Аннотация:Neural networks (NN) are widely used to solve various problems of interpretation and processing of geophysical data. In this paper, we consider the application of the approximation neural network (ANN) method for solving inverse problems (including multicriteria), which are reduced to a nonlinear operator equation of the first kind of the form (respectively, to a system of operator equations). ANN method consists of constructing an approximate inverse operator of the problem using neural network approximation constructions (MLP networks) based on a set of support solutions of direct and inverse problems built in advance. Surface inhomogeneities of the medium create a significant noise component in determining the parameters of the underlying regions, which leads to a significant increase in the error in solving the inverse problem. The proposed method of focusing NN approximators consists in the fact that several different approximators are constructed based on several training sets, which differ in the detail of the parameterization of the studied environment at different depths. Focusing NN approximators can achieve a reduction of its training error for environment parameters, which focuses on approximator. This allows one to significantly reduce the intrinsic errors of the NN method when solving nonlinear inverse 3D problems of geophysics.