P. Schmoldt, PhD - MTNet - DIAS

P. Schmoldt, PhD - MTNet - DIAS 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

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

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