Advertisement

Introduction

  • Balgaisha Mukanova
  • Igor Modin
Chapter
Part of the Innovation and Discovery in Russian Science and Engineering book series (IDRSE)

Abstract

In this chapter, we present a short review of the literature and a brief introduction to resistivity sounding methods and electrical resistivity tomography (ERT). We recall the very origin of that method and the most influential research in this field. Several advantages of the method and its relations with mathematical modeling, the boundary element method (BEM), and the theory of inverse problems are discussed.

Keywords

Electrical resistivity tomography BEM Inverse problems Data inversion Electrical sounding 

References

  1. L.M. Alpine, Istochniki polya v teorii electricheskoirazvedki. Prikladnaya Geophizika 3, 56–200 (1947)Google Scholar
  2. R.D. Barker, The offset system of electrical resistivity sounding and its use with a multicore cable. Geophys. Prospect. 29(1), 128–143 (1981)CrossRefGoogle Scholar
  3. R.D. Barker, A simple algorithm for electrical imaging of the subsurface. First Break 10(2), 53–62 (1992)Google Scholar
  4. A.A. Bobachyev, Resheniye pryamykh i obratnykh zadach elektrorazvedki metodom soprotivleniy dlya slozhno-postroyennykh sred, Dissertation, Moscow, MSU, 95 p, 2003Google Scholar
  5. A.A. Bobachyev, Programmnoye obespecheniye dlya odnomernoy interpretatsii krivykh VEZ, VEZ-VP i MTZ, in Voprosy teorii i praktiki geologichekoy geologicheskoy interpretatsii gravitatsionnykh, magnitnykh i elektricheskikh poley, Part 1: Proceedings of the 29th session of the International Seminar, 28 Jan–2 Feb 2002 (UGGA, Yekaterinburg, 2002)Google Scholar
  6. A.A. Bobachyev, М.N. Marchenko, I.N. Modin, E.V. Pervago, A.V. Urusova, V.A. Shevnin, Novye podkhody k elektricheskim zondirovaniyam gorizontal’no-neodnorodnykh sred. Physika Zemli 12, 79–90 (1995)Google Scholar
  7. A.A. Bobachyev, I.N. Modin, E.V. Pervago, V.A. Shevnin, Mnogoelektrodnyye elektricheskiye zondirovaniya v usloviyakh gorizontal'no-neodnorodnykh sred (Review), in Razvedochnaya geofizika, vol. 2 (JCS ‘Geoinformmark’, Мoscow, 1996)Google Scholar
  8. A.A. Bobachyev, A.A. Gorbunov, I.N. Modin, V.A. Shevnin, Elektrotomografiya metodom soprotivleniy i vyzvannoy polyarizatsii. Pribory i systemy razvedochnoi geophisiki 2, 14–17 (2006)Google Scholar
  9. L.S. Chanturishvili, Electro Investigation for the Design of Roads in Rough Terrain (Avtotransizdat, Moscow, 1959)Google Scholar
  10. L.S. Chanturishvili, Spetsial’nyye Zadachi Elektrorazvedki Pri Proyektirovanii Dorog (Transport, Moscow, 1983)Google Scholar
  11. J.H. Coggon, Electromagnetic and electrical modeling by the finite element method. Geophysics 36, 132–155 (1971)CrossRefGoogle Scholar
  12. T. Dahlin, On the automation of 2D resistivity surveying for engineering and environmental applications, PhD thesis, Lund University, 1993Google Scholar
  13. T. Dahlin, 2D resistivity surveying for environmental and engineering applications. First Break 14, 275–283 (1996)CrossRefGoogle Scholar
  14. T. Dahlin, The development of DC resistivity imaging techniques. Comput. Geosci. 27, 1019–1029 (2001)CrossRefGoogle Scholar
  15. T. Dahlin, B. Zhou, A numerical comparison of 2D resistivity imaging with 10 electrode arrays. Geophys. Prospect. 52, 379–398 (2004)CrossRefGoogle Scholar
  16. T. Dahlin, R. Wisen, D. Zhang, 3D Effects on 2D resistivity imaging modelling and field surveying results. In 13th European Meeting of Environmental and Engineering Geophysics, Session: Electrical and Electromagnetic Methods, vol. 1 (2007)Google Scholar
  17. 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 77(1), 67–75 (2012)CrossRefGoogle Scholar
  18. A. Dey, H.F. Morrison, Resistivity modeling for arbitrary shaped two-dimensional structures. Geophys. Prospect. 27, 106–136 (1979)CrossRefGoogle Scholar
  19. L.S. Edwards, A modified pseudosection for resistivity and IP. Geophysics 42, 1020–1036 (1977)CrossRefGoogle Scholar
  20. R.G. Ellis, D.W. Oldenburg, The pole-pole 3-D DC-resistivity inverse problem: a conjugate- gradient approach. Geophys. J. Int. 119, 187–194 (1994)CrossRefGoogle Scholar
  21. E. Erdogan, I. Demirci, M.E. Candasayar, Incorporating topography into 2D resistivity modeling using finite-element and finite-difference approaches. Geophysics 73(3), 135–142 (2008)CrossRefGoogle Scholar
  22. R.C. Fox, G.W. Hohmann, T.J. Killpack, L. Rijo, Topographic effects in resistivity and induced-polarization surveys. Geophysics 45, 75–93 (1980)CrossRefGoogle Scholar
  23. D.H. Griffits, J. Turnbill, A multi-electrode array for resistivity surveying. First Break 3(7), 16–20 (1985)Google Scholar
  24. Т. Gunther, C. Rucker, Boundless electrical resistivity tomography: BERT 2—the user tutorial, Ver. 2.0. (Geophysical Inversion and Modelling Library, https://www.pygimli.org/, 2013)Google Scholar
  25. Т. Gunther, C. Rucker, K. Spitzer, Three-dimensional modelling and inversion of dc resistivity data incorporating topography—I. Modelling. Geophys. J. Int. 166, 495–505 (2006)CrossRefGoogle Scholar
  26. G.W. Hohmann, Three-dimensional induced polarization and electromagnetic modeling. Geophysics 40, 309–324 (1975)CrossRefGoogle Scholar
  27. H.T. Holcombe, G.R. Jiracek, Three-dimensional terrain corrections in resistivity surveys. Geophysics 49, 439–452 (1984)CrossRefGoogle Scholar
  28. J.R. Inman, J. Ryu, S.H. Ward, Resistivity inversion. Geophysics 38(6), 1088–1108 (1973)CrossRefGoogle Scholar
  29. V.K. Khmelevskii, V.A. Shevnin, Geophyzicheskie Metody Issledoavnia (Nedra, Moscow, 1988), 296 pGoogle Scholar
  30. O. Koefoed, Geosounding Principles: Resistivity Sounding Measurements (Elsevier, Amsterdam, 1979)Google Scholar
  31. D.J. LaBrecque, M. Miletto, W. Daily, A. Ramirez, E. Owen, The effect of noise on Occam’s inversion of resistivity tomography data. Geophysics 61(2), 538–548 (1996)CrossRefGoogle Scholar
  32. R.E. Langer, An inverse problem in differential equations. Am. Math. Soc. Bull. 39, 814–820 (1933)CrossRefGoogle Scholar
  33. H. Lehrnann, Potential representation by independent configurations on a multielectrode array. Geophys. J. Int. 120, 331–338 (1995)CrossRefGoogle Scholar
  34. V. Lesur, M. Cuer, A. Straub, 2-D and 3-D interpretation of electrical tomography measurements, part 2: the inverse problem. Geophysics 64(2), 396–402 (1999)CrossRefGoogle Scholar
  35. M.H. Loke, in Topographic modeling in electrical imaging inversion: 62nd conference and technical exhibition, EAGE, Extended Abstracts, D-2 (2000)Google Scholar
  36. M.H. Loke, R.D. Barker, Rapid least-squares inversion of apparent resistivity pseudosections using a quasi-Newton method. Geophys. Prospect. 44, 131–152 (1996)CrossRefGoogle Scholar
  37. M.H. Loke, T. Dahlin, A combined Gauss-Newton and quasi-Newton inversion method for the interpretation of apparent resistivity pseudosections, Paper presented at the 3rd Meeting of the Environmental and Engineering Geophysics Society—European Section, Sept 1997 (Aarhus, Denmark, 1997)Google Scholar
  38. T.R. Madden, The resolving power of geoelectric measurements for delineating resistive zones within the crust. In The stincture and physical properties of the earth’s crust, ed. By J.G. Heacock, Am. Geophys. Union, Geophys. Monogr., vol. 14.955105 (1971)Google Scholar
  39. H. Maurer, K. Holliger, D.E. Boerner, Stochastic regularization: smoothness or similarity? Geophys. Res. Leu. 25(15), 2889–2892 (1998)CrossRefGoogle Scholar
  40. W. Menke, Geophysical Data Analysis: Discrete Inverse Theory (Academic, Orlando, FL, 1984)Google Scholar
  41. T. Mirgalikyzy, B. Mukanova, I. Modin, Method of integral equations for the problem of electrical tomography in a medium with ground surface relief. J. Appl. Math. 2015, 207021 (2015).  https://doi.org/10.1155/2015/207021 CrossRefGoogle Scholar
  42. I.N.Modin, V.A. Shevnin, V.K. Khmelevskii, A.G. Yakovlev et al. In Electricheskoye Zondirovanie Geologicheskoi Sredy. Part I (MSU, Moscow, 1988), p. 176Google Scholar
  43. I.R. Mufti, Finite-difference modeling for arbitrary-shaped two dimensional structures. Geophysics 41(62) (1976)Google Scholar
  44. B. Mukanova, T. Mirgalikyzy, D. Rakisheva, Modelling the influence of ground surface relief on electric sounding curves using the integral equations method. Math. Prob. En. 2017, 9079475 (2017).  https://doi.org/10.1155/2017/9079475
  45. M. Orunkhanov, B. Mukanova, The integral equations method in problems of electrical sounding, in Advances in High Performance Computing and Computational Sciences, ed. by Y.I. Shokin, N. Danaev, M. Orunkhanov, N. Shokina (Eds), vol. 93, (Springer, Berlin, 2006), pp. 15–21Google Scholar
  46. M.K. Orunkhanov, B.G. Mukanova, B.K. Sarbasova, Chislennaya realizacia metoda potencialov v zadache zondirovania nad naklonnym lpatom, in Computational Technologies, vol. 9, (Siberian Branch of Russian Academy of Sciences, Novosibirsk, 2004a), pp. 45–48Google Scholar
  47. M.K. Orunkhanov, B.G. Mukanova, B.K. Sarbasova, Chislennoe modelirovanie zadach electricheskogo zondirovania. In Computational Technologies, Special Issue, part 3, vol. 9 (Almaty-Novosibirsk, 2004b), pp. 259–263Google Scholar
  48. M. Orunkhanov, B. Mukanova, B. Sarbasova, Convergence of the method of integral equations for quasi three-dimensional problem of electrical sounding, in Computational Science and High Performance Computing II, ed. by E. Krause, Y. Shokin, M. Resch, N. Shokina (Eds), (Springer, Berlin, 2005), pp. 175–180Google Scholar
  49. S. Penz, H. Chauris, D. Donno, C. Mehl, Resistivity modeling with topography. Geophys. J. Int. 194(3), 1486–1497 (2013)CrossRefGoogle Scholar
  50. I.P. Skalskaya, Pole tochechnogo istochnika toka, raspolozhennogo na poverkhnosti Zemli nad naklonnym plastom. J. Tech. Phys. 18(10), 1243–1254 (1948)Google Scholar
  51. L.B. Slihter, The interpretation of resistivity prospecting method for horizontal structures. Physics 4, 307–322 (1933)CrossRefGoogle Scholar
  52. S.S. Stefanescu, C. Shlumberger, Sur la distribution electrique potencielle dans une terrain a couches horizontals, homogenes et isotropes. J. Phys. Radium 7, 132–141 (1930)CrossRefGoogle Scholar
  53. A.F. Stevenson, On the theoretical determination of earth resistance from surface potencial measurements. Physics 5, 114–124 (1934)CrossRefGoogle Scholar
  54. A. G. Tarkhov (ed.), Electrorazvedka, Sparvochnik Geophizika (Nedra, Мoscow, 1980)Google Scholar
  55. P.I. Tsourlos, J.E. Szymanski, G.N. Tsokas, The effect of topography on commonly used resistivity arrays. Geophysics 64(5), 1357–1363 (1999)CrossRefGoogle Scholar
  56. A.V. Veshev, Vliyaniye rel'yefa na rezul'taty rabot kombinirovannym elektroprofilirovaniyem, in Uchenye Zapiski LGU, vol. 278, (LSU, Leningrad, 1959)Google Scholar
  57. A.V. Veshev, In Electroprofilirovanie na Postoyannom I Peremennom Toke, 2nd ed. (Nedra, Leningrad, 1980). (in Russian)Google Scholar
  58. S.Z. Xu, The Boundary Element Method in Geophysics, Geophysical Monograph Series (Issue 9) (SEG Books, 2001)Google Scholar
  59. S.Z. Xu, S. Zhao, Y. Ni, A boundary element method for 2-D dc resistivity modeling with a point current source. Geophysics 63, 399–404 (1998)CrossRefGoogle Scholar
  60. S.A.Yerokhin, Primeneniye elektrotomografii pri resheniya rudnykh, inzhenernykh i arkheologicheskikh zadach, Dissertation, Moscow State University, Moscow, 2012Google Scholar
  61. S.A. Yerokhin, I.N. Modin, V.P. Novikov, A.M. Pavlova, Vozmozhnosti Elektricheskoy Tomografii Pri Izuchenii Karstovo-Suffozionnykh Voronok, in Ingenernye Izyskania, vol. 11, (Geomarketing, Moscow, 2011)Google Scholar
  62. A.A.R. Zohdy, A new method for the automatic interpretation of Schlumberger and Wenner sounding curves. Geophysics 54(2), 245–253 (1989)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Balgaisha Mukanova
    • 1
  • Igor Modin
    • 2
  1. 1.L.N. Gumilyov Eurasian, National UniversityAstanaKazakhstan
  2. 2.Lomonosov Moscow State UniversityMoscowRussia

Personalised recommendations