P. Schmoldt, PhD - MTNet - DIAS

4. Distortion of magnetotelluric data
λp βp αp
1D 0 0 undefined
2D 0 0 strike angle
3D 0 0 strike angle
Tab. 4.5.: Values of the parameters defined by Bibby et al. [2005] depending of the present dimensionality (note that in practise λ and
β are assumed to be zero when they fall below a chosen threshold value λc and βc); see text for further information on the parameters.
configuration, which quantify the validity of a 2D description and provide the geoelectric
strike direction (if existing), respectively. Values of λp, αp, and βp for 1D, 2D, and
3D cases are summarised in Table 4.5. Due to noise in real data, λp, and βp are usually
different from zero for all three cases. The ultimate decision about subsurface dimensionality
is therefore dependent on the thresholds below which λp and βp are considered close
enough to zero. Since modern MT inversion algorithms are capable of coping with 2D
situations, whereas the 3D case is still problematic, most workers focus on the verification
of the 2D assumption for a given dataset (as opposed to a full 3D treatment). Several authors
have investigated the threshold for βp, proposing a value of three degrees based on
results of their synthetic model studies [e.g. Caldwell et al., 2004; Martí, 2007; Ingham
et al., 2009]. Determination of an optimal λp value for the 1D – 2D discrimination, on the
other hand, received less attention; however, it was suggested by Martí [2007] to use the
standard deviation of the error in the determination of αp (σαp ) as a threshold for λp.
Bibby et al. [2005] point out that the criteria provided by the phase tensor are necessary
but not sufficient conditions for determining the dimensionality of the regional conductivity
structure. Furthermore, the authors state that the phase tensor at a single period, under
suitable conditions of symmetry, can have the characteristics of a lower dimension than
that of the regional structure. It is therefore suggested by Bibby et al. [2005] to take into
account data from neighbouring periods and locations to increase reliability of the phase
tensor analysis results.
Whereas the phase tensor method is excellent for determination of the geoelectric strike
direction it is limited in terms of recovering regional electric impedance values since the
set of equations is underdetermined, i.e. holding a set of four equations in five, six, or
eight unknowns for the 1D, 2D, or 3D case, respectively. The problem is therefore clearly
non-unique and further constraints need to be applied in order to identify the electric
impedance and therefore the apparent resistivity. This could be achieved either by using
information of other methods such as TEM soundings, or by introducing mathematical relationships
between the parameters similar to the approach by McNeice and Jones [2001]
for Groom-Bailey decomposition; see Bibby et al. [2005] for further examples of possible
relationships.
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