History of Development and Current Status of the Finite Element Approach in the Theory of Interpretation of Gravitational and Magnetic Anomalies

Abstract

Due to the discreteness of gravitational and magnetic fields measurements in the mathematical theory of interpretation, finite element models of the environment, which have universal capabilities to deploy various a priori information, are of paramount importance. Known methods for solving inverse problems for finite element models of field sources can be divided into two classes. The first, where the interpretation result is traditionally a single solution that is optimal according to some criterion, and the second, where the interpretation results reflect a representative subset of feasible solutions of the inverse problem, which increases their authenticity. The developments of the article authors for second class methods took shape in a guaranteed approach and additive technologies for interpreting geopotential fields. The proposed review aims to promote the second class methods in the practice of interpreting gravity and magnetic anomalies, which should contribute to a more complete extraction of information from geophysical data.