A fast inversion method for interpreting borehole electromagnetic data
Earth, Planets and Space volume 55, pages 249–254 (2003)
A fast and stable inversion scheme has been developed using the localized nonlinear (LN) approximation to analyze electromagnetic fields obtained in a borehole. The medium is assumed to be cylindrically symmetric about the borehole, and to maintain the symmetry a vertical magnetic dipole is used as a source. The efficiency and robustness of an inversion scheme is very much dependent on the proper use of Lagrange multiplier, which is often provided manually to achieve a desired convergence. We utilize an automatic Lagrange multiplier selection scheme, which enhances the utility of the inversion scheme in handling field data. In this selection scheme, the integral equation (IE) method is quite attractive in speed because Green’s functions, the most time consuming part in IE methods, are repeatedly re-usable throughout the selection procedure. The inversion scheme using the LN approximation has been tested to show its stability and efficiency using synthetic and field data. The inverted result from the field data is successfully compared with induction logging data measured in the same borehole.
Alumbaugh, D. L. and H. F. Morrison, Theoretical and practical considerations for crosswell electromagnetic tomography assuming a cylindrical geometry, Geophysics, 60, 846–870, 1995.
Alumbaugh, D. L. and G. A. Newman, Three-dimensional massively parallel electromagnetic inversion (II. Analysis of crosswell electromagnetic experiment, Geophys. J. Int., 128, 355–363, 1997.
Constable, S. C., R. L. Parker, and C. G. Constable, Occam’s inversion: A practical algorithm for generating smooth models from electromagnetic sounding data, Geophysics, 52, 289–300, 1987.
deGroot-Hedlin, C. and S. Constable, Occam’s inversion to generate smooth, two-dimensional models from magnetotelluric data, Geophysics, 55, 1613–1624, 1990.
Habashy, T. M., R. M. Groom, and B. R. Spies, Beyond the Born and Rytov approximations: a nonlinear approach to electromagnetic scattering, J. Geophys. Res., 98, 1795–1775, 1993.
Hohmann, G. W., Three-dimensional induced polarization and EM modeling, Geophysics, 40, 309–324, 1975.
Hohmann, G. W., Numerical modeling for electromagnetic methods of geophysics, in Electromagnetic Methods in Applied Geophysics, Vol. 1, edited by M. N. Nabighian, pp. 313–363, Soc. Expl. Geophys., 1988.
Lee, K. H., H. J. Kim, and M. Wilt, Efficient imaging of single-hole electromagnetic data, Geothermal Resources Council Transactions, 26, 399–404, 2002.
Lee, K. H., H. J. Kim, and T. Uchida, Electromagnetic fields in steel-cased borehole, Geophys. Prosp., 2003 (submitted).
Newman, G. A., Crosswell electromagnetic inversion using integral and differential equations, Geophysics, 60, 899–911, 1995.
Parker, R. L., Geophysical Inverse Theory, Prinston Univ. Press, 1994.
Sena, A. G. and M. N. Toksoz, Simultaneous reconstruction of permittivity and conductivity for crosshole geometries, Geophysics, 55, 1302–1311, 1990.
Tikhonov, A. N. and V. Y. Arsenin, Solutions to Ill-Posed Problems, John Wiley and Sons, Inc., 1977.
Ward, S. H. and G. W. Hohmann, Electromagnetic Theory for Geophysical Applications, in Electromagnetic Methods in Applied Geophysics, Vol. 1, edited by M. N. Nabighian, pp. 131–311, Soc. Expl. Geophys., 1988.
Wilt, M. J. and D. L. Alumbaugh, Electromagnetic Methods for Development and Production: State of the Art: The Leading Edge, 17, 487–490, 1998.
Wilt, M. J., D. L. Alumbaugh, H. F. Morrison, A. Becker, K. H. Lee, and M. Deszcz-Pan, Crosshole electromagnetic tomography: System design considerations and field results, Geophysics, 60, 871–885, 1995.
Wilt, M., R. Mallan, P. Kasameyer, and B. Kirkendahl, Extended 3D induction logging for geothermal resource assessment: Field results with the Geo-BILT system, Proc. 27th Stanford Geothermal Workshop, Stanford Univ., SGP-TR-171, 2002.
Zhdanov, M. S. and S. Fang, Quasi-linear approximation in 3-D EM modeling, Geophysics, 61, 646–665, 1996.
Zhdanov, M. S. and A. Gribenko, Three-dimensional imaging about a single borehole, 72nd Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 316–319, 2002.
Zhou, Q., A. Becker, and H. F. Morrison, Audio-frequency electromagnetic tomography in 2-D, Geophysics, 58, 482–495, 1993.
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Kim, H.J., Lee, K.H. & Wilt, M. A fast inversion method for interpreting borehole electromagnetic data. Earth Planet Sp 55, 249–254 (2003). https://doi.org/10.1186/BF03351756
- LN approximation
- electromagnetic fields
- cylindrical symmetry