P. Schmoldt, PhD - MTNet - DIAS

4. Distortion of magnetotelluric data
Parameter Geoelectrical application
I1 = (ξ 2 4 + ξ2 1 )1/2
I2 = (η 2 4 + η2 1 )1/2
I3 = (ξ 2 2 + ξ2 3 )1/2 /I1 }2D anisotropy
I4 = (η 2 2 + η2 3 )1/2 /I2
I5 = (ξ4η1 + ξ1η4)/(I1I2)
I6 = (ξ4η1 − ξ1η4)/(I1I2)
I7 = (d41 − d23)/Q
QW = [(d12 − d34) 2 + (d13 + d24) 2 ] 1/2
1D magnitude and phase of the geoelectric resistivity
(Eq. 4.47 and 4.48)
}Galvanic distortion
Tab. 4.3.: The seven independent (I1 - I7) plus one dependent parameter (Q) defined by Weaver et al. [2000] to describe the magnetotelluric
(MT) impedance tensor and its distortion. Each of the parameters is associated with a certain geological setup, and subsurface
characteristics in terms of dimensionality and distortion can be derived from the values of these parameters; see Table 4.4 for details
about the relation between parameter values and subsurface dimensionality. Relation of ξ, η, and d with the MT impedance tensor are
given in Equations 4.42 – 4.46
Values Dimensionality
I3 = I4 = I5 = I6 = 0; I7 = 0 or QW = 0 1D
I3 0 or I4 0; I7 = 0 or QW = 0 2D
I3 0 or I4 0; I5 0, I7 = 0 3D/2Dtwist (only twist)
I3 0 or I4 0; I5 0, I7 : undefined
I6 0
3D/2D1D (non-recoverable strike direction)
galvanic distortion over a 1D or 2D structure
3D/2D
general case of galvanic distortion over a 2D structure
I7 0 3D (affected or not by galvanic distortion)
Tab. 4.4.: The dimensionality of the subsurface derived from the parameters defined by Weaver et al. [2000], after [Martí et al., 2005]
and [Martí, 2007].
given via a Mohr circle diagram with the rotated impedance tensor elements Zxx and Zxy
forming the x and y-axis (Fig. 4.16).
Assumptions about the subsurface dimensionality can be made with the values WAL
parameters (Tab. 4.4). Due to noise in a real data set, the parameters will not exhibit
values of exactly zero and threshold values need to be introduced. Certainly, threshold
values have significant influence onto the derived dimensionality and have to be chosen
carefully. In their publication, Weaver et al. [2000] propose a value of 0.1 as tolerance
level for all parameters, whereas Martí et al. [2009b] use default threshold values of 0.15
for the independent parameters and 0.1 for QW in their program WALDIM, the latter being
an implementation of the theory by Weaver et al. [2000].
Information about the apparent resistivity and phase of the related 1D subsurface can
be obtained from invariants I1 and I2 giving an approximate idea about the conductivity
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