P. Schmoldt, PhD - MTNet - DIAS

4. Distortion of magnetotelluric data
4.1. Types of distortion
As a first approach, distortion of MT can be separated into two groups according to the
electromagnetic (EM) processes involved, i.e. cases where electric charges are accumulated
along boundaries of regions with different electric resistivities (referred to as galvanic
distortion), and cases where an anomalous EM fields is induced within a body of
different conductivity (referred to as inductive distortion) [Berdichevsky et al., 1989]. Using
the Born approximation [Born, 1933], measured electric fields E can be expressed
as a combination of primary field and superimposed galvanic and inductive distortion
[Habashy et al., 1993; Chave and Smith, 1994], i.e.
E(r) = Ep(r) : primary field
− ıωµ0
+ 1
∇
k 2
h
j
2
with g(r, r ′ ) = exp(ık|r−r ′ |)
4π|r−r ′ |
j
V j
V j
g(r, r ′ )∆σ j(r ′ )E(r ′ )dr ′ : inductive distortion
g(r, r ′ )∆σ j(r ′ )E(r ′ )dr ′ : galvanic distortion
(4.2)
: the Green’s function, k 2
h = ıωµ0σh + ωµ0εb: wave number of the
host medium, ω: angular frequency, µ0: magnetic permeability of free space, εb: electric
permittivity of the host medium, σh and σ j: conductivity of the host medium and the j-th
distorting body respectively, ∆σ(r ′ ) = σ j(r ′ ) − σh(r ′ ), and
dr
V j
′ : volume integral over
the j-th body. In Equation 4.2 the contribution of the anomalous current Ja, caused by the
distorting body, is directly apparent using Ohm’s Law (Eq. 3.5), i.e. Ja = ∆σE.
An equivalent expression for the magnetic field can be derived by applying Faraday’s
Law (Eq. 3.2) on Equation 4.2, yielding
B(r) = Bp(r) : primary field
+ µ0∇ ×
j
V j
g(r, r ′ )∆σ j(r ′ )E(r ′ )dr ′ : inductive distortion
(4.3)
Equation 4.3 does not contain a contribution of the galvanic distortion as ∇ × ∇ψ = 0
for an arbitrary scalar function ψ [Utada and Munekane, 2000], which suggests that the
magnetic field is not affected by galvanic distortion. However, Equation 4.2 is only valid
for cases in which the distorting body can be considered small in comparison to the EM
wavelength (implied in the Born approximation [Habashy et al., 1993]). The effect of
magnetic galvanic distortion is observable for a frequency range that is sensitive to the
distorting body; however, its contribution deteriorates quickly for lower frequencies [e.g.
Garcia and Jones, 2001]. For deep-probing MT studies, it is therefore often assumed
that the effect of magnetic galvanic distortion is negligible in comparison to the electric
galvanic distortion effect. Unlike magnetic galvanic distortion, and inductive distortion,
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