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( m )
} } ,
inf
p ( m )
{
( y
,
z )
} =
inf
p ( m ) {
I m {
( y
,
z )
}+ m {
( y
,
z )
(12
.
21)
where
}=
}
2
R
F m
I m {
( y
,
z )
F m {
y
,
z
=
0
, ,
( y
,
z )
z )
2
L 2
( m
1) ( y
m {
( y
,
z )
}=
( y
,
z )
,
( m
1) ( y
and
1)th inversion.
Step-by-step examination of the different response functions F m ,
,
z ) is a model obtained by the ( m
m
=
1
,
2
M reduces the solution of the multicriterion problem to a sequence of partial
inversions. Each partial inversion can be aimed to solving some specific problem
and focused on some specific structures.
Partial inversions comprehensively incorporate specific features of the response
functions, their informativeness, and their confidence intervals. They admit the
information exchange between various response functions, enable a convenient
interactive dialog, and are easily tested. And finally they decrease the number of
sought-for parameters and hence improve the stability of the inverse problem. We
believe that this direction of research is most promising for further development of
methods designed for the integrated interpretation of MVS and MTS data.
Magnetotelluric soundings carried out in various geological provinces showed
the proficiency of the SPI method (Trapeznikov et al., 1997; Berdichevsky et al.,
1998, 1999; Pous et al., 2001; Vanyan et al., 2002a, b). Below, we briefly describe
some model experiments elucidating the potentials of successive partial inversions
with MV priority.
Figure 12.16 displays a 2D model schematically illustrating geoelectric structure
of the Kirghiz Tien Shan (Trapeznikov et al., 1997). The model will be referred to
as the TS model. It includes (1) inhomogeneous sediments (resistivity varies from
10 to 100 Ohm
,...
m), (2) an inhomogeneous resistive crust (resistivity varies from
10 4 inthesouthto10 5 Ohm
·
m in the north), (3) a deep crustal layer with resistivity
increasing monotonically from 10 Ohm
·
m in the north,
(4) conductive zones A, B, and C branching from the crustal conductive layer, (5)
a poorly conductive mantle underlaid by a conductive asthenosphere at a depth of
150 km.
The forward problem has been solved with the finite element method
(Wannamaker et al., 1987). Gaussian white noise has been introduced into the
response functions: it has standard deviations of 5% for apparent resistivities
·
m in the south to 300 Ohm
·
,
, . To imitate the static
shift caused by small 3D near-surface inhomogeneities, the apparent resistivities
were multiplied by random real numbers uniformly distributed in the interval from
0.5 to 2.
It is interesting to estimate a frequency range within which the tipper
becomes virtually free of near-surface effects. Figure 12.17 demonstrates frequency
responses of Re W zy and Im W zy calculated for TS model and for the same model
but with a homogeneous upper layer of a resistivity of 10 Ohm
Im W zy and 2.5 for phases
and tippers Re W zy ,
·
m. Except for a few
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