Journal of Applied Mathematics

Method of Integral Equations for the Problem of Electrical Tomography in a Medium with Ground Surface Relief

Tolkyn Mirgalikyzy, Balgaisha Mukanova, and Igor Modin

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Abstract

The direct task of the subsurface exploration of a homogeneous medium with surface relief by the resistivity method is analyzed. To calculate the resistivity field for such a medium, the method of integral equations was successfully applied for the first time. The corresponding integral equation for the density of secondary current sources on the surface of the medium was established. The method of computational grid construction, adapted to the characteristics of the surface relief, was developed for the numerical solution of the integral equation. This method enables the calculation of the resistivity field of a point source on a surface that is not smooth and allows for steep ledges. Numerical examples of the calculation of resistivity fields and apparent resistivity are shown. The anomalies of apparent resistivity arising from the deviation of the surface shape from a flat medium were quantitatively established as model examples. Calculations of apparent resistivity for the direct current sounding method were carried out using modifications of the electrical tomography approach.

Article information

Source
J. Appl. Math., Volume 2015 (2015), Article ID 207021, 10 pages.

Dates
First available in Project Euclid: 17 August 2015

Permanent link to this document
https://projecteuclid.org/euclid.jam/1439816409

Digital Object Identifier
doi:10.1155/2015/207021

Citation

Mirgalikyzy, Tolkyn; Mukanova, Balgaisha; Modin, Igor. Method of Integral Equations for the Problem of Electrical Tomography in a Medium with Ground Surface Relief. J. Appl. Math. 2015 (2015), Article ID 207021, 10 pages. doi:10.1155/2015/207021. https://projecteuclid.org/euclid.jam/1439816409


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