Mapes of secondary sources in the problem of ERT probing 2D medium: numerical method and analytical solutions

Abstract

The paper considers a mathematical model of electrical tomography above the media with local inclusions. Numerical solutions of a system of integral equations for a medium with local inclusion are compared against a numerical implementation of the analytical solution of the problem for a case of a sphere in homogeneous space. The parameters of local inclusion and the depth of heterogeneity are varied. Maps of secondary sources in the ERT (Electrical Resistivity Tomography) probing problem are constructed: for local inclusion in the form of the ellipsoid, an ellipsoid in a homogeneous space (analytical solution of the problem) and for two-layer half-spaces as well. Numerical results are presented, and maps of secondary sources in the cases where the immersed heterogeneity is an insulator and a conductor are computed.