DC Electrical Resistance Tomography Inversion

Document Type : Research


1 Ph.D. Graduated, Department of Earth Physics, Institute of Geophysics, University of Tehran, Tehran, Iran

2 Assistant Professor, Department of Earth Physics, Institute of Geophysics, University of Tehran, Tehran, Iran


Direct current electrical resistivity imaging is provided by measuring the vertical and horizontal electrical potential variations of subsurface structures using surface and borehole records. To recover the resistivity tomograms from the observed data, a non-linear inverse problem is required to be iteratively solved. A 2.5-dimensional forward modeling based on the finite-difference method with rectangular meshes is also formulated. The two-dimensional reconstruction of earth resistivity data is implemented using a smoothness constrained inversion algorithm (i.e. Occam’s method), wherein a Gauss-Newton technique for updating the sensitivity function is proposed. After verifying the accuracy and efficiency of the forward modeling and the sensitivity function calculation, the inversion algorithm is tested on synthetic data from both geometrically simple and complicated bodies and a real data set. A stopping criterion based on the noise level, roughly estimated using the method of reciprocal resistance measurements, is also provided leading to preventing over-or under-interpreted structure during the inversion process. The numerical experiments reveal that the proposed inversion algorithm provides stable inversion results and an acceptable representation of the main features and structure of the models without producing spurious effects. Furthermore, to deal with the reliability of the recovered models, a model sensitivity analysis is implemented using the resolution density distribution. All used formulations and concepts are part of a Matlab source code developed during this study.


Main Subjects

Aster, R. C., Borchers, B. and Thurber, C. H., 2011, Parameter estimation and inverse problems: 2nd Edition, Elsevier Academic Press.
Chambers, J.E., Kuras, O., Meldrum, P.I., Ogilvy, R.D. and Hollands, J., 2006, Electrical resistivity tomography applied to geologic, hydro-geologic, and engineering investigations at a waste-disposal site. Geophysics, 71(6).
Constable, S.C., Parker R.L. and Constable, C.G., 1987, Occam's inversion: A practical algorithm for generating smooth models from electromagnetic sounding data. Geophysics, 52, 289-300.
Dahlin, T. and Zhou, B., 2001, A numerical comparison of 2D resistivity imaging with eight electrode arrays. In 7th Meeting of the Environmental and Engineering Geophysical Society (European Section), pages 977–983.
deGroot Hedlin, C. and Constable, S., 1990, Occam’s inversion to generate smooth, two-dimensional models from magnetotelluric data. Geophysics, 55(12), 1613–1624.
Dey, A. and Morrison, H.F., 1979, Resistivity modelling for arbitrarily shaped two-dimensional structures. Geophysical prospecting, 27(1), 106-136.
Fallahsafari, M., Ghanati, R., Hafizi, M.K. and Müller-Petke, M., 2020, A fast multi-exponential inversion of magnetic resonance sounding using iterative Lanczos bidiagonalization algorithm. Journal of Applied Geophysics, 175.
Ghanati, R., Azadi, Y. and Fakhimi, R., 2020, RESIP2DMODE: A MATLAB-Based 2D Resistivity and Induced Polarization Forward Modeling Software, Iranian Journal of Geophysics 13 (4), 60-78.
Ghanati, R. and Müller-Petke, M., 2021, A Homotopy continuation inversion of geo-electrical sounding data, Journal of Applied Geophysics, 191. https://doi.org/10.1016/j.jappgeo.2021.104356.
Günther, T., Rücker, C. and Spitzer, K., 2006, Three-dimensional modelling and inversion of DC resistivity data incorporating topography - II. Inversion. Geophysical Journal International, 166(2), 506–517.
Kim, H.J. and Kim, Y.H., 2011, A unified transformation function for lower and upper-bounding constraints on model parameters in electrical and electromagnetic inversion: Journal of Geophysics and Engineering. 8, 2126.
Loke, M.H. and Barker, R.D., 1996, Rapid least-squares inversion of apparent resistivity pseudo-sections by a quasi-Newton method. Geophysical Prospecting, 44, 131–152.
McGillivray, P.R. and Oldenburg, D.W., 1990, Methods for calculating Fréchet derivatives and sensitivities for the non-linear inverse problem: a comparative study. Geophys. Prospect., 38(5):499–524.
Oldenborger, G.A., Routh, P.S. and Knoll, M.D., 2007, Model reliability for 3D electrical resistivity tomography: application of the volume of investigation index to a time-laps monitoring experiment. Geophysics, 72 (4), F167–F175.
Pang, Y., Nie, L., Liu, B., Liu, Z. and Wang, N., 2020, Multiscale resistivity inversion based on convolutional wavelet transform, Geophysical Journal International, 22(1), 132–143.
Pelton, W. H., Rijo, L. and Swift, C. M., 1978, Inversion of two-dimensional resistivity and induced-polarization data. Geophysics, 43(4), 788–803.
Scales, J.A. and Snieder, R., 1997, To Bayes or not to Bayes? Geophysics 63, 1045–1046.
Smith, N.C. and Vozoff, K., 1984, Two dimensional DC resistivity inversion for dipole-dipole data IEEE Trans. Gemeience Remote Sensing, 22 21-8.
Tong, L.T. and Chieh‐Hou, Y., 1990, Incorporation of topography into two‐dimensional resistivity inversion, Geophysics, 55, 354-361.
Tripp, A.C., Hohmann, G.W. and Swift, C. M., 1984, Two dimensional resistivity inversion. Geophysics, 49, 708-1717.
Wilkinson, P.B., Chambers, J.E., Lelliott, M., Wealthall, G.P. and Ogilvy, R.D., 2008, Extreme sensitivity of cross-hole electrical resistivity tomography measurements to geometric errors. Geophysical Journal International, 173 (1), 49–62.
Zhdanov, M. and Tolstaya, E., 2006, A novel approach to the model appraisal and resolution analysis of regularized geophysical inversion. Geophysics 71, 79–90.
Zhou, B. and Dahlin, T., 2003, Properties and effects of measurement errors on 2D resistivity imaging surveying. Near Surface Geophysics, 1 (3), 105–117
Zhou, J., Revil, A., Karaoulis, M., Hale, D., Doetsch, J. and Cuttler, S., 2014, Image-guided inversion of electrical resistivity data, Geophysical Journal International, 197, 292–309.