Inversion of Electrical Resistivity Data: A Review
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 33122
Inversion of Electrical Resistivity Data: A Review

Authors: Shrey Sharma, Gunjan Kumar Verma

Abstract:

High density electrical prospecting has been widely used in groundwater investigation, civil engineering and environmental survey. For efficient inversion, the forward modeling routine, sensitivity calculation, and inversion algorithm must be efficient. This paper attempts to provide a brief summary of the past and ongoing developments of the method. It includes reviews of the procedures used for data acquisition, processing and inversion of electrical resistivity data based on compilation of academic literature. In recent times there had been a significant evolution in field survey designs and data inversion techniques for the resistivity method. In general 2-D inversion for resistivity data is carried out using the linearized least-square method with the local optimization technique .Multi-electrode and multi-channel systems have made it possible to conduct large 2-D, 3-D and even 4-D surveys efficiently to resolve complex geological structures that were not possible with traditional 1-D surveys. 3-D surveys play an increasingly important role in very complex areas where 2-D models suffer from artifacts due to off-line structures. Continued developments in computation technology, as well as fast data inversion techniques and software, have made it possible to use optimization techniques to obtain model parameters to a higher accuracy. A brief discussion on the limitations of the electrical resistivity method has also been presented.

Keywords: Resistivity, inversion, optimization.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1106169

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 6079

References:


[1] Backus G E and Gilbert J F 1967. Numerical applications of a formalism for geophysical inverse problems. Geophys. J. Asrron. Soc. A 266 123- 92.
[2] Barker, R.D. 1981. The offset system of electrical resistivity sounding and its use with a multicore cable. Geophysical Prospecting 29 (1), 128– 143.
[3] Bentley, L.R., Gharibi, M. 2004. Two- and three-dimensional electrical resistivity imaging at a heterogeneous remediation site. Geophysics 69 (3), 674–680.
[4] Bichara M., Lakshmanan, J. 1976. Fast automatic processing of resistivity soundings: Geophysical. Prospecting. 24, 354-370.
[5] Bouchedda, A., Chouteau, M., Binley, A., Giroux, B. 2012. 2-D joint structural inversion of cross-hole electrical resistance and ground penetrating radar data. Journal of Applied Geophysics 78, 52–67.
[6] Busby, J.P. 2000. The effectiveness of azimuthal apparent-resistivity measurements as a method for determining fracture strike orientations. Geophysical Prospecting 48 (4), 677–695.
[7] Coggon, J.H. 1971. Electromagnetic and electrical modeling by the finite element method. Geophysics 36 (1), 132–155.
[8] Constable et al. 1987. Occam's inversion: A practical algorithm for generating smooth models from electromagnetic sounding data, Geophysics volume 52 289-300.
[9] Chambers et al. 2006. Electrical resistivity tomography applied to geologic, hydrogeologic, and engineering investigations at a former waste-disposal site. Geophysics Volume 71, Issue 6.
[10] Chambers, J.E., Ogilvy, R.D., Kuras, O., Cripps, J.C., Meldrum, P.I. 2002. 3D electrical imaging of known targets at a controlled environmental test site. Environmental Geology 41 (6), 690–704.
[11] Chunduru et al. 1996.2-D resistivity inversion using spline parameterization and simulated annealing: Geophysics, vol. 61, no. 1 P. 151–161.
[12] Cyril Chibueze Okpoli 2013. Sensitivity and Resolution Capacity of Electrode Configurations, International Journal of Geophysics.
[13] Dahlin, T. 2001. The development of DC resistivity imaging techniques. Computers and Geosciences 27 (9), 1019–1029.
[14] Dahlin, T., Bernstone, C., Loke, M.H. 2002. A 3D resistivity investigation of a contaminated site at Lernacken in Sweden. Geophysics 60 (6), 1682–1690.
[15] Dahlin, T., Zhou, B. 2004. A numerical comparison of 2D resistivity imaging with ten electrode arrays. Geophysical Prospecting 52 (5), 379– 398.
[16] Dahlin, T., Zhou, B. 2006. Multiple gradient array measurements for multi-channel 2D resistivity imaging. Near Surface Geophysics 4 (2), 113–123.
[17] Daily, W., Owen, E. 1991. Cross-borehole resistivity tomography. Geophysics 56 (8), 1228–1235.
[18] Dey, A., Morrison, H.F. 1979. Resistivity modelling for arbitrary shaped two-dimensional structures. Geophysical Prospecting 27 (1), 106–136.
[19] Dey, A., Morrison, H.F. 1979. Resistivity modeling for arbitrarily shaped three-dimensional shaped structures. Geophysics 44 (4), 753–780
[20] Farquharson, C.G. 2008. Constructing piecewise-constant models in multidimensional minimum-structure inversions. Geophysics 73 (1), K1–K9
[21] Farquharson, C.G., Oldenburg, D.W., 1998. Nonlinear inversion using general measures of data misfit and model structure. Geophysical Journal International 134 (1), 213–227
[22] Friedel, S.2003.Resolution, stability and efficiency of resistivity tomography estimated from a generalized inverse approach. Geophysical Journal International 153 (2), 305–316.
[23] Gad El-Qady and K. Ushijima 2001. Inversion of DC resistivity data using neural networks -, Geophysical Prospecting 49, 417–430
[24] Ghosh, D.P. 1971. The application of linear filter theory to the direct interpretation of geoelectrical resistivity sounding measurements. Geophysical Prospecting 19 (2), 192–217.
[25] Goldberg, D.E. 1989. Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley Publishing Company Inc., New York, pp. 1–145.
[26] Goldberg, D.E., Deb, K. 1991. A Comparative Analysis of Selection Schemes used in Genetic Algorithms. Foundations of Genetic Algorithms, Morgan Kaufmann, San Francisco, CA, pp. 69–93.
[27] Greenhalgh, S.A., Zhou, B., Greenhalgh, M., Marescot, L., Wiese, T. 2009. Explicit expressions for the Frechet derivatives in 3D anisotropic resistivity inversion. Geophysics 70 (3), F31–F43.
[28] Greenhalgh, S., Wiese, T., Marescot, L. 2010. Comparison of DC sensitivity patterns for anisotropic and isotropic media. Journal of Applied Geophysics 70 (2), 103–112.
[29] Holcombe, J., and Jiracek, G. 1984. 3-D terrain corrections in resistivity surveys: Geophysics, Vol 49, 439-452.
[30] Inman, J.R., Ryu, J., Ward, S.H. 1973. Resistivity inversion, Geophysics 38 (6), 1088–1108.
[31] Inman, J.R., 1975. Resistivity inversion with ridge regression: Geophysics, 40, 798-817.
[32] Inman, J.R., Ryu, J., and Ward, S.H. 1973. Resistivity inversion: Geophysics, 38, 1088-1108.
[33] Jackson DD 1972. Interpretation of inaccurate, insufficient, and inconsistent data Geophys. J. R. Astron. Soc. 28 97-109.
[34] Jackson, D.D. 1979. The use of a priori data to resolve non-uniqueness in linear inversion. Geophysical Journal of the Royal Astronomical Society 35 (1–3), 121–136.
[35] Jha, M.K., Kumar, S., Chowdhury, A. 2008. Vertical electrical sounding survey and resistivity inversion using genetic algorithm optimization technique, Journal of Hydrology (2008), 359, 71-87.
[36] Karaoulis et al 2011. 4D active time constrained resistivity inversion, Journal of Applied Geophysics Volume 73 – 1.
[37] Kirkpatrick, S., Gelatt, C. D., Jr., and Vecchi, M. P. 1983.Optimization by simulated annealing: Science, 220, 671-680.
[38] LaBrecque, D.J., Miletto, M., Daily, W., Ramirez, A., Owen, E. 1996. The effects of noise on Occam's inversion of resistivity tomography data. Geophysics 61 (2),538–548
[39] Li Y, Oldenberg D W. 1992 .Approximate inverse mappings in DC problems. Geophys. J. Int., 109:343 -362
[40] Loke, M. H., Dahlin, T. 2010.Methods to reduce banding effects in 3-D resistivity inversion. Procs. 16th European Meeting of Environmental and Engineering Geophysics, 6–8 p. A16.
[41] Loke, M.H., Barker, R.D., 1996. Rapid least-squares inversion of apparent resistivity pseudo sections using a quasi-Newton method. Geophysical Prospecting 44 (1), 131–152.
[42] Matias, M.J.S. 2008. Electrical strike imaging and anisotropy diagnosis from surface resistivity measurements. Near Surface Geophysics 6 (1), 49–58.
[43] Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A., and Teller, E. 1953. Equation of state calculations by fast computing machines: J. Chem. Phys. 21. 1087-1092.
[44] Mitchell et al. 2011. Inversion of time-lapse electrical resistivity imaging data for monitoring infiltration: The Leading Edge. Volume 30, Issue 2
[45] Neuman et al 1985. Impedance-computed tomography algorithm and system, Applied Optics, Vol. 24, Issue 23, pp. 3985-3992.
[46] O Koefoed 1969: An analysis of equivalence in resistivity sounding, Geophysical Prospecting, Vol 17, No 3.
[47] Oldenburg, D.W., Li, Y. 1999. Estimating depth of investigation in dc resistivity and IP surveys. Geophysics 64 (2), 403–416.
[48] Oldenborger, G.A., Routh, P.S., Knoll, M.D. 2007. Model reliability for 3D electrical resistivity tomography: application of the volume of investigation index to a time-lapse monitoring experiment. Geophysics 72 (4), F167–F175
[49] Pelton et. al 1978 Inversion of 2d resitivity and induced polarization data; Geophysics Volume 43
[50] Rothman 1985 .Nonlinear inversion, statistical mechanics, and residual statics estimation -, Geophysics, vol. 50, no. 12 ; P. 2784-2796
[51] Ruth Hoffmann, Peter Dietrich 2004. An approach to determine equivalent solutions to the geoelectrical 2D inversion problem: Journal of Applied Geophysics 56 79–91.
[52] Sen, M. K., Stoffa, P. L. 1995. Global Optimization Methods in Geophysical Inversions. Elsevier Science Publisher, Amsterdam, p. 289.
[53] Sen, M. K., Bhattacharya, B. B., Stoffa, P. L.1993. Nonlinear inversion of resistivity sounding data. Geophysics, 58, 496-507.
[54] Shima H 1990. Two-dimensional automatic resistivity inversion technique using alpha centers; Geophysics 55 682-4
[55] Slichter, L. B. 1933. The interpretation of resistivity method for horizontal structure, Physics, 4,307–322
[56] Smith, N., and K. Vozoff 1984. Two dimensional DC resistivity inversion for dipole-dipole data: IEEE Transactions on Geoscience and Remote Sensing, 22, no. 1, 21–28.
[57] Spiegel, R. J., Sturdivant, V. R., Owen, T. E. 1980. Modeling resistivity anomalies from localized voids under irregular terrain. Geophysics 45 (7), 1164–1183.
[58] Stephen, J., Manoj, C., Singh, S.B. 2004. A direct inversion scheme for deep resistivity sounding data using artificial neural networks. Journal of Earth System Science 113 (1), 49–66.
[59] Telford W M. Geldart L P, Sheriff R E and Keys D A 1976 . Applied Geophysics (chapter 8 : pg 522)
[60] Tong L, Yang C 1990. Incorporation of topography into twodimensional resistivity inversion. Geophysics. 55: 354-361.
[61] Van der Baan, M. and Jutten, C. 2000. Neural networks in geophysical applications: Geophysics, 65, 1032-1047.
[62] Van Laarhoven, P. I. M., and Aarts, E. H. L. 1988. Simulated annealing: Theory and application: D. Riedel Publ. Co. Inc.
[63] Vozoff, K 1958.Numerical resistivity analysis horizontal layers, Geophysics, 23, 536—556.
[64] Ward, S.H., Hohmann, G. W. 1987. Electromagnetic theory for geophysical applications. In: Nabighian, M.N. (Ed.), Electromagnetic Methods in Applied Geophysics, Volume 1, Theory. Investigations in Geophysics No. 3. SEG.
[65] Wilkinson, P.B., Chambers, J.E., Lelliott, M., Wealthall, G.P., Ogilvy, R.D. 2008. Extreme sensitivity of crosshole electrical resistivity tomography measurements to geometric errors. Geophysical Journal International 173 (1), 49–62.
[66] Wilkinson, P.B., Chambers, J.E., Meldrum, P.I., Gunn, D.A., Ogilvy, R.D., Kuras, O., 2010. Predicting the movements of permanently installed electrodes on an active landslide using time-lapse geoelectrical resistivity data only. Geophysical Journal International 183 (2), 543– 556.
[67] Wright, A.H. 1991.Genetic algorithms for real parameter optimization: Presented at the Foundation of Genetic Algorithm
[68] Xu Hai-Lang, Wu Xiao-Ping 2006. 2-D Resistivity Inversion Using the Neural Network Method-,Chinese Journal of Geophysics: Volume 49, Issue 2, pages 507–514
[69] Yorkey T J 1986 .Comparing reconstruction methods for electrical impedance tomography
[70] Zhou, B., Dahlin, T. 2003. Properties and effects of measurement errors on 2D resistivity imaging surveying. Near Surface Geophysics 1 (3), 105–117
[71] Zohdy AA R 1972. Automatic interpretation of resistivity sounding curves using modified Dar Zarrouk functions Proc. 42nd Int. SEC Annual Meeting