Inverse problems of gravity prospecting as a decision-making problem under uncertainty and risk

Abstract

A new class of algorithms for solving the inverse problems of gravity prospecting is considered. The best interpretation is selected from the set Q of the admissible versions by the optimality criteria that are borrowed from the solution-making theory and adapted for the geophysical problems. The concept of retrieving the information about the sources of gravity anomalies, which treats the result of the interpretation as a set of locally optimal solutions of the inverse problem but not as a single globally optimal solution is discussed. The locally optimal solutions of the inverse problem are sort of singularity points of set Q. They are preferable to the other admissible solutions by a certain criterion formulated in terms of the geologically important information about the anomalous bodies. The admissible versions of the interpretation of the gravimetry data that meet the criteria of the decision-making theory are the primary candidates for the singularity points. The results of the numerical calculations are presented. The set of the admissible solutions from which the locally optimal versions of interpretation are selected is formed by the modifications of the assembly method developed by V.N. Strakhov.