Statement of Inverse Problem - Models and Methods of Magnetotellurics - page 357

Here arises a paradoxical situation. The narrower the correctness set is, the more
stable will be the inverse problem. The more stable is the inverse problem, the higher
is its resolution, but the poorer is the detailedness of its solutions. The resolution of
the inverse problem and the detailedness of its solutions appear to be antagonistic.
We call this situation the paradox of instability . Desiring to improve the detailedness
of an inversion, we extend the correctness set. But as a consequence, the resolution
is decreased and the practical stability deteriorates. Thus, the details of the inversion
may be lost in errors. It is clear that in solving an inverse problem, it is vital to find
the optimal relation between detailedness and resolution. The detailedness of an
inversion must be correlated with the resolution.
The correctness set, in which the solution to the inverse problem is sought
for, forms an interpretation model . The latter should incorporate ideas (hypothe-
ses) on the Earth's stratification and local and regional structures disturbing this
stratification.
The interpretation models of magnetotellurics are divided into two classes: (1)
quasi-homogeneous layered models ,(2) locally inhomogeneous layered models
(Fig. 10.4).
A quasi-homogeneous layered model consists of a finite number of infinite or
pinching-out layers. In this model class, the electrical conductivities of layers and
their boundaries slowly vary in horizontal directions (easy dipping, gentle folding).
A very important feature of the quasi-homogeneous layered models is the presence
of high-resistivity layers playing the role of galvanic screens. The screening effect
characterized by the galvanic parameter of the model determines the intensity of
near-surface galvanic anomalies and the sensitivity of the magnetotelluric sounding
to deep conductive structures.
A locally inhomogeneous layered model consists of a finite number of layers with
breaks and sharp variations of their conductivity and boundaries. It may include
Fig. 10.4 Quasi-
homogeneous and
locally-inhomogeneous
layered models