. If they formed as
joints, they would be associated with a 110° directed compression. Further study is
needed to constrain the nature and origin of this fracture set, but this is not crucial for
constraining the fold growth as we view set I as having formed before folding and as
having been rotated with bedding during folding.
Early Laramide compression: onset of faulting and folding
Set II joints strike parallel to the NE-SW direction of Laramide compression
(Dickinson and Snyder, 1978; Engebretson et al., 1985; Bird, 2002) and are
perpendicular to bedding. We showed using abutting relations at some localities that
set II joints predate the fold-parallel hinge-restricted set III joints. Thus, we interpret
the set II joints as having formed in response to early Laramide compression, prior to
significant development of the fold (Fig. A2.110).
288

Joints initiating parallel to an early compressive event are documented in the
literature (Engelder and Geiser, 1980; Engelder et al., 1997). Joints with the same
orientation as set II are found in several locations in proximity to Sheep Mountain: at
Garland and Little Sand Draw in the southeast Bighorn basin (Garfield et al., 1992), at
Teapot Dome in Wyoming (Allison, 1983; Cooper et al., 1998) and in the southeast
Bighorn basin near the Tensleep fault (Allison, 1983), confirming their regional status.
At Sheep Mountain, we find set II joints in the backlimb, the hinge, and the nose.
Fractures of this set are notably absent in the forelimb (Fig. A2.109), however,
suggesting that an early structure, most likely the incipient fold or the underlying
thrust fault, may have influenced their formation (Fig. A2.110).
Fold growth: intermediate stage
In the hinge, joints striking parallel to the fold axis and dipping perpendicular to
bedding are classified as fracture set III. Their geometry and spatial location indicates
that they formed due to the curvature of bedding layers. This set could have formed at
any time during folding. Set III joints also are found in the fold nose. In the backlimb
of the nose, the joint strike changes along the fold from 135° to 160° (Fig. A2.41).
This change roughly coincides with the change in fold limb orientation, as the strike of
the layers changes from 130° to 150°, south to north (Fig. A2.4). The layers in this
area are curved and this bending can explain the rotation of the Set III joints. In the
nose hinge zone, set III is the main joint set, where it most likely initiated due to layer
bending.
Fold growth: late stage
During the late stage of fold growth, the fracture patterns in the hinge and in the
nose did not change, although some fold-parallel joints may have continued to form.
In the limbs, however, new fractures initiated and others were reactivated (Fig.
A2.110).
289

In the forelimb, we observe small thrust faults with oblique slip (Figs. A2.86,
A2.110). Given the geometric similarities to set I fractures, these structures are
interpreted as reactivated set I fractures. They are reverse faults that dip approximately
30° from the horizontal, perpendicular to bedding. Thus, we infer that the reactivation
occurred late in the fold evolution. Incorporated into this interpretation is the
assumption that the set I fractures rotated passively with the strata and were
reactivated when their dip reached a value low enough to allow a thrust offset along
them. This mechanism implies a horizontal greatest compressive stress striking
perpendicular to the fold and a vertical least compressive stress.
In the backlimb, we observed a second late fracture set, set IV, which is
composed of vertical joints striking 110° (Figs. A2.57, A2.109 and A2.110). They are
interpreted as late due to their vertical dip that is oblique to bedding. We suggest that
this joint set was influenced by the presence of the earlier set I fractures, because they
strike oblique to the fold axis and parallel to the set I fractures. Such influence by pre-
existing fractures has been suggested recently in Guiton et al. (2003a, 2003b) and
Bergbauer and Pollard (2004).
290

c)
Set I
d)
a)
b)
Set I
Set III
Set III
Set II
N E
Set IV
Fracture Sets
Set I
Set II
Set III
Set IV
Figure A2.110. Schematic representation of the fracturing history at SMA. (a) Set I
(110°) fractures form prior to the Laramide compression in horizontal beds. (b) Set II
(045°) joints are initiated as early compression-parallel fractures. (c) Set III (135°)
joints develop in the hinge during folding. (d) Vertical set IV (110°) joints initiate
parallel to set I fractures in the backlimb, while in the forelimb, set I fractures are
reactivated as reverse faults during a late stage of (or posterior to) folding. After
Bellahsen et al., 2006a.
291

Constraints on fold kinematics
Fixed hinge
At Elk Basin Anticline, a basement-cored fold in Montana and Wyoming, fold
perpendicular fractures comprise only a minor fracture set, and they are interpreted as
a late set formed in response to an axis-parallel stretching (Gross and Engelder, 1995;
Gross et al., 1998; Fig. A2.111). A mechanism for this type of joint formation is
curvature related to a doubly-plunging, non cylindrical fold geometry (Fischer and
Wilkerson, 2000). For such a mechanism, rather than a regional deformation, to be an
explanation for set II fractures at Sheep Mountain anticline, the present-day fold shape
(quite cylindrical in its central part) would have had to have evolved from a more non-
cylindrical shape. However, a perturbation in the strike of set II fractures occurs only
in the present-day fold nose, and similar perturbations, which would represent
previous locations of the fold nose, are not found. Therefore, we infer that the fold
nose did not migrate laterally, and the early fold length was very similar to the current
fold length.
The localized occurence of set III joints is also consistent with a fixed-hinge
model of fold evolution (Allmendinger, 1982; Fischer et al., 1992; Fisher and
Anastasio, 1994; McConnell, 1994). Had the hinge migrated, we would expect to find
fold-parallel joints elsewhere. The hinge is very tight, so it is unlikely that the
observed hinge curvature could have been accommodated without joint formation.
Figure A2.111. Figure showing that hinge perpendicular joints may open during
folding due to along hinge stretching. This stretching can be the result of a doubly
plunging anticline. Modified from Gross et al., 1998.
292

Understanding spatial variations
Set III fractures
We find some fold-parallel set III joints in the backlimb (Figs. A2.109, A2.110
sites 17 to 20). These joints might be related to areas where layer curvature is greater.
To test this hypothesis, we computed a curvature map (Fig. A2.112) to assess the
relative curvature of various fold locations. Forster et al. (1996) published a structure
contour map of a reference horizon at the base of the Jurassic Sundance Fm. We
assume that changes in formation thicknesses across the fold between the Upper
Carboniferous Amsden Fm. and the Sundance (about 300m) are not substantial and
therefore that this map can be used to study layers that are stratigraphically below the
Sundance from the Amsden to the Permian Phosphoria Fm. We digitized the structure
contour map and calculated the maximum curvature across the resulting three
dimensional surface using gOcad, a 3D geomodeling software program (Mallet, 2002).
The algorithm for maximum curvature selects the prinicipal curvature with the greater
absolute value and plots that curvature with its sign. Thus, positive curvature (concave
upward) may be differentiated from negative curvature (concave downward). In figure
A2.112, warm colors have positive curvature and mark synclinal hinges, whereas cool
colors have negative curvature and mark anticlinal hinges.
The darkening of the blue colors of the curvature plot toward the north along the
fold axis reflects the tightening of the fold in this direction. Looking along lines
perpendicular to the fold hinge, note that in the northwest, zero or near zero curvature
values are reached just a short distance from the fold hinge, whereas further southeast,
this distance is greater. The set III joints are more common toward the southeast, the
direction in which the fold shape changes from a tight to a more rounded profile (Fig.
A2.112). This supports our hypothesis that there is a link between curvature and the
existence of set III joints. Where the hinge is tight in the north, the limbs are
approximately planar with lesser curvature and set III is confined to the hinge.
293

Hinge
Backlimb
curvature (m -1 )
x10 -3
6
4
2
0
-2
-4
-6
Hinge
Subsidiary fold
1 km
Forelimb
N
Syncline
Figure A2.112. Curvature map of SMA calculated from the structure contour map in
Forster et al., (1996). Reds represent synclinal folding and blues represent anticlinal
folding. Black contour traces the line of zero curvature. From Bellahsen et al., 2006a
294

Set II fractures
We consider a regional deformation as the most likely formation mechanism for
set II fractures and suggest that the paucity of set II joints in the forelimb is due to a
stress perturbation resulting from slip on the underlying basement thrust fault. To test
this hypothesis, we use Poly3D (Thomas, 1993), a 3D BEM program based on linear
elasticity, and forward model for the stress perturbation resulting from a single slip
event along the underlying thrust fault. A specified remote contraction is applied
perpendicular to the strike of the underlying fault to represent the prevailing tectonic
deformation during early Laramide time. The model setup is illustrated in figure
A2.113.
vertical
observation
grid
gravity
thrust fault
contraction
(-)
extension
(+)
Remote strain boundary conditions:
εy = - 1%, εx = 0.1%
Local fault plane boundary conditions:
tx = 0, ty = 0, bz = 0
Figure A2.113. Model geometry. A vertical plane perpendicular to fault strike and
located at its center is designated as an observation grid. The arrows represent the
remote extension and contraction. Modified from Bellahsen et al., 2006b.
The model space is homogeneous, but we want to observe stresses and
displacements at a level that correlates to the Tensleep sandstone in which the majority
of our field measurements were taken. At Laramide time, the sediment pile on top of
granitic basement was approximately 3 km thick (Fig. A2.114). The vertical
separation between early Laramide layers and the Tensleep Formation is
approximately 2200 m (Fig. A2.114). To be able to compare model results with
outcrop interpretations, we observe stresses and displacements at 2200m.
295

Model results indicate that at a depth equivalent to the Tensleep, near the upper
tip line in the model fault footwall, slip creates a zone of tensile stress (Fig. A2.114),
while in the hanging wall, a zone of compression. To relate these perturbations to
various structural positions on the fold (i.e. backlimb, hinge or forelimb), we plot the
vertical displacements across the layer (Fig. A2.114a). Figure A2.114a shows the
development of the early fold with the backlimb, hinge, and forelimb readily
distinguishable. Correlating the location of the forelimb to the stress perturbation
(black rectangle, Fig. A2.114b), we find that it coincides with the zone of enhanced
compression in the fault hanging wall. In this zone, the formation of joints striking
parallel to the maximum compression direction would be inhibited. In the field, we
observed a similar zone in the forelimb of SMA, where joints parallel to the
compression direction (set II) are sparse. If these two zones correspond to each other
(Fig. A2.115), we can conclude that the forelimb was located above the fault and in
the hanging wall of the fault in the early stages of the folding.
(a)
(b)
tension
(+)
compression
(-)
vert. displ. (m)
300
150
0
0 500
1000 1500 2000 2500
3000 m
MPa
50
- 150
- 350
- 550
- 750
horizontal distance
296

Figure A2.114 (opposite page). (a) Vertical displacement profile across the fold at the
depth of the Tensleep Fm. at early Laramide time. (b) Least compressive principal
stress magnitude across the observation grid. This stress component trends
perpendicular to the grid and controls the formation of new joints striking parallel to
the grid, the orientation of the set II fractures. A zone of enhanced compressive stress
is located just behind the upper fault tip line in the hanging wall (compressive
quadrant, black rectangle) at the paleodepth of the Tensleep Fm. The model space is
homogeneous and the layering shown on the observation grid is solely to point out
the depth of the Tensleep and the depth of the sediment-basement contact at
Laramide time. Modified from Bellahsen et al., 2006b.
σ 1
σ 2
σ 3
backlimb forelimb
σ 1
σ 2
σ 3
Figure A2.115. Forward modeled effective stresses in the backlimb and forelimb can
be linked to the heterogeneity in set II fracture formation observed in the field.
297

This spatial constraint on the location of the forelimb relative to the thrust fault
enables us to describe the folding process in more detail. In the case of SMA, the
basement fault most likely formed prior to the Laramide orogeny (Fig. A2.116a)
(Stanton and Erslev, 2004; Bellahsen et al., 2006a). With the onset of NE
compression, the fault was reactivated (Fig. A2.116b), perturbing the stress field in its
vicinity. With ongoing regional contraction, the fold developed above the fault, within
the hanging wall, because the forelimb was located above the fault before folding
(Figs. A2.116c, A2.116d). Seismic lines (Stanton and Erslev, 2004; Stone, personal
communication) in close proximity to the fold show that the fold is above the fault, as
in other basement fault-cored anticlines (Stone, 1993) and not ahead of the upper tip
line, as in the forced fold model.
a)
Pre-existing
fault
cover
basement
c) d)
b)
future forelimb
fixed hinge
Figure A2.116. Conceptual model for basement fault-cored anticlines. a) Pre-
Laramide configuration. The thrust fault is inherited. b) Onset of Laramide faulting.
The basement starts deforming, as does the cover. Both are affected by the stress
field perturbation resulting from the superposition of the slip related stresses and the
shortening related stresses. c) Fold initiation and d) fold amplification with a fixed
hinge and rotating limbs. The basement hanging wall block is internally deformed.
The fault is represented as propagating through the cover. From Bellahsen et al.,
2006b.
298

Role of shearing of set I fractures
Set I fractures played a role in the folding deformation at Sheep Mountain in
both the forelimb (Figs. A2.84, A2.86, A2.97, A2.100) and the backlimb (Figs. A2.58
– A2.63), but little evidence has been found to suggest that set I fractures were
reactivated to relieve folding related stresses in the hinge. Instead, in the hinge, we see
dispersion in the strike direction of set III hinge parallel fractures (Figs. A2.106,
A2.107).
In the forelimb, set I fractures were reactivated as thrust faults after having been
rotated with bedding to a shallow angle (Fig. A2.117). In the backlimb, shearing of set
I fractures is consistent with the kinematics of hinge perpendicular compression and
folding of the anticline. The set I fractures are oriented obliquely to the inferred
maximum compression direction, so left-lateral shearing results (Fig. A2.118, stage 2).
In the hinge, no shearing of set I fractures has been recorded.
pre-folding configuration
late-folding
configuration
Figure A2.117. Conceptual model for development of set IR fractures in the forelimb
of SMA.
Perhaps this lack of shearing in the hinge, along with the recorded higher
intensity of fracturing in the hinge and the disperse set III fracture orientations can
help to constrain the state of stress throughout the fold. As detailed by Bourne and
Willemse (2001), whether a rock will fail in tension or shear depends upon where the
299

Figure A2.118. Conceptual model for left-lateral shearing of set I fractures in the
backlimb and development of set III fractures in the hinge with a wide range of
orientations.
300

Mohr Circle for the stress state intersects the failure envelope (Fig. A2.119). In the
locations where we see shearing of set I fractures, we infer that the Mohr circle was
closer to the shear failure portion of the envelope. This implies a relatively greater
principal stress difference. In the hinge, where the highest curvature values exist, the
lack of shearing related kinematic indicators suggests that the stress state was closer to
the tensile failure portion of the envelope during folding. Rather than shear occurring
along pre-existing fractures, new joints formed (Fig. A2.118, stage 4), and this implies
a relatively lesser principal stress difference.
Figure A2.119. Proximity of a stress state to brittle failure is represented by the
smallest stress increment required to reach that stress state from either the shear part
of the brittle failure envelope, χshear or the tensile part of the brittle failure envelope,
χtensile. [Reprinted from Journal of Structural Geology, v. 23., Bourne, S. J. and E. J.
M. Willemse, Elastic stress control on the pattern of tensile fracturing around a small
fault network at Nash Point, UK, p. 1753-1770, Copyright 2001, with permission from
Elsevier].
301

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