P. Schmoldt, PhD - MTNet - DIAS

4.2. Dimensionality
Fig. 4.12.: The four figures represent the induction area for different period ranges at the same station (indicated by the inverted black
triangle); the longest period is increased from left to right. The subsurface model is the same for all figures (two quarter-spaces, one
with an imbedded small-scale 3D body), only the observed dimensionality varies with period range.
4.2.1. Frequency-dependent dimensionality
To illustrate the phenomenon of frequency dependent dimensionality, the model of a
small-scale surficial 3D body, imbedded in one half of a regional 2D structure is considered.
The regional structure contains two homogeneous quarter-spaces (except for the
small 3D body) with different electric resistivity (cf. rightmost model in Figure 4.12).
The response from a MT station, located on top of the 3D body (inverted black triangle in
Figure 4.12), is examined first theoretically and later by studying a synthetic model (Sec.
4.2.1).
For short periods, the station is sensitive to the boundaries of the 3D body and the
response curve simply represents the resistivity of the body, exhibiting 1D behaviour.
Once longer periods are included, effects of the boundaries between the 3D body and the
surrounding material are observed, indicated by a change in the shape of the response
curve. Assuming that responses are only affected by the lateral boundary of the 3D body
and not by its bottom, the data are 2D in nature. Further increasing the period range
yields data that are also sensitive to bottom and the other lateral interfaces of the 3D body,
resulting in the so-called 3D/1D case (it is assumed here that the distance between the
3D body and the contact zone of the two quarter-spaces is sufficient large). Data at the
longest periods contain effects of the 3D body, superimposed on the regional 2D structure
response, which is referred to as 3D/2D case. When the coordinate system is aligned
to the 2D regional strike direction, the 3D body will only cause a frequency independent
shift in the long-period apparent resistivity response curves. This static shift is due electric
galvanic distortion, i.e. electric charge build up on the faces of the 3D body.
Synthetic model
A synthetic model study is conducted to illustrate the effect of a local 3D distorter embedded
in a regional 2D structure on the response for a MT stations located on top of
the distorting body. The 3D/2D model (‘3D body’ in Fig. 4.13) was created using the
WinGLink software package [WinGLink, 2005] wherein the MT3DFWD forward algorithm
[Mackie et al., 1994] was used to calculated the response data. A second model is gen-
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