Inverse Problems of Geoelectrics: Basic Principles and Development Trends

A systematic review of modern methods for solving inverse problems in geoelectrics is presented. Three main paradigms are considered: a deterministic framework based on Tikhonov regularization, a probabilistic approach based on Bayesian statistical inference, and an approximation strategy based on neural network (NN) method. Particular attention is paid to fundamental aspects of the inverse problem related to solutions non-uniqueness and its dependence on depth of investigation and parameterization density. The evolution of NN approach is analyzed, from classical methods using a simple perceptron to multilayer physics- informed neural networks (PINN) using deep machine learning (DML) techniques. Numerical results are presented.