Method of integro-differential equations for interpreting the results of vertical electrical sounding of the soil

The paper is devoted to the problem of determining the geoelectric structure of the soil within the procedure of testing the grounding arrangements of existing power plants and substations to the required depth in conditions of dense development. To solve the problem, it was proposed to use the Schlumbergers method , which has a greater sounding depth compared to the Wenner electrode array. The purpose of the work is to develop a mathematical model for interpreting the results of soil sounding by the Schlumberger method in the form of a four-layer geoelectric structure. Methodology. To construct a mathematical model, it is proposed to use the solution of a particular problem about the field of a point current source, which, like the observation point, is located in the first layer of a four-layer soil. Based on this expressions, a system of linear algebraic equations of the 7-th order with respect to the unknown coefficients ai and bi was compiled. On the basis of its analytical solution, an expression for the potential of the electric field was obtained for conducting VES (the point current source and the observation point are located only on the soil surface). Results. Comparison