Modeling Earth Systems and Environment

, Volume 4, Issue 3, pp 1059–1083 | Cite as

Automated optimization of electrode locations for electrical resistivity tomography

  • Ndifreke Udosen
  • Roland Potthast
Original Article


This work describes the automated search for optimal electrode locations that will improve reconstructions of a 2D electrical resistivity tomography problem within a meta inverse framework. The meta inverse framework was incorporated into a finite integration forward solver developed for simulating the measurement data, and into an inverse solver developed for reconstructing the resistivity distribution within the subsurface. The meta inverse framework solver then searched to find optimal electrode locations at which best reconstructions of the resistivity distribution within the subsurface could be obtained. The numerical results obtained from applying the forward, inverse and meta inverse solvers to search for resistance anomalies in an electrical resistivity tomography problem are presented. The results show that these solvers are successful for simulations, reconstructions, and for determining the optimal electrode locations at which the best reconstruction of the resistivity distribution can be obtained.


Optimization Electrical resistivity tomography Meta-inverse framework Finite integration Reconstruction 


  1. Athanasiou EN, Tsourlos PI, Papazachos CB, Tsokas GN (2006) Optimizing resistivity array configurations by using a non-homogeneous background model. In: Proceedings, 12th Annual Meeting EAGE-Near Surface Geophysics, Helsinki, FinlandGoogle Scholar
  2. Athanasiou EN, Tsourlos PI, Papazachos CB, Tsokas GN (2009) Optimizing electrical resistivity array configurations by using a method based on the sensitivity matrix. In: Proceedings, 15th Annual Meeting EAGE-Near Surface Geophysics, Dublin, IrelandGoogle Scholar
  3. Barker RD (1981) The offset system of electrical resistivity sounding and its use with a multicore cable. Geophys Prospect 29(1):128–143CrossRefGoogle Scholar
  4. Cardarelli E, Fischanger F (2006) 2D data modeling by electrical resistivity tomography for complex subsurface geology. Geophys Prospect 54(2):121–133CrossRefGoogle Scholar
  5. Cherkaeva E, Tripp AC (1996) Optimal survey design using focused resistivity arrays. IEEE Trans Geosci Remote Sens 34(2):358–366CrossRefGoogle Scholar
  6. Coggon JH (1971) Electromagnetic and electrical modeling by the finite element method. Geophysics 36(1):132–155CrossRefGoogle Scholar
  7. Colton D, Kress R (1992) Inverse acoustic and electromagnetic scattering theory, volume 93 of Applied Mathematical Sciences. Springer, BerlinCrossRefGoogle Scholar
  8. Dahlin T (1993) On the automation of 2D resistivity surveying for engineering and environmental applications. PhD thesis, Lund UniversityGoogle Scholar
  9. Dahlin T (1996) 2D resistivity surveying for environmental and engineering applications. First Break 14(7): 275–283Google Scholar
  10. Dahlin T (2001) The development of DC resistivity imaging techniques. Comput Geosci 27(9):1019–1029CrossRefGoogle Scholar
  11. Dahlin T, Bernstone C (1997) A roll-along technique for 3D resistivity data acquisition with multi-electrode arrays. In: Proceedings of the Symposium on the Application of Geophysics to Engineering and Environmental Problems (SAGEEP), Reno, NevadaGoogle Scholar
  12. Dahlin T, Loke MH (1998) Resolution of 2D Wenner imaging as assessed by numerical modeling. J Appl Geophys 38(4):237–249CrossRefGoogle Scholar
  13. Dahlin T, Zhou B (2002) Gradient and mid-point-referred measurements for multi-channel 2D resistivity imaging. In: Proceedings, 8th Meeting Environmental and Engineering Geophysics, Aveiro, PortugalGoogle Scholar
  14. Dey A, Morrison HF (1979) Resistivity modeling for arbitrarily shaped two-dimensional structures. Geophys Prospect 27(1):106–136CrossRefGoogle Scholar
  15. Engl HW, Hanke M, Neubauer A (1996) Regularization of inverse problems, volume 375 of Mathematics and its Applications. Kluwer Academic Publishers Group, DordrechtCrossRefGoogle Scholar
  16. Fernandez-Martinez JL, Fernandez-Alvarez JP, Garcia-Gonzalo ME, Perez COM, Kuzma HA, (2008) Particle Swarm Optimization (PSO): a simple and powerful algorithm for geophysical inversion. Society of Exploration Geophysicists (SEG) Expanded AbstractsGoogle Scholar
  17. Furman A, Ferre TPA, Warrick AW (2003) A sensitivity analysis of electrical resistivity tomography array types using analytical element modeling. Vadose Zone J 2(3):416–423CrossRefGoogle Scholar
  18. Furman A, Ferre TPA, Warrick AW (2004) Optimization of ERT surveys for monitoring transient hydrological events using perturbation sensitivity and genetic algorithms. Vadose Zone J 3(4):1230–1239CrossRefGoogle Scholar
  19. Furman A, Ferre TPA, Heath GL (2007) Spatial focusing of electrical resistivity surveys considering geologic and hydrologic layering. Geophysics 72(2):F65–F73CrossRefGoogle Scholar
  20. Gautam PK, Biswas A (2016) 2D geo-electrical imaging for shallow depth investigation in Doon Valley Sub-Himalaya, Uttarakhand, India. Model Earth Syst Environ 2:175CrossRefGoogle Scholar
  21. Ghosh DP (1971) The application of linear filter theory to the direct interpretation of geoelectrical resistivity sounding measurements. Geophys Prospect 19(2):192–217CrossRefGoogle Scholar
  22. Gordon R, Herman GT, Johnson SA (1975) Image reconstruction from projections. Sci Am 233(4):56–68CrossRefGoogle Scholar
  23. Griffiths D, Turnbull J (1985) A multi-electrode array for resistivity surveying. First Break 3(7):16–20Google Scholar
  24. Griffiths D, Turnbull J, Olayinka AI (1990) Two-dimensional resistivity mapping with a computer-controlled array. First Break 8(4):121–129Google Scholar
  25. Groetsch CW (2007) Integral equations of the first kind, inverse problems and regularization: a crash course. J Phys Conf Ser. Inverse Probl Appl Sci-Towar Breakthr 73:1–32Google Scholar
  26. Henderson RP, Webster JG, Swanson DK (1976) A thoracic electrical impedance camera. In: Proceedings of the 29th Annual Conference on Engineering in Medicine and Biology, Boston, MassachusettsGoogle Scholar
  27. Hennig T, Weller A (2005) Two dimensional object orientated focusing of geoelectrical multielectrode measurements. In: Proceedings, 11th Annual Meeting EAGE-Environmental and Engineering Geophysics, Palermo, SicilyGoogle Scholar
  28. Hennig T, Weller A, Moller M (2008) Object orientated focussing of geoelectrical multielectrode measurements. J Appl Geophys 65:57–64CrossRefGoogle Scholar
  29. Inman JR (1975) Resistivity inversion with ridge regression. Geophysics 40(5):798–817CrossRefGoogle Scholar
  30. Isaacson D (1986) Distinguishability of conductivities by electric current computed tomography. IEEE Trans Med Imaging 5(2):91–95CrossRefGoogle Scholar
  31. Keller GV, Frischknecht FC (1966) Electrical methods in geophysical prospecting, volume 10 of International Series of Monographs on Electro-magnetic Waves. Pergamon Press, New YorkGoogle Scholar
  32. Kirsch A (1996) An introduction to the mathematical theory of inverse problems. Applied Mathematical Sciences. Springer, BerlinCrossRefGoogle Scholar
  33. Kress R (1999) Linear integral equations, volume 82 of Applied Mathematical Sciences. Springer, New YorkCrossRefGoogle Scholar
  34. LaBrecque D, Miletto M, Daily W, Ramirez A, Owen E (1996) The effects of noise on Occam’s inversion of resistivity tomography data. Geophysics 61(2):538–548CrossRefGoogle Scholar
  35. Loke MH, Barker RD (1995) Least-squares deconvolution of apparent resistivity pseudosections. Geophysics 60(6):1682–1690CrossRefGoogle Scholar
  36. Loke MH, Barker RD (1996) Rapid least-squares inversion of apparent resistivity pseudo-sections by a quasi-Newton method. Geophys Prospect 44(1):131–152CrossRefGoogle Scholar
  37. Loke MH, Wilkinson PB (2009) Rapid parallel computation of optimized arrays for electrical imaging surveys. In: Proceedings, 15th Annual Meeting EAGE-Near Surface Geophysics, Dublin, IrelandGoogle Scholar
  38. Loke MH, Acworth I, Dahlin T (2003) A comparison of smooth and blocky inversion methods in 2D resistivity imaging surveys. Explor Geophys 34:182–187CrossRefGoogle Scholar
  39. Loke MH, Alfouzan FA, Nawawi NM (2007) Optimisation of electrode arrays used in 2D resistivity imaging surveys. In: Extended Abstracts, 19th ASEG Geophysical Conference and Exhibition, AustraliaGoogle Scholar
  40. Lytle RJ, Dines KA (1978) An impedance camera: a system for determining the spatial variation of electrical conductivity. Technical Report UCRL-52413, Lawrence Livermore National LaboratoryGoogle Scholar
  41. Mufti IR (1976) Finite-difference resistivity modeling for arbitrarily shaped two-dimensional structures. Geophysics 41(1):62–78CrossRefGoogle Scholar
  42. Olagunju E, Ariyibi E, Awoyemi M, Adebayo A, Dasho O, Adenika C (2017) Application of geochemical and geophysical approach to environmental impact assessment: a case study of Emirin active open dumpsite, Ado-Ekiti Southwestern Nigeria. Model Earth Syst Environ. Google Scholar
  43. Oldenburg DW, Li Y (1994) Inversion of induced polarization data. Geophysics 59(9):1327–1341CrossRefGoogle Scholar
  44. Pelton WH, Rijo L, Swift CM (1978) Inversion of two-dimensional resistivity and induced-polarization data. Geophysics 43(4):788–803CrossRefGoogle Scholar
  45. Plonsey R, Fleming D (1969) Bioelectric Phenomena. McGraw-Hill Inc, New YorkGoogle Scholar
  46. Pridmore DF, Hohmann GW, Ward SH, Sill WR (1981) An investigation of finite-element modeling for electrical and electromagnetic data in three dimensions. Geophysics 46(7):1009–1024CrossRefGoogle Scholar
  47. Sasaki Y (1992) Resolution of resistivity tomography inferred from numerical simulation. Geophys Prospect 40(4):453–463CrossRefGoogle Scholar
  48. Smith NC, Vozof K (1984) Two-dimensional DC resistivity inversion for dipole-dipole data. IEEE Trans Geosci Remote Sens GE 22(1):21–28CrossRefGoogle Scholar
  49. Stummer P, Maurer H, Green AG (2004) Experimental design: electrical resistivity data sets that provide optimum subsurface information. Geophysics 69(1):120–139CrossRefGoogle Scholar
  50. Swindell W, Barrett (1977) Computerized tomography: taking sectional X-rays. Phys Today 30(12):32–41CrossRefGoogle Scholar
  51. Telford WM, Geldart LP, Sheriff RE (1990) Applied geophysics. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  52. Tong L, Yang C (1990) Incorporation of topography into two-dimensional resistivity inversion. Geophysics 55(3):354–361CrossRefGoogle Scholar
  53. Tripp AC, Hohmann GW, Swift CM (1984) Two-dimensional resistivity inversion. Geophysics 49(10):1708–1717CrossRefGoogle Scholar
  54. Udosen NI, George NJ (2018) A finite integration forward solver and a domain search inverse solver for electrical resistivity tomography. Model Earth Syst Environ 4:1–12CrossRefGoogle Scholar
  55. Van Nostrand RG, Cook KL (1966) Intepretation of resistivity data. Geological survey professional paper 499, US Geological SurveyGoogle Scholar
  56. Van Overmeeren RA, Ritsema IL (1988) Continuous vertical electrical sounding. First Break 6(10):313–324Google Scholar
  57. Weiland T (1977) A discretization method for the solution of Maxwell’s equations for six-component fields. Electron Commun AEU 31(3):116–120Google Scholar
  58. Weiland T (1985) On the unique numerical solution of Maxwellian eigenvalue problems in three dimensions. Part Accel 17:227–245Google Scholar
  59. Wilkinson PB, Kuras O, Meldrum PI, Chambers JE, Ogilvy RD (2006a) Comparison of the spatial resolution of standard and optimised electrical resistivity tomography arrays. In: Proceedings of the 12th meeting of the EAGE Near Surface Geophysics Conference, Helsinki, FinlandGoogle Scholar
  60. Wilkinson PB, Meldrum PI, Chambers JE, Kuras O, Ogilvy RD (2006b) Improved strategies for the automatic selection of optimized sets of electrical resistivity tomography measurement configurations. Geophys J Int 167(7):1119–1126CrossRefGoogle Scholar
  61. Wilkinson PB, Ogilvy RD, Chambers JE, Meldrum PI, Kuras O (2007) Array optimisation for multi-channel electrical resistivity tomography instruments. In: Proceedings, 13th Annual Meeting EAGE-Near Surface Geophysics, Istanbul, TurkeyGoogle Scholar
  62. Wilkinson PB, Meldrum PI, Chambers JE, Kuras O, Ogilvy RD (2009) Optimised survey design for geoelectrical resistivity tomography. In: Short Abstracts, 10th International Conference on Biomedical Applications of Electrical Impedance Tomography (EIT 2009), Manchester, United KingdomGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Physics, Geophysics Research Group (GRG)Akwa Ibom State UniversityMkpat-EninNigeria
  2. 2.University of Reading, WhiteknightsReadingUK

Personalised recommendations