Formalized Inversion of Geophysical Data Using Neural Network Technologies with Application to the Tasks of Geoelectrics and Gravimetry

Abstract

Summary The approximation neural network (ANN) method for solving conditionally well-posed nonlinear inverse problems of geophysics is presented. The method is based on the neural network approximation of the inverse operator. The ANN method and its modifications make it possible to find stable approximate solutions of 2D and 3D inverse coefficient problems of geoelectrics in the class of grid models of media on a regularized parameterization grid with a practically acceptable accuracy without setting the first approximation. Estimates of the ambiguity degree (error), which do not depend on the inversion method applied, can be calculated for resulting approximate solutions of the inverse problem. The a posteriori estimates of the degree of ambiguity of the approximated solutions are calculated. The work of the method is illustrated by the example of the 3D inversion of synthesized area data and 2D real geoelectric data by the method MTS. It is shown that it is possible in principle to use the ANN method for solving solving conditionally well-posed nonlinear 3D gravity inverse problems (determining the geometry of the lower boundary).