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Mathematical Problems in Engineering
Volume 2017, Article ID 9079475, 10 pages
Research Article

Modelling the Influence of Ground Surface Relief on Electric Sounding Curves Using the Integral Equations Method

L.N. Gumilyov Eurasian National University, Astana 010008, Kazakhstan

Correspondence should be addressed to Balgaisha Mukanova; moc.liamg@10ahsbm

Received 27 March 2017; Accepted 15 June 2017; Published 26 July 2017

Academic Editor: Eric Feulvarch

Copyright © 2017 Balgaisha Mukanova et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The problem of electrical sounding of a medium with ground surface relief is modelled using the integral equations method. This numerical method is based on the triangulation of the computational domain, which is adapted to the shape of the relief and the measuring line. The numerical algorithm is tested by comparing the results with the known solution for horizontally layered media with two layers. Calculations are also performed to verify the fulfilment of the “reciprocity principle” for the 4-electrode installations in our numerical model. Simulations are then performed for a two-layered medium with a surface relief. The quantitative influences of the relief, the resistivity ratios of the contacting media, and the depth of the second layer on the apparent resistivity curves are established.