The work develops the approximation approach to solving the inverse MTS problem with the use of neural networks. The inverse problem is considered in model classes of parametrized geoelectric structures, whose electric conductivity is controlled by a few hundreds of macroparameters (N ∼ 300). An approximate inverse operator of the problem is constructed for each model class as a neural network, whose coefficients are determined in the process of training on a representative sample of standard examples of forward problem solutions. The problem of determination of the model class of geolectric structures corresponding to the presented input MT data is solved with the use of the neural network classifier constructed for the available set of model classes of structures. Regularizing factors and errors of the neural network method are analyzed. The operation of the algorithm is illustrated by examples of the 2-D inversion of synthetic MT data.

—The approximation neural network (ANN) method for solving the inverse geoelectric problem in the piecewise constant classes of media with the subsequent refinement of the model by random search method is presented. A conditionally well-posed magnetotelluric inverse problem is considered on a regularized parameterization grid. The total number of the sought-for parameters in this problem can be \(\sim n \times {\text{1}}{{0}^{{\text{3}}}}\). The work of the algorithm is illustrated by the example of 3D inversion of the field survey data. The posterior ambiguity characteristics of the obtained solution were calculated. The proposed methods are implemented using supercomputing cluster resources and parallel computing technology.

—Neural networks (NNs) are successfully used to solve inverse and other problems in geophysics. The aim of this work, which is a continuation of a series of works by a group of authors, is to improve the efficiency of the NN method for solving nonlinear inverse 3D problems of geoelectrics, based on the construction of the author’s convolutional neural network. The network includes a number of additional special transformations (data compression, suppression of the influence of an unknown background environment, etc.) preceding the training of a classical MLP neural network and adapted to the inverse problem that is being solved. This allows us to formally, excluding the human factor, solve inverse problems of geoelectrics of large dimensions without specifying a first approximation based on data measured in areas whose dimensions exceed the dimensions of the network training area. The inversion speed is a few tens of seconds and does not depend on the physical dimensionality (2D or 3D) of the data. The solution to the inverse problem found using a trained neural network can, if necessary, be refined using a random search method. Numerical results of solving 3D geoelectric problems on model and field data are presented, confirming the stated development parameters.