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

D.S. Rakisheva, И. Н. Модин, Balgaisha Mukanova

BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2020

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DOI 10.31489/2020m2/204-213

Data confidence 70 medium

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Abstract

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