zbMATH — the first resource for mathematics

FDFD: A 3D finite-difference frequency-domain code for electromagnetic induction tomography. (English) Zbl 0984.78012
A new 3D code for electromagnetic induction tomography with intended applications to environmental imaging problems has been developed. The approach consists of calculating the fields within a volume using an implicit finite-difference frequency-domain formulation. The volume is terminated by an anisotropic perfectly matched layer region that simulates an infinite domain by absorbing outgoing waves. Extensive validation of this code has been done using analytical and semianalytical results from other codes, and some of those results are presented in this paper. The new code is written in Fortran 90 and is designed to be easily parallelized. Finally, an adjoint field method of data inversion, developed in parallel for solving the fully nonlinear inverse problem for electrical conductivity imaging (e.g., for mapping underground conducting plumes), uses this code to provide solvers for both forward and adjoint fields. Results obtained from this inversion method for high-contrast media are encouraging and provide a significant improvement over those obtained from linearized inversion methods.

78M20 Finite difference methods applied to problems in optics and electromagnetic theory
78-04 Software, source code, etc. for problems pertaining to optics and electromagnetic theory
Full Text: DOI
[1] Telford, W.M.; Geldart, L.P.; Sheriff, R.E.; Keys, D.A., Applied geophysics, (1976)
[2] Ramirez, A.; Daily, W.D.; LaBrecque, D.; Owen, E.; Chesnut, D., Monitoring an underground steam injection process using electrical resistance tomography, Water resour. res., 29, 73, (1993)
[3] Alumbaugh, D.L., Iterative electromagnetic Born inversion applied to Earth conductivity imaging, (1993)
[4] Tseng, H.-W.; Becker, A.; Wilt, M.J.; Deszcz-Pan, M., A borehole-to-surface electromagnetic survey, Geophys., 73, 1565, (1998)
[5] Ebeling, F.; Klatt, R.; Krawczyk, F.; Lawinsky, E.; Weiland, T.; Wipf, S.G.; Steffen, B.; Barts, T.; Browman, M.J.; Cooper, R.K.; Deaven, H.; Rodenz, G., The 3-D MAFIA group of electromagnetic codes, IEEE trans. magn., 25, 2962, (1989)
[6] Dehler, M.; Dohlus, M.; Fischerauer, A.; Fischerauer, G.; Hahne, P.; Klatt, P.; Krawczyk, F.; Propper, T.; Schutt, P.; Weiland, T.; Ebeling, F.; Marx, M.; Wipf, S.G.; Steffen, B.; Barts, T.; Browman, J.; Cooper, R.K.; Rodenz, G.; Rusthoi, D., Status and future of the 3D-MAFIA group of codes, IEEE trans. magn., 26, 751, (1990)
[7] Berenger, J.P., A perfectly matched layer for the absorption of electromagnetic waves, J. comput. phys., 114, 185, (1994) · Zbl 0814.65129
[8] G. W. Hohmann, Numerical modeling for electromagnetic methods of geophysics, in Electromagnetic Methods in Applied Geophysics Volume 1, Theory, M. N. Nabighian, Society of Exploration Geophysicists Tulsa, Oklahoma, 1987, pp. 314-363.
[9] Mackie, R.L.; Smith, J.T.; Madden, T.R., 3-dimensional electromagnetic modeling using finite-difference equations—the magnetotelluric example, Radio sci., 29, 923, (1994)
[10] Torres-Verdin, C.; Habashy, T.M., Rapid 2.5-dimensional forward modeling and inversion via a new nonlinear scattering approximation, Radio sci., 29, 1051, (1994)
[11] Newman, G.A.; Alumbaugh, D.L., Frequency-domain modeling of airborne electromagnetic responses using staggered finite-differences, Geophys. prospecting, 43, 1021, (1995)
[12] Newman, G.A.; Alumbaugh, D.L., Three-dimensional massively parallel electromagnetic inversion. 1. theory, Geophys. J. int., 128, 345, (1997)
[13] Newman, G.A.; Alumbaugh, D.L., Three-dimensional magnetotelluric inversion using nonlinear conjugate gradients, Geophys. J. int., 140, 410, (2000)
[14] Smith, J.T., Conservative modeling of 3-D electromagnetic fields. part I. properties and error analysis, Geophys., 61, 1308, (1996)
[15] Smith, J.T., Conservative modeling of 3-D electromagnetic fields. part II. biconjugate graident solution and an accelerator, Geophys., 61, 1319, (1996)
[16] Zhdanov, M.S.; Varentsov, I.M.; Weaver, J.T.; Golubev, N.G.; Krylov, V.A., Methods for modeling electromagnetic fields: results from COMMEMI—the international project on the comparison of modeling methods for electromagnetic induction, J. appl. geophys., 37, 133, (1997)
[17] Wilt, M.J.; Alumbaugh, D.L.; Morrison, H.F.; Becker, A.; Lee, K.H.; Deszcz-Pan, M., Crosswell electromagnetic tomography: system design considerations and field results, Geophys., 60, 871, (1995)
[18] Buettner, H.M.; Berryman, J.G., An electromagnetic induction tomography field experiment at lost hills, CA,, Proceedings of the symposium on the application of geophysics to engineering and environmental problems (SAGEEP), Oakland, CA, 663-672, (March 14-18, 1999)
[19] Beilenhoff, K.; Heinrich, W.; Hartnagel, H.L., Improved finite-difference formulation in frequency domain for three-dimensional scattering problems, IEEE trans. microwave theor. tech., 40, 540, (1992)
[20] Wu, J.Y.; Kingsland, D.M.; Lee, J.F.; Lee, R., A comparison of anisotropic PML to Berenger’s PML and its application to the finite-element method for EM scattering, IEEE trans. antennas prop., 45, 40, (1997)
[21] Dorn, O.; Bertete-Aguirre, H.; Berryman, J.G.; Papanicolaou, G.C., A nonlinear inversion method for 3D-electromagnetic imaging using adjoint fields, Inverse probl., 15, 1523, (1999) · Zbl 0943.35101
[22] Davis, J.L.; Annan, A.P., Ground penetrating radar for high resolution mapping of soil and rock stratigraphy, Geophys. prospect., 37, 531, (1989)
[23] Fisher, E.; McMechan, G.A.; Annan, A.P., Acquisition and processing of wide-aperature ground penetrating radar data, Geophys., 57, 495, (1992)
[24] Sacks, Z.S.; Kingsland, D.M.; Lee, R.; Lee, J.F., A perfectly matched anisotropic absorber for use as an absorbing boundary condition, IEEE trans. antennas prop., 43, 1460, (1995)
[25] Kuzuoglu, M.; Mittra, R., Frequency dependence of the constitutive parameters of causal perfectly matched anisotropic absorbers, IEEE microwave guided wave lett., 6, 447, (1996)
[26] Zhdanov, M.S.; Feng, S., Quasi-linear approximation in 3D electromagnetic modeling, Geophys., 61, 646, (1996)
[27] Wu, T.T.; King, R.W.P., The cylindrical antenna with nonreflecting resisitive loading, IEEE trans. antennas prop., 13, 369, (1965)
[28] Champagne, N.J.; Williams, J.T.; Sharpe, R.M.; Hwu, S.U.; Wilton, D.R., Numerical modeling of impedance loaded multi-arm Archimedian spiral antennas, IEEE trans. antennas prop., 40, 102, (1992)
[29] van der Vorst, H.A., Bi-CGSTAB: A fast and smoothly converging variant of bi-CG for the solution of non-symmetric linear systems, SIAM J. sci. stat. comput., 13, 631, (1992) · Zbl 0761.65023
[30] H. A. van der Vorst, Minimum residual modifications to Bi-CG and to the preconditioner, in Recent Advances in Iterative Methods, G. Golub, A. Greenbaum, and M. LuskinSpringer-Verlag, New York, 1994, pp. 217-225. · Zbl 0803.65060
[31] Druskin, V.L.; Knizhnerman, L.A.; Lee, P., New spectral Lanczos decomposition method for induction modeling in arbitrary 3-D geometry, Geophys., 64, 701, (1999)
[32] Claerbout, J.F., Fundamentals of geophysical data processing: with applications to petroleum prospecting, (1976)
[33] Zhdanov, M.S.; Traynin, P.; Booker, J.R., Underground imaging by frequency-domain electromagnetic migration, Geophys., 61, 666, (1996)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.