Neural Network Solution of Inverse Problems of Geological Prospecting with Discrete Output

Abstract

The inverse problems of exploration geophysics are to reconstruct the spatial distribution of the properties of the medium in the Earth’s thickness from the geophysical fields measured on its surface. In particular, this paper deals with the problems of gravimetry, magnetometry, and magnetotelluric sounding, as well as their integration, i.e., the simultaneous use of several geophysical fields to restore the desired distribution. To implement the integration, a 4-layer 2D model was used, where the inverse problem was to determine the lower boundary of the layers, and each layer was characterized by variable values of the depth of the lower boundary along the section and fixed values of density, magnetization, and resistivity, both for the layer and for the entire data set. To implement the neural network solution of the inverse problem, a data set was generated by solving the direct problem, where for each pattern, the distribution of layer depth values was set randomly in a given range and with a given step, i.e. it took discrete values from a certain set. In this paper, we consider an approach involving the use of neural networks to solve the problem of multiclass classification, where class labels correspond to discrete values of the determined layer depths. The results of the solution are compared with the results of the solution of the same inverse problem in the formulation