The Combinatorial–Variational Approach to Solving Linear and Nonlinear Inverse Problems in Geophysics

The problem of interpreting heterogeneous and multiprecision geophysical data is considered from the point of view of combinatorics within the framework of the approximation approach. The discrete nature of information about physical fields and their sources imposes a number of limitations on the possibilities of adequate data interpretation. Combinatorial methods of discrete mathematics make it possible to describe accurately the criteria for selecting data to approximate the elements of anomalous potential fields, as well as for controlling the quality of the approximate solution of inverse problems, both linear and nonlinear.