P. Schmoldt, PhD - MTNet - DIAS

Parameter Geoelectrical application
4.4. Removal of distortion effects
ηB = √ C/|D2| Descriptiveness of MT tensor by superimposed model
µB = ([D1, S 2] + [S 1, D2]) 1/2 /|D2| Phase difference in the MT tensor
ΣB = (D2 1 + S 2 2 )/D2 2
Two-dimensionality
Tab. 4.2.: Parameters defined by Bahr [1988] (with modifications by Prácser and Szarka [1999]) to describe distortion of the MT
impedance tensor; see text for details about parameters.
This concept was later advanced by Jones and Groom [1993], who suggest decomposing
for an impedance tensor rotated 45 degrees against the strike direction instead of an
impedance tensor orientated parallel to strike. The authors’ modification is based on the
fact that in the case of no distortion, or symmetric distortion, the angles φex and φey are un-
defined, because the off-diagonal elements of the distortion matrix cxy and cyx (Eq. 4.21)
are zero. Incorporating this modification in Equation 4.39 yields
φ1(Θ)
φ2(Θ)
=
=
Im[(Zxx(Θ) + Zxy(Θ))/(Zyx(Θ) + Zyy(Θ))]
arctan
,
Re[(Zxx(Θ) + Zxy(Θ))/(Zyx(Θ) + Zyy(Θ))]
Im[(Zxx(Θ) − Zxy(Θ))/(Zyx(Θ) − Zyy(Θ))]
arctan
.
Re[(Zxx(Θ) − Zxy(Θ))/(Zyx(Θ) − Zyy(Θ))]
(4.40)
(4.41)
4.4.3. Weaver-Agarwal-Lilley tensor invariants
Weaver et al. [2000] use seven independent plus one dependent parameter that are invariant
under horizontal rotation of the coordinate system plus an angle Θ to describe the
MT impedance tensor Z, the dimensionality of the subsurface, and the distortion type
(Tab. 4.3). Θ defines therein the angle between the x-axis of the coordinate system used
for the processing and a fixed direction (e.g. magnetic north). The methods of Weaver
et al. [2000] is an extension of the work by [Bahr, 1988] (Sec. 4.4.2), with the last three
Weaver-Agarwal-Lilley’s (WAL) independent parameter (Tab. 4.3, i.e. parameters I5, I6,
I7) are retraces of Bahr’s parameters (Tab. 4.2).
Weaver et al. [2000] define their parameters through the variables ξ, η, and di j representing
real and imaginary parts of the impedance tensor:
(2µ0) −1 [Zxx + Zyy] = ξ1 + ıη1 (4.42)
(2µ0) −1 [Zxy + Zyx] = ξ2 + ıη2 (4.43)
(2µ0) −1 [Zxx − Zyy] = ξ3 + ıη3 (4.44)
(2µ0) −1 [Zxy − Zyx] = ξ4 + ıη4 (4.45)
ξiη j − ξ jηi
I1I2
= di j (4.46)
with µ0 the permeability of free space. A visual representation of the parameters can be
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