P. Schmoldt, PhD - MTNet - DIAS
P. Schmoldt, PhD - MTNet - DIAS P. Schmoldt, PhD - MTNet - DIAS
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 46 and 47: 2. Sources for magnetotelluric reco
- Page 48 and 49: 2. Sources for magnetotelluric reco
- Page 50 and 51: 2. Sources for magnetotelluric reco
- Page 52 and 53: 2. Sources for magnetotelluric reco
- Page 54 and 55: 2. Sources for magnetotelluric reco
- Page 56 and 57: 2. Sources for magnetotelluric reco
- Page 58 and 59: 2. Sources for magnetotelluric reco
- Page 60 and 61: 2. Sources for magnetotelluric reco
- Page 62 and 63: 2. Sources for magnetotelluric reco
- Page 64 and 65: 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
Symbol SI unit Denotation<br />
φ · phase (of the electric impedance)<br />
Φ · Caldwell phase tensor<br />
Φ11, Φ12, Φ21, Φ22<br />
elements of Φ<br />
Φ1 − Φ4 · Caldwell parameters (coordinate independent)<br />
π · Ludolf’s number<br />
ψ · error function<br />
Qh · distortion of the horizontal magnetic field<br />
Qxx, Qxy, Qyx, Qyy<br />
Qz Qzx, Qzy<br />
R<br />
·<br />
·<br />
·<br />
Ω (=<br />
elements of Qh in Cartesian coordinates<br />
distortion of the vertical magnetic field<br />
elements of Qz in Cartesian coordinates<br />
1<br />
R<br />
) σ<br />
·<br />
resistance (integrated electric resistivity)<br />
rotation matrix<br />
Rdd · error covariance matrix<br />
S xy · cross-spectral density<br />
Qe<br />
C<br />
mn QW<br />
ρ<br />
·<br />
Ωm (=<br />
electric charge density<br />
Weaver tensor invariant<br />
Vm<br />
ρa<br />
S<br />
) A<br />
Ωm<br />
S (=<br />
electric resistivity<br />
apparent electric resistivity<br />
1<br />
S 1<br />
) Ω<br />
Ωm<br />
conductance (integrated electric conductivity)<br />
sum of diagonal elements / trace (of the<br />
impedance tensor)<br />
S 2 Ωm sum of off-diagonal elements (of the<br />
sD ·<br />
impedance tensor)<br />
telluric anisotropic distortion<br />
σ<br />
ΣB<br />
S 1 (= ) m Ωm<br />
·<br />
electric conductivity<br />
Bahr parameter: Two-dimensionality<br />
T s period<br />
T · geomagnetic transfer function/tipper<br />
Tx, Ty · elements of T in Cartesian coordinates<br />
t s time<br />
τ<br />
S<br />
m2 , S<br />
m3 , Ω, or Ω<br />
m Smoothness parameter in inversion, e.g. ∇σ,<br />
∇2σ, ∇ρ, ∇2ρ, or logarithmic values<br />
tD · telluric twist distortion<br />
Θ ° or rad angle<br />
v<br />
ω<br />
x, y, z<br />
m<br />
s<br />
1<br />
s<br />
m (or km)<br />
velocity<br />
angular frequency<br />
Cartesian coordinates (z pos. downwards)<br />
Continued on Next Page. . .<br />
xxv