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Adopting this strategy, we start with magnetovariational inversions, which is free
from distorting effects of local near-surface inhomogeneities, and then proceed to
magnetotelluric inversion with a starting model, constructed from the results of mag-
netovariational inversion.
10.4.3 Regularization Method
Regularization of solutions substantially widens the possibilities of interpretation.
Given a sufficient amount of a priori information, this approach provides maximum
geoelectric information consistent with the accuracy of field observations and mod-
eling. The main peculiarity of the
regularization method
is that criterion for choos-
ing an approximate solution is included directly in the algorithm of inversion. When
solving the inverse problem, the compactum
M
narrows around the exact model
solution. The regularization method admits the introduction of any type of a priori
information with control of its influence on the solution of the inverse problem.
What is more, the regularization method enables one to focus the inversion on the
target layers and structures.
This approach is based on the
regularization principle
: the criterion for the selec-
tion of solution should be such that the inferred approximate solution tends to the
exact model solution of the inverse problem, when the errors in the initial infor-
mation tend to zero. The regularization principle for MT (1.1
a
) and MV (1.1
b
)
inversions takes the form
Z
(
x
Z
(
x
lim ˆ
,
y
,
z
)
=
ˆ
,
y
,
z
)
,
Z
→
0
(10
.
64)
W
(
x
W
(
x
lim ˆ
,
y
,
z
)
=
ˆ
,
y
,
z
)
,
W
→
0
Z
W
Z
W
where ˆ
,
ˆ
and ˆ
,
ˆ
are approximate and exact model solutions of MT and
MV problems, and
Z
,
W
are errors in the initial data.
The regularization principle is implemented with the help of a
regularizing oper-
ator
. The regularizing operator
R
of an inverse problem is referred to as a set of
analytical and numerical operations that allows one to obtain an approximate solu-
tion satisfying the regularization principle. In inverse problems of geophysics, it is
advantageous to use a regularizing operator
R
depending on a numerical parameter
>
0, which is called the
regularization parameter
. As the error
in the initial data
tends to zero, the regularization parameter
should also tend to zero:
lim
Z
→
→
0
MT inversion
0
(10
.
65)
lim
W
→
0
→
0
MV inversion
and the regularizing operator, when applied to the approximate response function,
should yield the exact model solution.
