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12.2 The Hypotheses Test Mode
We consistently stress that the interpretation efficiency considerably depends on the
amount of a priori geological and geophysical information. However the require-
ments imposed upon a priori information can be reduced when the inverse problem
is considered as a problem of hypotheses testing.
Let us entertain a hypothesis that the upper mantle contains a conductive zone
(asthenosphere) originated from partial melting. The blocky interpretation model
for this inverse problem should include some conductive blocks corresponding to
the supposed asthenosphere. To execute the inversion, we introduce a stabilizer
determining the deviation of the solution from the tested hypothesis. By minimizing
Tikhonov's functional and computing the model misfit, we can answer the question
whether the tested hypothesis is consistent with the observation data. Moreover,
when changing the conductivity and the position of the “asthenosphere” blocks and
controlling these changes by the model misfit, we correct the tested hypothesis.
A similar approach can be applied to compare the alternative hypotheses. Let
one of hypotheses provide the misfit that does not exceed the uncertainty in the field
data and is far less than the misfits of the other hypotheses. Then this hypothesis
is taken as the most credible. But if different hypotheses are characterized by the
misfits of the same order, then we conclude that all these hypotheses are equivalent.
It means that we dramatically need an additional information to choose the most
credible one.
12.3 Quasi-One-Dimensional MT Inversion
This approach can be used in investigating quasi-homogeneous layered media (verti-
cal conductivity distribution is piecewise constant, while conductivity and thickness
of the layers change slowly in horizontal directions). The quasi-one-dimensional
inversion is efficient in regions with gentle sedimentary tectonics, say, on the vast
platform. Here the magnetovariational anomalies can be rather weak so that mag-
netovariational soundings are hardly applicable and we restrict ourselves to magne-
totelluric soundings.
The concept of the quasi-one-dimensional inversion is simple (Dmitriev, 1987;
Barashkov and Dmitriev, 1990; Oldenburg and Ellis, 1993). We look for a 3D con-
ductivity distribution such that the magnetotelluric response function (impedance or
apparent resistivity) at each observation site is close to the locally normal response
function and admits the one-dimensional inversion. The quasi-one-dimensional
inversion is controlled by the misfit of the 3D model obtained by synthesizing the
one-dimensional inversions.
12.3.1 Synthesizing the One-Dimensional Inversions
By way of example, consider a quasi-homogeneous layered medium and take
apparent-resistivity curves ˜
brd
(
x
m
,
y
m
,
T
) measured at sites
O
m
,
=
,
,...
m
1
2
M
.
