Numerical algorithm for solving of electrical prospecting problems for medium with a surface relief

Abstract

Nowadays the problem of the influence of the ground surface relief on the distribution of the electric field is a pressing issue in the interpretation of electromagnetic fields studied in the direct current electrical prospecting. The paper deals with testing the algorithm for the numerical solution of the problem of electrical sensing of a medium with the ground surface relief by means of modeling using integral equations. The idea of the method of integral equations is to represent the electric field as the sum of the primary field and the field of the secondary charges. The contact boundaries and the surface of the geoelectric section act as a secondary creators of the electric field. The problem of calculating the fields is reduced to the systems of integral equations on the density of secondary sources induced on the contact surfaces of conducting media and on the relief surface of the medium. A mathematical description of this phenomenon leads to Fredholm equations of the second kind with a polar core. The calculation algorithm was tested by comparing the results with the solutions given in the open access works on taking into account the influence of the relief, setting the same environmental parameters. Comparisons are made using the finite-element and finite-difference methods obtained by different approaches to take into account the effect of relief in 2D environments. Comparisons are also made with the physical modeling data obtained. We can say that our results of calculations curves of apparent resistivity are in good agreement with the available research in this area.