Statement of Inverse Problem - Models and Methods of Magnetotellurics - page 358

discontinuities, displacements, subductions, intersections, bounded inclusions and
channels of more or less complicated geometry.
The interpretation model should meet the following two requirements: (1) it
should be simple (being determined by a small number of free parameters that
ensure the practical stability of the inverse problem), and (2) it should be informative
(reflecting main properties of the geoelectric medium and containing target layers
and structures). These conditions are opposite: the simpler is the model, the less
informative it is. Here the paradox of instability manifests itself. Thus, we have to
choose an optimal model, that is, it should be reasonably informative yet sufficiently
simple. The detailedness of an inversion should be provided by the resolution of
the inverse problem.This is a crucial point of the interpretation, predetermining not
only the strategy for inversion, but also, to some degree, its result. At this stage of
interpretation, the factors such as intuition of a researcher, his professional skill and
academic experience, his understanding of the actual geological situation and goals
of the MT survey, his adherence to traditions and willingness to deviate from these
traditions - all plays a role.
Constructing an interpretation model, a researcher is limited by a priori infor-
mation and by results of qualitative analysis of field measurements as well as by
hypotheses tests. Just in this sense we say that the interpretation of MT and MV data
is effective under the condition of sufficiently reasonable constrains. The statement
“the better we know the medium under consideration, the better we can determine
its geoelectric structure” seems paradoxical. But it actually means that, solving the
inverse problem, we improve and widen our knowledge of the Earth's structure, and
therefore, the better is this structure known, the more meaningful and detailed are
the new results.
The amount of a priori information required for constructing an optimal inter-
pretation model depends on the complexity of the medium and on the goals of the
interpretation. Whereas rather detailed a priori information on tectonics and geo-
dynamics are required in rift or subduction zones, only very general ideas on the
Earth's stratification are sufficient for stable platforms with gentle folding.
Moreover, we can reject a priori information at the preliminary stage of inter-
pretation and perform the smoothing Occam inversion. This simple transformation
provides a gross geoelectric regionalization helpful for the identification of zones of
interest for further interpretation.
Tikhonov's theory of ill-posed problems offers two basic approaches to the
interpretation of MT and MV data: (1) optimization method , and (2) regulariza-
tion method (Berdichevsky and Dmitriev, 1991, 2002). We briefly describe these
approaches.
10.4.2 Optimization Method
This approach is effective in studying simple media, described by a small number
of parameters. Return to inverse problem (10.1) and assume that available a priori
information constrains a sufficiently narrow compact set M of admissible solutions