P. Schmoldt, PhD - MTNet - DIAS

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List of Symbols Symbol SI unit Denotation ɛ Ω or log(Ωm) model misfit, i.e. the difference between ε = ε0 · εr ε0 εr As Vm −12 As 8.854 · 10 Vm · model response and measured data electric permittivity electric permittivity of the vacuum relative electric permittivity ε∗ · breakdown point of an estimator η C electric charge density m3 ηB (Ωm) 1/2 Bahr parameter: Descriptiveness of MT tensor f Hz = by superimposed model 1 G s · frequency Transformation matrix between model and observed data h m (or km) height of a body H Hx, Hy, Hz I A m A m A magnetising field elements of H in Cartesian coordinates current I1 − I2 m s2 I3 − I7 J · A Weaver tensor invariants Weaver tensor invariants electric current density J f m2 A m2 electric current density of free charges k k κ 1 m 1 m · (Maxwellian term) horizontal wave number norm of horizontal wave number Swift skew Λ m (or km) adjustment distance / horizontal skin depth λp m (or km) ellipticity of Caldwell phase tensor L (i) m (or km) length (of body i) M (i) · induction number (of body i) m Ωm or log(Ωm) subsurface model data µ = µ0 · µr µ0 V s Am −7 V s 4π · 10 Am V s magnetic permeability magnetic permeability of the vacuum relative magnetic permeability µr Am µB (Ωm) −1/2 Bahr parameter: Phase difference in the MT tensor P · distortion of the electric field Pxx, Pxy, Pyx, Pyy elements of P in Cartesian coordinates φ · Porosity (of a rock) Continued on Next Page. . . xxiv
Symbol SI unit Denotation φ · phase (of the electric impedance) Φ · Caldwell phase tensor Φ11, Φ12, Φ21, Φ22 elements of Φ Φ1 − Φ4 · Caldwell parameters (coordinate independent) π · Ludolf’s number ψ · error function Qh · distortion of the horizontal magnetic field Qxx, Qxy, Qyx, Qyy Qz Qzx, Qzy R · · · Ω (= elements of Qh in Cartesian coordinates distortion of the vertical magnetic field elements of Qz in Cartesian coordinates 1 R ) σ · resistance (integrated electric resistivity) rotation matrix Rdd · error covariance matrix S xy · cross-spectral density Qe C mn QW ρ · Ωm (= electric charge density Weaver tensor invariant Vm ρa S ) A Ωm S (= electric resistivity apparent electric resistivity 1 S 1 ) Ω Ωm conductance (integrated electric conductivity) sum of diagonal elements / trace (of the impedance tensor) S 2 Ωm sum of off-diagonal elements (of the sD · impedance tensor) telluric anisotropic distortion σ ΣB S 1 (= ) m Ωm · electric conductivity Bahr parameter: Two-dimensionality T s period T · geomagnetic transfer function/tipper Tx, Ty · elements of T in Cartesian coordinates t s time τ S m2 , S m3 , Ω, or Ω m Smoothness parameter in inversion, e.g. ∇σ, ∇2σ, ∇ρ, ∇2ρ, or logarithmic values tD · telluric twist distortion Θ ° or rad angle v ω x, y, z m s 1 s m (or km) velocity angular frequency Cartesian coordinates (z pos. downwards) Continued on Next Page. . . xxv
Page 1: Multidimensional isotropic and anis
Page 4 and 5: Contents 2.3. Deviation from plane
Page 6 and 7: Contents 8.3. Inversion of 3D model
Page 9 and 10: List of Figures 2.1. Amplitude of t
Page 11 and 12: List of Figures 4.17. Visual repres
Page 13 and 14: List of Figures 8.2. Ambient noise
Page 15 and 16: List of Figures 10.10.RMS misfit va
Page 17: List of Figures A.15.Result of anis
Page 20 and 21: List of Tables xviii 5.5. Parameter
Page 22 and 23: List of Acronyms FE finite element
Page 25: List of Symbols Below is a list of
Page 29: Abstract The Tajo Basin and Betic C
Page 32 and 33: Publications Poster presentations x
Page 34 and 35: Acknowledgements Team, namely Colin
Page 37 and 38: Introduction 1 The Iberian Peninsul
Page 39 and 40: ections from enhanced one-dimension
Page 41: Part I Theoretical background of ma
Page 44 and 45: 2. Sources for magnetotelluric reco
Page 67 and 68: Mathematical description of electro
Page 69 and 70: yields 3.2. Deriving magnetotelluri
Page 71 and 72: 3.2. Deriving magnetotelluric param
Page 73 and 74: 3.3. Magnetotelluric induction area
Page 75 and 76: Depth d s d 1 d 2 d n-2 d n-1 t 1 t
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3.4. Boundary conditions materials
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3.5. The influence of electric perm
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Distortion of magnetotelluric data
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4.1. Types of distortion Fig. 4.1.:
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J s 0 s 0 4.1. Types of distortion
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Scale Type Terminology Example Atom
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4.1. Types of distortion the use of
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4.2. Dimensionality Fig. 4.12.: The
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1D 2D local 3D/1D 3D/2D regional 4.
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4.3. General mathematical represent
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4.4. Removal of distortion effects
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Parameter Geoelectrical application
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4.4.5. Caldwell-Bibby-Brown phase t
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Method Applicability Swift angle 2D
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5. Earth’s properties observable
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6. Using magnetotellurics to gain i
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Part II Geology of the study area I
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7. Geology of the Iberian Peninsula
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Recovering a synthetic 3D subsurfac
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direction direction Depth: 12 - 30
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8.2. Generating synthetic 3D model
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Distance from the centre of the mes
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3D N45W 3D-crust TE Rho TE Phi Peri
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8.3. Inversion of 3D model data sch
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Model variation RMS misfit Optimal
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Profile: 3D-crust (TM-only) Depth (
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Parameter Value 8.3. Inversion of 3
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Depth (km) 10 -2 10 -1 10 0 10 1 10
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Depth (km) 10 -2 10 -1 10 0 10 1 10
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Step 1: Isotropic 2D inversion Step
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8.3. Inversion of 3D model data par
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8.4. Summary and conclusions bution
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Regularisation order Smoothing para
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S N 1% 0 Depth (km) 3% Depth (km) 1
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9.1. Profile location Data collecti
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Location (degrees) Recording period
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Geological region Stations Geologic
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9.4. Segregation of data acquired w
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Phase (degrees) 135 90 45 0 Z xy -4
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0 km 10 km 30 km 100 km 300 km Dept
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Pseudo-sections crustal strike dire
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9.8. Analysis of vertical magnetic
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9.8. Analysis of vertical magnetic
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10. Data inversion WinGLink softwar
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a (horizontal smoothing) 10. Data i
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10. Data inversion Short period ran
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10. Data inversion TM+TE Depth (km)
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10. Data inversion (a) Constrained
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10. Data inversion the model into u
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10. Data inversion Depth (km) S N 0
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Depth (km) 10. Data inversion S N 0
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10. Data inversion Group velocity m
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10. Data inversion ductivity of thi
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10. Data inversion Shtrikman upper
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10. Data inversion in the lithosphe
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10. Data inversion isotropic 2D lay
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10. Data inversion Depth (km) Depth
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10. Data inversion tigation is usua
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Depth (km) Depth (km) 10. Data inve
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Modelled Observed Modelled Observed
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Depth (km) 10. Data inversion 0 30
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10. Data inversion Depth off LAB (k
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10. Data inversion Depth (km) S 0 5
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10. Data inversion 10.3. Summary an
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10. Data inversion owing to availab
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11 Summary and conclusions The key
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11.2. PICASSO Phase I investigation
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A. Appendix Eocene 54 Ma 42 Ma 36 M
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A. Appendix A.2. Auxiliary informat
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A. Appendix 292 Fig. A.3.: Issues i
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A. Appendix A.2.4. Computation time
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296 3D-mantle profile Inversion res
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298 07-centre profile The profile 0
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300 3D-crust profile The profile 3D
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302 J-centre profile The J-centre p
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A. Appendix Anisotropy Resistivity
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A. Appendix A.4. Auxiliary figures
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A. Appendix 314 ρ TE(Ω−m) φ T
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A. Appendix 320 pic003 (off-diagona
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A. Appendix 322 pic013 (off-diagona
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Bibliography Abalos, B., J. Carrera
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Bibliography Artemieva, I. M. (2006
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Bibliography Berdichevsky, M., V. D
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Bibliography Cebriá, J.-M., and J.
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Bibliography de Vicente, G., J. Gin
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Bibliography Egbert, G. D., and J.
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Bibliography Ganapathy, R., and E.
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Bibliography Haak, V., and R. Hutto
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Bibliography Hutton, R. (1972), Som
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Bibliography Jones, A. G., and R. W
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Bibliography Kurtz, R. D., J. A. Cr
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Bibliography Lviv Centre of Institu
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Bibliography Merrill, R. T., and M.
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Bibliography Newman, G., and G. Hoh
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Bibliography Pádua, M. B., A. L. P
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Bibliography Prácser, E., and L. S
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Bibliography Ritter, J. R. R., M. J
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Bibliography Serson, P. H. (1973),
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Bibliography Spitzer, K. (2006), Ma
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Bibliography Tikhonov, A. N., and V
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Bibliography Wanamaker, B. J., and
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Bibliography Xu, Y., C. McCammon, a
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