Information Technology Reference
In-Depth Information
its resolution. The resolution of the inverse problem and the detailedness of its solu-
tion are antagonistic. The inverse problem should be solved with optimum relation
between stability, resolution and detailedness (Berdichevsky and Dmitriev, 2002).
We have to fit the solution detailedness to the inversion resolution and smooth or
schematize models of the geoelectric medium (to diminish a number of parameters).
This complies with the diffusive nature of the low-frequency magnetotelluric field
that can offer only a smoothed integral image of the geoelectric medium. Existing
in the Earth buried sharp conductivity contrasts can be introduced into the inter-
pretation model using a priori information or hypotheses. Thus, the most complete
interpretation is performed by a compromise between
smoothing inversion
and
con-
trasting inversions
. An interpretation model with a small number of layers and
structures is preferable. The additional layers and structures should be introduced
providing the magnetotelluric and magnetovariational indications demand their
presence.
10.1.3 On Redundancy of Observation Data
Solving a 1D inverse problem, we determine a conductivity distribution
(
z
)from
the scalar complex-valued Tikhonov-Cagniard impedance
Z
, i.e., from two scalar
response functions
|
Z
|
and arg
Z
, which have different resolving power and can
nicely complement each other.
When increasing the interpretation dimensionality, we significantly extent the
number of response functions derived from observation data. The two-dimensional
and three-dimensional inverse problems are
multicriterion problems
. Magnetotel-
luric inversion aimed at determining the conductivity distribution involves complex-
valued matrices of the impedance tensor (2
×
2), the phase tensor (2
×
2), the
horizontal magnetic tensor (2
2). Summing up, we say that
a scalar real function defining a two-dimensional or three-dimensional distribution
of the electrical conductivity is going to be derived from 28 scalar real functions.
These functions have different sensitivity to parameters of the interpretation model
and different immunity to galvanic distortions that ruin information on buried geo-
electric structures. How can we cope with such a great body of observation data
which have quite divergent properties? On joint simultaneous inversion they can
bother each other impairing the inversion accuracy. The challenge is to devise the
interpretation scenarios combining the inversions of different response functions in
the most efficient way.
×
2), the tipper (1
×
10.2 Inverse Problem as a Sequence of Forward Problems
Solving inverse problem (10.1)
,
(10.2), we compare the observed response func-
tions with model response functions derived from hypothetical conductivity dis-
tributions
,
,
z
) and sequentially minimize the model misfit by means of the
iterative procedure. So, the inverse problem reduces to a sequence of the forward
(
x
y
