The Solution of the Direct Problem of Electrical Prospecting with Direct Current under Conditions of Ground Surface Relief
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The Solution of the Direct Problem of Electrical Prospecting with Direct Current under Conditions of Ground Surface Relief

Authors: Balgaisha Mukanova, Tolkyn Mirgalikyzy

Abstract:

Theory of interpretation of electromagnetic fields studied in the electrical prospecting with direct current is mainly developed for the case of a horizontal surface observation. However in practice we often have to work in difficult terrain surface. Conducting interpretation without the influence of topography can cause non-existent anomalies on sections. This raises the problem of studying the impact of different shapes of ground surface relief on the results of electrical prospecting's research. This research examines the numerical solutions of the direct problem of electrical prospecting for two-dimensional and three-dimensional media, taking into account the terrain. The problem is solved using the method of integral equations. The density of secondary currents on the relief surface is obtained.

Keywords: Ground surface relief, method of integral equations, numerical method.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1100224

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References:


[1] R. C. Fox, G. W. Hohmann, T. J. Killpack, L. Rijo, "Topographic effects in resistivity and induced-polarization surveys", Geophysics, vol. 45, no. 1, pp. 75-93, 1980.
[2] T. R. Madden, "The resolving power of geoelectric measurements for delineating resistive zones within the crust, in The structure and physical properties of the earth's crust": J. G. Heacock, Ed., Am. Geophys. Union, Geophys. Monogr., 14.955105, 1971.
[3] L. М. Alpin, "Field source in the theory of electrical prospecting", Applied geophysics, vol. 3, pp. 56-200, Moscow, 1947. (in Russian)
[4] K. Dieter, N. R. Paterson, F. S. Grant, "KP and resistivity type awes for three- dimensional bodies", Geophysics, vol. 34, no. 4, pp. 615-632, 1969.
[5] G. W. Hohmann, "Three dimensional induced polarization and electromagnetic modeling", Geophysics, vol. 40, no. 2, pp. 309-324, 1975.
[6] I. R. Mufti, "Finite-difference modeling for arbitrary-shaped two dimensional structures", Geophysics, vol. 41, no. 1, pp. 62-78, 1976.
[7] A. Dey, H. F. Morrison, "Resistivity modeling for arbitrary shaped two-dimensional structures", Geophysical Prospecting, vol. 27, no. 1, pp. 106-136, 1979.
[8] J. H. Coggon, "Electromagnetic and electrical modeling by the finite element method", Geophysics, vol. 36, no. 1, pp. 132-155, 1971.
[9] S. Z. Xu, S. Zhao and Y. Ni, "A boundary element method for 2-D dc resistivity modeling with a point current source". Geophysics 63, 399-404, 1998.
[10] L. S. Chanturishvili, "On account of the quantitative impact of relief for some cases of direct current intelligence", Proceedings of the Institute of Geophysics, Academy of Sciences of the Georgian SSR. 1955. T. 14. S. 199-209.
[11] M. H. Loke, "Topographic modelling in resistivity imaging inversion", 62nd EAGE Conference and Technical Exhibition, Extended Abstracts, Glasgow, Scotland, 29 May - 2 June, 2000.
[12] E. Erdogan, I. Demirci, M. E. Candasayar, "Incorporating topography into 2D resistivity modeling using finite-element and finite-difference approaches", Geophysics, vol. 73, no.3, pp. 135-142, 2008.
[13] I. Demirci, E. Erdogan, M. E. Candasayar, "Two-dimensional inversion of direct current resistivity data incorporating topography by using finite difference techniques with triangle cells: Investigation of Kera fault zone in western Crete", Geophysics, vol. 77, no. 1, pp. 67-75, 2012.
[14] S. Penz, H. Chauris, D. Donno, C. Mehl, "Resistivity modeling with topography", Geophys. J. Int., 194, pp. 1486–1497, 2013.
[15] P. Queralt, J. Pous, A. Marcuello, "2D resistivity modelling: an approach to arrays parallel to the strike direction", Geophysics, vol. 56, no. 7, pp. 941- 950, 1991.
[16] P.I. Tsourlos, J.E. Szymanski, G.N. Tsokas, "The effect of topography on commonly used resistivity arrays", Geophysics, vol. 64, no. 5, pp. 1357-1363, 1999.
[17] Т. Gunther, С. Rucker, K. Spitzer, "Three-dimensional modelling and inversion of dc resistivity data incorporating topography – I. Modelling", Geophys. J. Int. 166, pp. 495–505, 2006.
[18] Т. Gunther, С. Rucker, "Boundless Electrical Resistivity Tomography", BERT 2 - the user tutorial, version 2.0, 2013.
[19] M.K. Orunkhanov, B.G. Mukanova, B.K. Sarbasova, "Convergence of an integral equation on geoelectric sounding problem above a local patch", Computational technologies, vol. 9, no. 6, pp. 68-72, 2004. (in Russian), View at Google Scholar
[20] M. K. Orunkhanov, B. G. Mukanova, B. K. Sarbasova, "Convergence of the method of integral equations for quasi three-dimensional problem of electrical sounding", In: Computational Science and High Performance Computing II, Springer-Berlin-Heidelberg, pp.175-180, 2006.
[21] M. Orunkhanov, B. Mukanova, "The integral equations method in problems of electrical sounding", In: Advances in High Performance Computing and Computational Sciences, Springer-Berlin-Heidelberg, pp.15-21, 2006.
[22] M. K. Orunkhanov, B. G. Mukanova, B. K. Sarbasova, "Numerical implementation of method of potentials for sounding above an inclined plane", Computational technologies, vol. 9, Special issue, pp. 45-48, 2004. (in Russian), View at Google Scholar
[23] S. Yilmaz, N. Coskun, "A study of the terrain-correction technique for the inhomogeneous case of resistivity surveys", Scientific Research and Essays, vol. 6, no. 24, pp. 5213-5223, 2011.
[24] Dahlin, T., and Zhou, B. A numerical comparison of 2D resistivity imaging with 10 electrode arrays. Geophysical Prospecting, 52, 2004, 379-398.