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contrasty model
0
. This form of Tikhonov's regularization is named the
contrasting
inversion
. It has been realized in programs INV2D, II2DC and IGF-MT2D
developed by Varentsov and Novozhynsky (Varentsov, 2002; Novozhynski and
Pushkarev, 2001).
The contrasty interpretation model usually consists of reasonably small num-
ber of homogeneous blocks with fixed geometry of their boundaries. The density
of blocky partition is larger in zones with expected structures and less in empty
zones. Position of the blocks and their shape are chosen using a priori information,
qualitative magnetotelluric and magnetovariational indications, tentative smoothing
inversions, and hypotheses. Stability of the contrasting inversion is ensured by the
blocky stabilizer
g
l
0
2
L
(
l
)
(
l
)
(
)
=
−
,
(12
.
3)
l
=
1
where
g
l
is a weight controlling the contribution of the
l
th block.
The smoothing and contrasting inversions operate at different levels of automa-
tion.
The smoothing inversion is best suited to automatic operation. Let the geoelec-
tric survey be carried out in a region with supposedly gentle tectonics. If analysis
of magnetotelluric impedances shows sufficiently small values for the parame-
ters of inhomogeneity, the smoothing inversion calls for stratifying the geoelectric
medium, defining the normal background, correlating the
S
distribution, analyzing
the model misfits and estimating the inversion accuracy. So, the smoothing inversion
enables rather fast interpretation of the large amounts of field data and is particularly
attractive in the commercial magnetotelluric surveys.
On the contrary, the contrasting inversion calls for intensive contacts between
the geophysicist and the computer. The point is that results of the inversion may
depend on the partition of the blocky model and in the course of inversion we have
to follow the misfit minimization and improve the shape and position of the blocks
associated with target structures. Besides, we have to take into account the properties
of the different response functions and on this basis to divide the interpretation into a
succession of interrelated partial inversions focused upon different target structures.
Moreover, we can accomplish some tentative inversions intended for the hypothe-
ses testing and correct the interpretation model. The contrasting inversion helps to
obtain rather complete and meaningful description of the intricately built medium,
but it is time-consuming. Its application is usually limited by regional studies and
deep academic investigations.
In closing, let us mention two recent developments that may extend the capabili-
ties of the smoothing and contrasting inversions: (1) Zhdanov suggested a focusing
stabilizers that exposes the sharp conductivity variations against a smoothed back-
ground (Zhdanov, 2002), (2) Varentsov constructed a scanning windows that super-
imposes smoothed conductivity variations upon a piecewise homogeneous blocky
background (Varentsov, 2002).
−
