Approximation Approach to Solving The Inverse Problem of Geoelectrics Using Neural Networks

Abstract

Summary The paper presents an approximation neural network algorithm for solving conditionally correct coefficient inverse problems of geoelectrics in the class of media with piecewise constant electrical conductivity given on a parametrization grid. It is shown that the degree of ambiguity (error) of solutions monotonically increases with an increase in the dimension of the parametrization grid. A method is proposed for constructing an optimal parametrization grid, which has the maximum dimension provided that the a priori estimates of the ambiguity of the solutions do not exceed a given value. It is shown that the inverse problem in the considered class of media is reduced to the classical approximation-interpolation problem using neural network polynomials, the solution of which is the essence of the approximation neural network (ANN) method. The intrinsic error of the ANS method is determined, a posteriori estimates of the ambiguity (error) of the obtained approximate solutions are calculated with the achieved synthesis discrepancy. The method makes it possible to formalize and uniformly obtain solutions to the inverse problem of geoelectrics with the total number of the required parameters of the medium ∼ n 10 ^ 3.