2D DC resistivity forward modeling based on the integral equation method and a comparison with the RES2DMOD results

نویسندگان

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

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

چکیده

A 2D forward modeling code for DC resistivity is developed based on the integral equation (IE) method. Here, a linear relation between model parameters and apparent resistivity values is proposed, although the resistivity modeling is generally a nonlinear problem. Two synthetic cases are considered for the numerical calculations and the results derived from IE code are compared with the RES2DMOD that is a standard software for 2D resistivity forward modeling. For the first synthetic case, a model of resistive block surrounded by a homogenous medium is considered in different depths from 0.5 m to 4 m. For the nearest case to the surface, the IE pseudo-section is similar to its counterpart derived by RES2DMOD but its RMS error is a large value of 13.9 %. Increasing the depth of the anomaly results in decreasing of RMS values to 5.4 % for the deepest case and it is in correspondence with diminishing of the nonlinearity effects of electric fields for larger distances from the sources. The second model is composed of four conductive anomalies embedded in different depths. Visual comparison of IE response with software is indicative of high similarity of them, and RMS error for this relatively complex model is 7.5%, which can be an acceptable misfit for a linear forward operation. A very simple inversion algorithm using linear forward operator is applied on a real data set of a landfill survey in Germany collected by Wenner alfa array to demonstrate its productivity for practical applications. Reconstructed model using IE method is comparable with the inverted model derived by RES2DINV software, and it represents a good similarity with the original model.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

2D DC resistivity forward modeling based on the integral equation method and a comparison with the RES2DMOD results

نویسندگان [English]

  • Ramin Varfinezhad 1
  • Behrooz Oskooi 2
1 Ph.D. Student, Department of Earth Physics, Institute of Geophysics, University of Tehran, Tehran, Iran
2 Associate Professor, Department of Earth Physics, Institute of Geophysics, University of Tehran, Tehran, Iran
چکیده [English]

A 2D forward modeling code for DC resistivity is developed based on the integral equation (IE) method. Here, a linear relation between model parameters and apparent resistivity values is proposed, although the resistivity modeling is generally a nonlinear problem. Two synthetic cases are considered for the numerical calculations and the results derived from IE code are compared with the RES2DMOD that is a standard software for 2D resistivity forward modeling. For the first synthetic case, a model of resistive block surrounded by a homogenous medium is considered in different depths from 0.5 m to 4 m. For the nearest case to the surface, the IE pseudo-section is similar to its counterpart derived by RES2DMOD but its RMS error is a large value of 13.9 %. Increasing the depth of the anomaly results in decreasing of RMS values to 5.4 % for the deepest case and it is in correspondence with diminishing of the nonlinearity effects of electric fields for larger distances from the sources. The second model is composed of four conductive anomalies embedded in different depths. Visual comparison of IE response with software is indicative of high similarity of them, and RMS error for this relatively complex model is 7.5%, which can be an acceptable misfit for a linear forward operation. A very simple inversion algorithm using linear forward operator is applied on a real data set of a landfill survey in Germany collected by Wenner alfa array to demonstrate its productivity for practical applications. Reconstructed model using IE method is comparable with the inverted model derived by RES2DINV software, and it represents a good similarity with the original model.

کلیدواژه‌ها [English]

  • Forward modeling
  • integral equation
  • resistivity
  • RES2DMOD

Auken, E. and Christiansen, A. V., 2004, Layered and laterally constrained 2D inversion of resistivity data, Geophysics, 69(3), 752–761.

Candansayar, M. E. and Başokur, A.T., 2001, Detecting small-scale targets by the 2D inversion of two-sided three-electrode data: application to an archaeological survey, Geophysical Prospecting, 49(1), 13–25.

Cardarelli, E., Cercato, M., Cerreto, A., Filippo, G. D., 2009, Electrical resistivity and seismic refraction tomography to detect buried cavities.

Coggon, J. H., 1971, Electromagnetic and electrical modelling by the finite element method. Geophysics, 36, 132–155.

Dey, A. and Morrison, H. F., 1979, Resistivity modelling for arbitrarily shaped three-dimensional structures. Geophysics, 44, 753–780.

Daniels, J. J., 1977, Three-dimensional resistivity and induced polarization modelling using buried electrodes. Geophysics, 42, 1006–1019.

Dieter, K., Paterson, N. R. and Grant, F. S., 1969, IP and resistivity type curves for three-dimensional bodies. Geophysics, 34, 615–632.

Fehdi, C., Baali, F., Boubaya, D. and Rouabhia, A., 2011, Detection of sinkholes using 2D electrical resistivity imaging in the Cheria Basin (north-east of Algeria). Arab. J. Geosci., 14(1-2), 181-187, DOI: 10.1007/s12517-009-0117- 2.

Fox, R. C., Hohmann, G. W., Killpack, T. J. and Rijo, L., 1980, Topographic effects in resistivity and induced-polarization surveys. Geophysics, 45, 75–93.

Jahandari, H. and Farquharson, C. G., 2013, Forward modeling of gravity data using finite-volume and finite-element methods on unstructured grids. Geophysics, 78(3), G69-G80.

Hohmann, G. W., 1975, Three-dimensional induced polarization and electromagnetic modelling. Geophysics, 40, 309–324.

Holcombe, H. T. and Jiracek, G. R., 1984, Three-dimensional terrain correction in resistivity surveys. Geophysics, 49, 439–452.

Lee, T., 1975, An integral equation and its solution for some two- and three-dimensional problems in resistivity and induced polarization. Geophysical Journal of the Royal Astronomical Society, 42, 81–95.

Li, Y. and Spitzer, K., 2002, 3D direct current resistivity forward modeling using finite element in comparison with finite-difference solutions, Geophys. J. Int., 151, 924–934.

Li, Y. and Spitzer, K., 2005, Finite-element resistivity modeling for 3D structures with arbitrary anisotropy. Phys. Earth Planet. Inter., 150, 15–27.

Marescot, L., Lopes, S. P., Rigobert, S. and Green, A. G., 2008, Nonlinear inversion of geoelectric data acquired across 3D objects using a finite-element approach, Geophysics, 73, F121–F133.

Mendez-Delgado, S., Gomez-Trevino, E., and Perez-Flores, M. A., 1999, Forward modelling of direct current and low-frequency electromagnetic fields using integral equations. Geophys. J. Internal., 137, 336–352.

Mufti, I. R., 1976, Finite-difference resistivity modeling for arbitrarily shaped two-dimensional structures. Geophysics, 41, 62–78.

Nwankwo, L. I., 2011, 2D resistivity Survey for Groundwater Exploration in a Hard Rock Terrain: A case Study of MAGDAS Observatory, UNILORIN, Nigeria. Asian J. Earth Sci., 4(1), 46-53.

Okabe, M., 1981, Boundary element method for the arbitrary inhomogeneities problem in electrical prospecting. Geophysical Prospecting, 29, 39–59.

Oppliger, G. L., 1984, Three-dimensional terrain corrections for misea-la-masse and magnetometric resistivity surveys. Geophysics, 49, 1718–1729.

Perez-Flores, M. A., Méndez-Delgado, S. and Gomez-Treviño, E., 2001, Imaging low frequency and dc electromagnetic fields using a simple linear approximation. Geophysics, 66, 1067–1081.

Pratt, D. A., 1972, The surface integral approach to the solution of the 3D resistivity problem. Bulletin of the Australian Society for Exploration Geophysics, 3, 33–50.

Pridmore, D. F., Hohmann, G. W., Ward, S. H. and Sill, W. R., 1981, An investigation of finite element modelling for electrical and electromagnetic data in three dimensions. Geophysics, 46, 1009–1024.

Ren, Z. and Tang, J., 2010, 3D direct current resistivity modeling with unstructured mesh by adaptive finite-element method. Geophysics, 75, H7–H17.

Sasaki, Y., 1994, 3D resistivity inversion using the finite-element method, Geophysics, 59, 1839–1848.

Schoor, M. V, 2002, Detection of sinkholes using 2D electrical resistivity imaging. Journal of Applied Geophysics, 50, 393–399.

Scribe, H., 1981, Computations of the electrical potential in the three-dimensional structure. Geophysical Prospecting, 29, 790–802.

Simpson, F. and Bahr, K., 2005, Practical magnetotellurics. Cambridge University Press.

Spitzer, K., 1995, A 3D finite difference algorithm for DC resistivity modelling using conjugate gradient methods. Geophysical Journal International, 123, 903–914.

Tsourlos, P. I. and Ogilvy, R. D., 1999, An algorithm for the 3D inversion of tomographic resistivity and induced polarization data: preliminary results. J. Balkan Geophys. Soc., 2, 30–45.

Xu, S. Z., Guo, Z. C. and Zhao, S. K., 1988, An integral formulation for three-dimensional terrain modelling for resistivity surveys. Geophysics, 53, 546–552.

Wu, X., Xiao, Y., Qi, C. and Wang, T., 2003, Computations of secondary potential for 3D DC resistivity modeling using an incomplete Choleski conjugate-gradient method. Geophysical Prospecting, 51, 567–577.

Zhdanov, M. S., 2009, Geophysical Electromagnetic Theory and Methods. Elsevier.

Zhao, S. K. and Yedlin, M. J., 1996, Some refinements on the finite difference method for 3D DC resistivity modelling. Geophysics, 61, 1301–1307.