P. Schmoldt, PhD - MTNet - DIAS
P. Schmoldt, PhD - MTNet - DIAS 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, 50
4.1. Types of distortion Fig. 4.1.: Model of the potential galvanic and inductive effects in a magnetotelluric (MT) survey; from Garcia and Jones [2001]. electric galvanic distortion affects MT data, below a distorter-depth dependent frequency, to a similar extent [Habashy et al., 1993; Garcia and Jones, 2001; Ledo, 2005; Simpson and Bahr, 2005] (Fig. 4.1). The frequency dependence of the inductive distortion is directly evident from the related term in Equation 4.2; note that the galvanic term contains an additional inverse relation to frequency via the wave number k. Unlike galvanic distortion, inductive distortion effects cause a phase shift of secondary EM fields (cf. complex nature of induction term in Equation 4.2). The phases of the secondary fields are in the range 0 to π/2, relative to the primary fields, dependent on the degree of the inductive distortion [e.g. Ward, 1967; Ward and Hohmann, 1987]. A secondary field phase of π/2 denotes the “resistive limit” case [Jiracek, 1990] in which the contribution of the inductive distortion is negligible, whereas the opposite case (phase approximately zero) indicates that inductive distortion effects prevail. The degree of galvanic and inductive distortion effects onto the response of TE and TM modes is not only dependent on characteristics of the EM wave and conductivity of the distorting body (cf. Eqs. 4.2, 4.3), but also on the shape of the distorting body. Ledo [2005] uses a synthetic model containing an elongated 3D body in the proximity of a regional 2D structure, to investigate distortion effect on the responses of both modes in relation to the angle between 3D body orientation and regional strike (see Fig. 4.2). The author finds that for the case of an orthogonal orientation the TE mode is affected mainly by galvanic effects, whereas the TM mode is affected by both, galvanic and inductive effects. On the contrary, when the 3D body is parallel to the regional 2D strike, the TE mode is affected by galvanic and inductive effects, and the TM mode is affected mainly by galvanic effects. 51
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4.1. Types of distortion<br />
Fig. 4.1.: Model of the potential galvanic and inductive effects in a magnetotelluric (MT) survey; from Garcia and Jones [2001].<br />
electric galvanic distortion affects MT data, below a distorter-depth dependent frequency,<br />
to a similar extent [Habashy et al., 1993; Garcia and Jones, 2001; Ledo, 2005; Simpson<br />
and Bahr, 2005] (Fig. 4.1). The frequency dependence of the inductive distortion is<br />
directly evident from the related term in Equation 4.2; note that the galvanic term contains<br />
an additional inverse relation to frequency via the wave number k.<br />
Unlike galvanic distortion, inductive distortion effects cause a phase shift of secondary<br />
EM fields (cf. complex nature of induction term in Equation 4.2). The phases of the<br />
secondary fields are in the range 0 to π/2, relative to the primary fields, dependent on<br />
the degree of the inductive distortion [e.g. Ward, 1967; Ward and Hohmann, 1987]. A<br />
secondary field phase of π/2 denotes the “resistive limit” case [Jiracek, 1990] in which<br />
the contribution of the inductive distortion is negligible, whereas the opposite case (phase<br />
approximately zero) indicates that inductive distortion effects prevail.<br />
The degree of galvanic and inductive distortion effects onto the response of TE and TM<br />
modes is not only dependent on characteristics of the EM wave and conductivity of the<br />
distorting body (cf. Eqs. 4.2, 4.3), but also on the shape of the distorting body. Ledo<br />
[2005] uses a synthetic model containing an elongated 3D body in the proximity of a<br />
regional 2D structure, to investigate distortion effect on the responses of both modes in<br />
relation to the angle between 3D body orientation and regional strike (see Fig. 4.2). The<br />
author finds that for the case of an orthogonal orientation the TE mode is affected mainly<br />
by galvanic effects, whereas the TM mode is affected by both, galvanic and inductive<br />
effects. On the contrary, when the 3D body is parallel to the regional 2D strike, the TE<br />
mode is affected by galvanic and inductive effects, and the TM mode is affected mainly<br />
by galvanic effects.<br />
51