Approximational approach has been used in practice of interpretational works for a long time already. Let us pay attention to some sides of this important and many-sided question.
The first one. It is a question of information basis replacement - about transition from fields' elements maps to analytical approximation of these elements. Initial gravitational or the magnetic field is replaced with a field of some auxiliary model. The interpreter receives the whole set of geophysical fields. It essentially raises the level of qualitative interpretation.
In the discussed works it is possible to create an auxiliary model in such a way, that along with the analytical description of the initial field, the interpreter receives geometrical characteristics of abnormal weights distribution (fig. 1). Otherwise the problem becomes more complicated. It becomes nonlinear. The steady mathematical apparatus of such problems decision was developed.
The second one. Problems of geological interpretation are often solved with the help of trial-and-error method. At the first stage the interpreter creates the hypothetical geological model, whose weights could create the needed abnormal field. Such geological model should be parametrized. It means that some sequence of parameters with numerical values, which define geometrical features of the model, density or magnetic characteristics of weights, is established. There is a possibility to receive a theoretical field which is conditioned by weights of geological model. The theoretical field is compared with the initial. Now the problem consists in finding new numerical values of model parameters, which minimise the divergence of compared fields.
Thus, interpretational problem is always solved in model class, fixed beforehand. It is possible to allocate works, which are devoted to the general questions of the theory and practice of gravimetric and magnitometric fields’ interpretation.
In some works cycle problems of analytical model of initial abnormal field creation are considered (fig. 2).
Results of the inverse problems solution in various model classes are considered. These are inverse problems for contact surfaces. Here it is necessary to divide both two-dimensional problems, and problems in which by the abnormal field the relief of interface of geological formations division is restored.
Solution series of return problems is given, if the abnormal field is caused by star objects or bodies of L.N.Sretenskiy class. In this class the average horizontal plane is allocated and the configuration of body cover and its sole is defined. The solution of problems from one class allows to define change of density or magnetisation of rocks which are placed in the fixed horizontal layer.
Main results are published in periodical scientific journals. Mainly, they are NASU Reports; Earth physics, Moscow: Ed. RAS; Geophysical magazine. Kiev: Ed. NASU; Geoinformatics. Kiev: Ed. NASU.
Fig. 1. Inverse gravimetric problem solution for two contact surfaces by the variation field of gravitation force.