Consideration of induced polarization effects in solving inverse problems of geoelectrical sounding

The paper aims to develop an algorithm for identifying the physical (polarizability and resistivity) and geometric (center of mass, orientation, and dimensions) characteristics of local heterogeneities. This is achieved by analyzing induced polarization (IP) potential field data measured at the boundary of the object, using the indirect near-boundary element method. Methodology. A piecewise homogeneous half-plane was chosen as a model of the Earth's crust, where the components are in non-ideal contact. An efficient combination of the indirect near-boundary element method with a cascade iterative algorithm for parameter identification was developed to solve the inverse two-dimensional problem of the IP potential field theory. At each step of the algorithm, a series of direct problems was solved, in which the Laplace equations were transformed into integral representations. This transformation utilized the Green's function for a half-plane, which automatically satisfies the boundary condition and eliminates the need for boundary discretization. Additionally, a fundamental solution for the inclusion was applied.  The conditions of non-ideal contact were satisfied in the collocation sense at the midpoints of each boundary element. This made it possible to determine the intensities of the unknown sources introduced into the near-boundary elements and approximated by constants. The medium and the inclusion were then treated as independent regions, and the desired IP field potential and flow across their boundaries were calculated. Results. A computational experiment was conducted for the problem of geoelectrical sounding using a constant artificial field (electrical profiling method). Initial estimates of the physical and geometric characteristics of the inclusion were obtained based on the behavior of apparent resistivity and apparent polarizability. Through two cascades of iterations, the location and approximate dimensions of the inclusion were first refined, followed by adjustments to its shape and spatial orientation. A necessary condition for successful identification was the presence of a boundary segment with an excess of boundary conditions, which enabled the minimization of the selected functional on that segment. Originality. The problem of geoelectrical sounding by direct current in piecewise homogeneous polarized media was reduced, via mathematical modeling, to a potential theory problem with non-ideal contact conditions at the interfaces between different media. Practical significance. An efficient computational approach was developed for solving the inverse problem of geoelectrical sounding using direct current. It considers the effect of induced polarization, including surface, volume, and mixed polarization. Computational efficiency was achieved through a two-stage cascade- iterative algorithm that refined initial approximations and eliminated parameters with negligible impact on the results.