3D beam prestack depth migration - PGS

A Publication of Petroleum Geo-Services Vol. 8 No. 8
August 2008
3D beam prestack depth migration with examples
from around the world
Introduction
In 1999 AGS specialized in 2D seismic depth
processing. It was commercially necessary to progress
into 3D depth migration, but it seemed unrealistic to utilize
Kirchhoff or wave equation methods and be able to
compete with large companies, their compute resources,
and their economies of scale. Consequently, it was
decided to attempt the commercial development of an
alternative approach that would hopefully provide similar or
improved technical quality, but with capital outlay and
economics that were more appropriate to a small
company. A very straightforward approach referred to as
Beam Pre-Stack Depth Migration (BPSDM) was adopted,
this even having its origins in work performed as long ago
as the 1930’s by Frank Rieber. The anticipated merits of
BPSDM were overall simplicity, economy, flexibility and
future development possibilities. The unknowns were the
migration accuracy and quality achievable. BPSDM was
essentially developed independently, but aspects of it
obviously are related to much recently published work on
other beam migrations and stereotomography
Method
The input seismic data is assumed to have been
prepared with conventional preprocessing. Thereafter,
BPSDM consists of three important steps: decomposition,
migration, and reconstruction.
Decomposition
A multidimensional slant stack decomposes the data
into a basis of seismic wavelets, from 100-200 ms in time
duration, within local surface spatial superbins each being
centered on a uniform Cartesian grid of CDP xline and
inline co-ordinates (x,y) and S-R half offset co-ordinates
(hx,hy). Each wavelet should thus have a center location
(x,y,hx,hy,t) and determined dip components (dt/dx, dt/dy,
dt/dhx, dt/dhy), these contributing to the properties of the
wavelet. For each spatial axis the grid interval between
superbin centers is typically around 200 to 400 m, and the
superbin width is chosen somewhat larger in order to have
overlap.
Summary
In 1999 AGS (now part of PGS) started
development of Beam Pre-Stack Depth Migration
(BPSDM). The anticipated merits were simplicity,
economy, flexibility and future development
possibilities. The unknowns were the migration
accuracy and quality.
BPSDM consists of three important steps;
decomposition, migration, and reconstruction.
Decomposition is a multidimensional slant stack
which decomposes the data into a basis of seismic
wavelets. Each wavelet has a center location and
determined dip components. These contribute to
the properties of the wavelet. Migration computes
a point to point mapping between the unmigrated
and the migrated wavelet centers. Reconstruction
composites each wavelet into its local region in
migrated space and outputs seismic depth traces.
Initial results in 1999 were poor, but with
further development BPSBM proved to have some
superior aspects to Kirchhoff and wave equation
migration. The quality and flexibility of BPSDM
includes capability for handling steep and
overturned dips, demultiple options, the ability to
reject coherent noise, incorporation of anisotropy,
speed for migration iteration, calculation of residual
3D RNMO, extension to multi- and wide azimuth
data acquisition, and the capacity to handle land and
marine data. Data examples from around the world
illustrate the quality and flexibility of the technique.
Figure 1 is a variable density display of typical seismic
trace behavior in time and one spatial dimension, x. It is
evident that these data are a superposition of several
wavelets with both positive and negative dips
components, dt/dx, all of which can be estimated with a
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TechLink August 2008 Page 2
Method
Continued from Page 1
slant stack method. A schematic representation of one
such wavelet with time dip, px=dt/dx, is displayed in
Figure 2.
It is significant to note that this decomposition
performs a desirable uniform spatial gridding or binning of
the data, the result being essentially independent of minor
variations in the data acquisition geometry (minimized
acquisition footprint). Also, the individual wavelets should
not exhibit any aliasing effects, even for very steep time
dips. Thus, the BPSDM procedure bypasses the aliasing
issues that are a very significant problem in both Kirchhoff
and downward continuation, wave equation migration.
Note also that the wavelet amplitude is preserved, a vital
issue for any future AVO or inversion operations, and that
some random noise suppression is achieved at this early
stage.
Figure 1: Variable density display of
typical data in time and a single
spatial dimension, x..
Figure 2: Schematic
representation of a single
wavelet in time and a single
spatial dimension, x.
Migration
Given a wavelet’s center (x,y,hx,hy,t) and dip
components (dt/dx, dt/dy, dt/dhx, dt/dhy), plus a current
earth velocity model, it is possible to 3D ray trace from
source and receiver locations and determine some
corresponding “best” reflector migration location
(xmig,ymig,zmig), together with ancillary properties such
as reflector dip, reflector azimuth, angle of incidence at
reflector, shot and receiver wave front curvatures, local
interval velocity, etc. It is of paramount significance that a
point to point mapping exists between the unmigrated
and the migrated center of each seismic wavelet. This
means that the seismic wavelet decomposition forms a
basis in the migrated domain as well as the unmigrated
domain, the mapping function being the earth velocity
model.
Note that migration is applied directly to each coherent
wavelet without creating a travel time table in Cartesian
coordinates. This bypasses the need to select a single
raypath when gridding raypaths; the source of the multipath
traveltime problem encountered in Kirchhoff
migration. Also, note that BPSDM does not suffer from the
severe steep dip and turning wave limitations of typical
wave equation migrations. Economics often force aperture
limits in Kirchhoff migration and can result in not imaging
steep dips and turning waves. The BPSDM independent
point to point mapping of each wavelet clearly has no
migration aperture issue.
Figure 3: Schematic representation of the point to point mapping
between a wavelet’s recording parameters (surface location, dip
components, and time) and its migrated reflector location and dip.
Figure 3 is a schematic for an ideal primary turning
wave reflection, where the ray paths with estimated dips
at the shot and receiver intersect at the associated
reflector at the correct two way traveltime. However, since
shot and receiver rays corresponding to a wavelet’s
properties normally will not intersect to give a model two
way traveltime exactly equal to the wavelet center time, t,
it is also sensible to estimate a focusing quality factor, q.
This is an additional valuable wavelet property. If the
wavelet is truly a primary reflection then q is representative
of traveltime discrepancy along the computed ray path, and
can be included in a tomography method. Alternatively, a
poor focus value can be used to recognize a multiple
reflection wavelet, or a converted wave event with its
NMO offset dip (dt/dhx, dt/dhy) significantly different from
that of a corresponding primary reflection.
In summary, for a current earth velocity model the
migration operation determines and stores reflector
location and associated properties along with each wavelet
and its surface location and dip parameters. This stored
point to point mapping between unmigrated and
migrated space is very valuable, and is not directly available
with the Kirchhoff and wave equation methods.
Reconstruction
A seismic wavelet can easily contributed to its local
region in either unmigrated space or migrated space. In
particular, the local nature of a wavelet and its associated
migration properties enables a very limited wavefront
Kirchhoff migration contribution to a 3D migrated depth
volume (x,y,z) for the common offset (hx,hy). This yields
certain improved signal-to-noise characteristics over
normal full wavefront Kirchhoff migration, where data from

Page 3 A Publication of Petroleum Geo-Services
millions of seismic traces do not necessarily cancel in an
output quiet reflector area, such as salt.
Figure 4 illustrates the contribution to the migrated
reflector space of the wavelet depicted in the point to
point mapping in Figure 3.
Figure 4: A single wavelet contributes to a local region of the output
migrated depth volume.
Relevant ray path spreading properties enable
amplitude correction of each primary reflection for its
actual propagation path through the interval velocity
model. This facilitates later AVO or inversion operations.
Note that any wavelet can be excluded or weighted
down based upon a variety of individual or joint criteria for
the wavelet properties, for example the quality of focus,
thereby providing a powerful flexibility for coherent noise
reduction in the unmigrated or the depth migrated data.
Inline, xline or full volumes are output on appropriate grids,
both for quality control and for residual moveout analysis
on common reflection point depth gathers.
The residual moveout field is interpreted either
manually or automatically, depending on the complexity of
the data. This information is supplied to a tomography
routine and enables the updating of the earth interval
velocity model. The migration, reconstruction, and
tomography steps are then iterated until a satisfactory
velocity model is developed for which the common
reflection point depth gathers are adequately flat. The final
common offset volumes are reconstructed on an
appropriately fine (x,y,z) grid. Since this operation is
reasonably economic, it is normal to output volumes over
the entire (x,y) common mid-point range of the input data.
Results
Initial results within 1999 were poor, but after one or
two years of further development proved to be superior to
Kirchhoff and wave equation results in several respects.
The quality and flexibility of BPSDM has been illustrated in
many ways, such as its unique capability for handling steep
and overturned dip, its demultiple options, the ability to
handle extraneous coherent noise, the adaptability to
anisotropic velocity earth models, its speed for iteration
and the calculation of residual 3D RNMO for input to 3D
tomography, the extension to multi- and wide azimuth data
acquisition, and the capacity to handle both land and
marine data.
Figure 5 is a comparison of Kirchhoff time migration
and BPSDM applied to data from the Beaufort Sea (both
plotted in time to help direct comparison). BPSDM was
very successful at imaging steep dips where Kirchhoff
PSTM had failed. Based on these images the structure is
interpreted as an inversion anticline, not a shale diapir. The
interpretation is thus utterly different.
Figure 6 shows CRP offset gathers and stacks created
using BPSDM on data from the KG-D4 basin from
southwest India. After several iterations of migration and
Continued on next page
Figure 5: Kirchhoff prestack time migration (left) and BPSDM (right) on Beaufort Sea data. The beam migration imaged steep and overturned events.

TechLink August 2008 Page 4
Results
Continued from Page 3
tomography there was still residual moveout due to
unresolved local velocity anomalies associated with a
rugose water bottom, slump sequences, and a strong
velocity increase at the basement. After our efforts to solve
the problem using velocity estimation and depth migration,
further improvement was achieved using a non-hyperbolic
residual moveout. The migrated offset gathers output by
BPSDM allowed the flexibility required to address these
data problems.
Figure 7 is a line processed with BPSDM in the central
Gulf of Mexico. Several known fields are indicated on this
cross section. Play 1 appears as a high amplitude that
correlates with structure. Subsalt play 2 and the recent
discovery are truncations against the base salt. There are
some interesting large amplitudes near the Play 2. Play 3
appears as high amplitudes associated with an anticline, a
fault, and pinchouts on the top salt. Subsalt Play 4 is
associated with truncations on the base salt near the right
edge of the section.
Figure 6: BPSDM from the KG-D4 basin, southwest of India. The stack and migrated gathers show residual moveout due to local unresolved velocity
anomalies associated with a rugose water bottom and slump sequences. Residual moveout can be used to flatten the gathers and improve the
stack.
Figure 7: BPSDM of a line from the deep water Gulf of Mexico through proven hydrocarbon fields and a recent discovery.

Page 5 A Publication of Petroleum Geo-Services
Figures 8 through 12 show
BPSDM results from southwest India.
Volcanics were expected in this area
and a strong velocity increase was
identified below an unconformity
identified in Figure 8. Seismic
analyses indicate the velocity is
significantly faster below the
unconformity, but not fast enough to
be basalt. Depth migration velocity of
approximately 4000 m/s indicates this
is potentially the top of a carbonate
zone. Deeper, potentially volcanic
Figure 8: BPSDM of a line from southwest India. Velocity analysis indicates the unconformity is
structures are identified on the inline
and cross-line sections (Figures 8 and
potentially the top of a carbonate zone. There are deeper, potentially volcanic structures.
9). The depth structure map of the horizon we identified as
potentially the top of a carbonate zone (Figure 10) shows
several faults or channels. One fault or channel shows
offset when it crosses another fault. A structural high
appears above the volcanics identified in Figures 8 and 9.
Amplitude extraction maps on the right half of the
structure map in Figure 10 are shown in Figure 11. The plot
on the left is the amplitude 112 m above the horizon and
the one on the right is 114 m above the horizons. Two
interesting high amplitude anomalies are labeled Amp 1
and Amp 2. These amplitudes are high on structure (see
Figure 12). Current water depth (1500 m) is very deep for
reefs. Perhaps the area was much shallower water at the
time of deposition and these amplitudes are hydrocarbon
indicators.
Continued on next page
Figure 9: Xline section from southwest India project with
unconformity and volcanic structures identified.
Figure 10: Potential Top of Carbonate Depth Structure Map from the southwest India project. Several faults or channels are identified. One fault or
channel shows offset when it crosses another fault. A structural high appears above the volcanics identified in Figures 8 and 9.

TechLink August 2008 Page 6
Results
Continued from Page 5
Figure 13 shows the BPSDM
result from a line in the Arabian Sea.
The depth migrated section is corendered
with the velocity estimated
with depth migration tomography.
Blocks can be seen that slip down a
large extensional fault. The blocks
detach producing a series of toe
thrusts. The low velocity (blue and
green) beneath the toe thrusts may
indicate shale.
Conclusions
BPSDM does have the anticipated
merits of simplicity, economy,
flexibility, and future development
possibilities. Migrated images have
excellent accuracy and quality,
especially in areas of poor signal-tonoise
ratio and steep dip. BPSDM’s
relative economy makes it an excellent
velocity estimation tool to use prior to
other more compute intensive depth
migration methods.
Acknowledgements
The authors thank Devon Canada
for permission to show the Beaufort
Sea data, PGS’ MultiClient group for
permission to show the deep water
Gulf of Mexico data, Reliance for
permission to show the KG-D4, southwest India, and
Arabian Sea data. We also thank the AGS data processing
and interpretation staff for their truly dedicated efforts
applying BPSDM to numerous datasets.
London
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© 2008 Petroleum Geo-Services. All Rights Reserved
Figure 11: Amplitude extraction maps on the right half of the structure map in Figure 10.
Amplitude extracted 112 m above the depth mapped in Figure 10 (left plot) shows a high
amplitude anomaly in blue labeled Amp 1. A similar high amplitude on the amplitude extracted
144 m above the horizon depth (right plot) is labeled Amp 2. These amplitudes are high on
structure (see Figure 12). Current water depth (1500 m) is very deep for reefs. Perhaps the area
was much shallower water at the time of deposition and these amplitudes are hydrocarbon
indicators.
Figure 12: Cross-line through the amplitude anomalies identified on Figure 11. These amplitude
anomalies are high on structure and there is interesting signal attenuation below the high
amplitudes.
Figure 13: BPSDM from the Arabian Sea. The depth migrated section
is co rendered with the velocity estimated with depth migration
tomography. Blocks can be seen that slip down a large extensional
fault. The blocks detach producing a series of toe thrusts. The low
velocity (blue and green) beneath the toe thrusts may indicate shale.
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