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Three-dimensional inversion of borehole-surface electrical data based on quasi-analytical approximation

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Abstract

3D inversion of borehole-surface electrical data for complex geo-electrical models is still a challenging problem in geophysical exploration. We have developed a program for 3D inversion to borehole-surface electrical data based on the quasi-analytical approximation (QA) and re-weighted regularized conjugate gradient method (RRCG) algorithms using Visual Fortran 6.5. Application of the QA approximation to forward modeling and Frechet derivative computations speeds up the calculation dramatically. The trial calculation for synthetic data of theoretical model showed that the program is fast and highly precise.

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References

  • Anderson, W. L., 1984, Computation of Green’s tensor integrals for three-dimensional electromagnetic problems using fast Hankel transforms: Geophysics, 49, 1754–1759.

    Article  Google Scholar 

  • Dmitriev, V. I., and Nesmeyanova, N. I., 1992, Integral equation method in three-dimensional problems of low-frequency electrodynamics: Computational Mathematics and Modeling, 3(3), 313–317.

    Article  Google Scholar 

  • Habashy, T. M., Groom, R. W., and Spies, B. R., 1993, Beyond the Born and Rytov approximations: a nonlinear approach to electromagnetic scattering: Journal of Geophysical Research, 98(B2), 1759–1775.

    Article  Google Scholar 

  • He Zhanxiang, Liu Xuejun, Qiu Weiting, and Huang Zhou, 2004, High-power surface-borehole electrical method in predicting reservoir boundary and its application: Petroleum exploration and Development (in Chinese), 2004, 31,74–76.

    Google Scholar 

  • He Zhanxiang, Liu Xuejun, Qiu Weiting, and Huang Zhou, 2005, Mapping reservoir boundary by boreholesurface TFEM: The Leading Edge, 24, 896–900.

    Article  Google Scholar 

  • Hohmann, G. W., 1975, Three-dimensional induced polarization and EM modeling: Geophysics, 40, 309–324.

    Article  Google Scholar 

  • Hohmann, G. W., 1988, Numerical modeling for electromagnetic methods of geophysics, in Nabighian, M. N., Ed., Electromagnetic methods in applied geophysics: Soc. Expl. Geophys., 313–363.

  • Hursán, G. and Zhdanov, M. S., 2002, Contraction integral equation method in three-dimensional electromagnetic modeling: Radio Science, 37, 1089–1102.

    Article  Google Scholar 

  • Newman, G. A., and Hohmann, G. W., 1988. Transient electromagnetic responses of high-contrast prisms in a layered earth: Geophysics, 53, 691–706.

    Article  Google Scholar 

  • Oristaglio, M. L., 1989, An inverse scattering formula that uses all the data: Inverse Problems, 5, 1097–1105.

    Article  Google Scholar 

  • Portniaguine, O. N., and Zhdanov, M. S., 1999, Focusing geophysical inversion images: Geophysics, 64, 874–887.

    Article  Google Scholar 

  • SanFilipo, W. A., and Hohmann, G. W., 1985, Integral equation solution for the transient electromagnetic response of a three-dimensional body in a conductive half-space: Geophysics, 50, 798–809.

    Article  Google Scholar 

  • Singer, B. S., and Fainberg, E. B., 1997, Fast and stable method for 3-D modeling of electromagnetic field: Exploration Geophysics, 28, 130–135.

    Google Scholar 

  • Tikhonov, A. N., and Arsenin, V. Y., 1977, Solution of illposed problems: John Wiley and Sons, New York.

    Google Scholar 

  • Wannamaker, P. E., Hohmann, G. W., and SanFilipo, W. A., 1984, Electromagnetic modeling of three-dimensional bodies in layered earths using integral equations: Geophysics, 49, 60–74.

    Article  Google Scholar 

  • Wannamaker, P. E., 1991, Advances in three-dimensional magnetotelluric modeling using integral equations: Geophysics, 56, 1716–1728.

    Article  Google Scholar 

  • Xiong, Z., 1992, Electromagnetic modeling of threedimensional structures by the method of system iterations using integral equations: Geophysics, 57, 1556–1561.

    Article  Google Scholar 

  • Xiong, Z., and Kirsch, A., 1992, Three-dimensional earth conductivity inversion: Journal of Comp. and Appl. Math., 42, 109–121.

    Article  Google Scholar 

  • Zhdanov, M. S., and Fang, S., 1996, Quasi-linear approximation in 3-D electromagnetic modeling: Radio Science, 31, 741–754.

    Article  Google Scholar 

  • Zhdanov, M. S., Fang, S., and Hursan, G., 2000a, Electromagnetic inversion using quasi-linear approximation: Geophysics, 65, 1501–1513.

    Article  Google Scholar 

  • Zhdanov, M. S., Dmitriev, V. I., Fang, S., and Hursan, G., 2000b, Quasi-analytical approximations and series in electromagnetic modeling: Geophysics, 65, 1746–1757.

    Article  Google Scholar 

  • Zhdanov, M. S., and Hursan, G., 2000, 3-D electromagnetic inversion based on quasi-analytical approximation: Inverse Problems, 16, 1297–1322.

    Article  Google Scholar 

  • Zhdanov, M. S., 2002, Geophysical inverse theory and regularization problems: Elsevier.

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Wang Zhigang is a PhD student at China University of Geosciences (Beijing). He received a master’s degree in Earth Survey and Information Technology from the China of Geosciences (Beijing) in 2004. His research work mainly focuses on the borehole-surface electrical method and MT.

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Zhigang, W., Zhanxiang, H. & Haiying, L. Three-dimensional inversion of borehole-surface electrical data based on quasi-analytical approximation. Appl. Geophys. 3, 141–147 (2006). https://doi.org/10.1007/s11770-006-0021-4

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  • DOI: https://doi.org/10.1007/s11770-006-0021-4

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