Singularity-free Green’s function for EM sources embedded in a stratified medium
Weng Ai-Hua1, Liu Yun-He1, Yin Chang-Chun1, and Jia Ding-Yu2
1. College of Geoexploration Science and Technology, Jilin University, Changchun 130026, China.
2. Institute of Geophysical and Geochemical Exploration, CAGS, Langfang 065000, China.
Abstract We present a method to unify the calculation of Green’s functions for an electromagnetic (EM) transmitting source embedded in a homogeneous stratified medium. A virtual interface parallel to layer interfaces is introduced through the source location. The potentials for Green’s function are derived by decomposing the partial wave solutions to Helmholtz’s equations into upward and downward within boundaries. The amplitudes of the potentials in each stratum are obtained recursively from the initial amplitudes at the source level. The initial amplitudes are derived by coupling with the transmitting sources and following the discontinuity of the tangential electric and magnetic fields at the source interface. Only the initial terms are related to the transmitting sources and thus need to be modified for different transmitters, whereas the kernel connected with the stratified media stays unchanged. Hence, the present method can be easily applied to EM transmitting sources with little modification. The application of the proposed method to the marine controlled-source electromagnetic method (MCSEM) demonstrates its simplicity and flexibility.
This work is supported by CNSF (Granted No. 40874050) and Chinese High Technology Project (Granted No. 2011YQ05006010).
Cite this article:
Weng Ai-Hua,Liu Yun-He,Yin Chang-Chun et al. Singularity-free Green’s function for EM sources embedded in a stratified medium[J]. APPLIED GEOPHYSICS, 2016, 13(1): 25-36.
[1]
Bhattacharyya, A. K., 1994, Electromagnetic fields in multilayered structures, MA: Artech House, Boston.
[2]
Börner, R. U., Ernst, O.G., and Spitzer, K., 2008, Fast 3-D simulation of transient electromagnetic fields by model reduction in the frequency domain using Krylov subspace projection: Geophysical Journal International, 173, 766-780.
[3]
Chave, A. D., 1983, Numerical integration of related Hankel transforms by quadrature and continued fraction expansion: Geophysics, 48, 1671-1686.
[4]
Chew, W. C., 1990, Waves and fields in inhomogeneous media: Van Nostrand Reinhold, New York.
[5]
Commer, M., and Newman, G. A., 2008, New advances in three-dimensional controlled-source electromagnetic inversion: Geophysical Journal International, 172, 513-535.
[6]
Constable, S., and Weiss, C., 2006, Mapping thin resistors and hydrocarbons with marine EM method: insights from 1D modeling: Geophysics, 71, G43-G51.
[7]
Das, U., 1995, A reformalism for computing frequency- and time-domain EM responses of a buried, finite-loop: SEG Annual Meeting, Extended Abstracts, 811-814.
[8]
Das, U., and Hoop, A., 1995, Efficient computation of apparent resistivity curves for depth profiling of a layered earth: Geophysics, 60, 1691-1697.
[9]
Fu, C. M., Di, Q. Y., and Wang, M. Y., 2010, Calculate electromagnetic fields in stratified medium with layer matrix method: Journal of Chinese Geophysics (in Chinese), 53(1), 177-188.
[10]
Goldman, M., 1990, Non-conventional Methods in Geoelectrical Prospecting: Ellis Horwood Ltd Publisher, New York.
[11]
Harrington, R. F., 1961, Time-harmonic electromagnetic fields, MacGraw-Hill Book Co., New York.
[12]
Harrington, R. F., 1983, Fields computation by moment method, Malabar, FL: Krieger, Florida.
[13]
Kaufman, A. A., and Keller, G. V., 1983, Frequency and transient soundings: Elsevier, New York.
[14]
Kaufman, A. A., and Keller, G. V., 1989, Induction logging: Elsevier, New York.
[15]
Krivochieva, S., and Chouteau, M., 2002, Whole-space modeling of a layered earth in time-domain electromagnetic measurements: Journal of Applied Geophysics: 50, 375-391.
[16]
Liu, Y. H., Liu, G. X., and Weng, A. H., 2011, Calculation of low frequency electromagnetic Green’s functions using two-level approximated discrete complex image method: Chinese Journal of Geophyscis (in Chinese), 54(4), 1114-1121.
[17]
Moghadas, D., André, F., Vereecken, H., and Lambot, S., 2010, Efficient loop antenna modeling for zero-offset, off-ground electromagnetic induction in multilayered media: Geophysics, 75, WA125-WA134.
[18]
Michalski, K. A., and Mosig, J.R., 1997, Multilayered media Green’s functions in integral equation formulations: IEEE Transactions on Antennas and Propagation, 45, 508-519.
[19]
Nabighian, M. N., 1987, Electromagnetic methods in applied geophysics (Vol.1), SEG, Tulsa, Oklahoma.
[20]
Pardo, D. and Torres-Verdín, C., 2015, Fast 1D inversion of logging-while-drilling resistivity measurements for improved estimation of formation resistivity in high-angle and horizontal wells: Geophysics, 80, E111-E124.
Singer, B. Sh., and Atramonova, S., 2013, Vertical electric source in transient marine CSEM: Effect of 3D Inhomogeneities on the Late Time Response: 2013, 78, E173-E188.
[23]
Streich, R., and Becken, M., 2011, Electromagnetic fields generated by finite-length wire sources: comparison with point dipole solutions: Geophysical Prospecting, 59, 361-374.
[24]
Stratton, J. A., 1941, Electromagnetic theory. MaGraw-Hill, New York.
[25]
Tsang, L., Njoku, E., and Kong, J. A., 1975, Microwave thermal emission from a stratified medium with nonuniform temperature distribution: J. Appl. Phys., 46, 5127-5133.
[26]
Wait, J. R., 1981, Wave propagation Theory: Pergamon Press, New York.
[27]
Wait, J. R., 1982, Geo-Electromagnetism: Academic Press, Massachusetts.
[28]
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(1), 60-74.
[29]
Ward, S. H., and Hohmann, G. W., 1988, Electromagnetic theory for geophysical applications: Electromagnetic methods in applied geophysics (Vol.1): Society for Exploration Geophysicists, Tulsa.
Yla-Oijala, P., and Taskinen, M., 2003, Efficient formulation of closed-form Green’s functions for general electric and magnetic sources in multilayered media: IEEE Transactions on Antennas and Propagation, 51(8), 2106-2115.
2016, Vol. 13 
