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In this paper, the two-dimensional Fourier transform and wave decomposition technique are used to transform Maxwell’s equation in transversely isotropic (TI) formation into two independent sets of transmission line equations about transverse magnetic (TM) wave and transverse electric (TE) wave. According to both transmission line theory and superposition principle, an improved transmission line method is advanced to simplify the computational process of TM wave and TE wave only by introducing the transmission line Green’s functions of the current source. Thus, the new algorithm and the new expressions of current source electromagnetic (EM) dyadic Green’s functions in frequency-wavenumber domain are established for realizing the efficient simulation of marine controlled-source electromagnetic (MCSEM) responses in the horizontally layered TI formation. On this base, the basic solutions of the transmission line Green’s functions and EM boundary conditions are utilized to derive the recursive formula of the generalized reflections and amplitudes of the TE and TM waves, and the analytic solutions of the Green’s functions in each bed are obtained. Then, by using Fourier inverse transform and Bessel integral formula, the MCSEM responses in frequency-spatial domain are expressed in the Sommerfeld integral form. A combination of the cubic spline interpolation with the Lommel integral is used to efficiently compute the MCSEM responses. Finally, we validate the modeling algorithm and investigate the influences of changes in operation frequency and anisotropic coefficient on the MCSEM response in the TI formation.
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Keywords:
- transmission line method /
- transversely isotropic formation /
- marine controlled-source electromagnetic system /
- Sommerfeld integral
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[19] Chen G B, Wang H N, Yao J J, Han Z Y, Yang S W 2009 Chin. J. Geophys. 52 2174 (in Chinese)[陈桂波, 汪宏年, 姚敬金, 韩子夜, 杨守文 2009 地球 52 2174]
[20] Wang H N, Tao H G, Yao J J, Zhang Y 2012 IEEE Trans. on Geosci. Remote Sens. 50 3383
[21] Wang H N, Tao H Gg, Yao J J, Chen G B, Yang S W 2008 Chin. J. Geophys. 50 1591 (in Chinese) [汪宏年, 陶宏根, 姚敬金, 陈桂波, 杨守文 2008 地球 50 1591]
[22] Zhou J M, Wang H N, Yao J J, Yang S W, Ma Y Z 2012 Acta Phys. Sin. 61 0891011 (in Chinese) [周建美, 汪宏年, 姚敬金, 杨守文, 马寅芝 2012 61 0891011]
[23] Zhou J M, Wang J X, Shang Q L, Wang H N, Yin C C 2013 J. Geophys. Eng. (in Review)
[24] Michalski K A, Mosig J R 1997 IEEE Trans. Anten. Propag. 45 508
[25] Yang S W, Wang J X, Zhou J M, Zhu T Z, Wang H N 2013 IEEE Trans. On Geosci. Remote Sens. (in press)
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[1] He J S 2012 Principle of Marine Electromagnetic Measurement (Beijing: Higher Education Publish House) p210 (in Chinese) [何继善 2012 海洋电磁法原理(北京: 高等教育出版社)第210页]
[2] Constable S 2010 Geophysics 75 75A67
[3] Eidesmo T, Ellingsrud S, MacGregor L M, Constable S, Sinha M C, Johansen S, Kong F N, Westerdahl H 2002 First Break 20 144
[4] Key K 2009 Geophysics 74 F9
[5] Chimedsurong Z, Wang H N 2003 Chin. J. Comput. Phys. 20 161 (in Chinese) [其木苏荣, 汪宏年 2003 计算物理 20 161]
[6] Liu C S, Everett M E, Lin J, Zhou F D 2010 Chin. J. Geophys. 53 1940 (in Chinese) [刘长胜, Everett M. E. 林君, 周逢道 2010 地球 53 1940]
[7] Zhang J P, Wu Z S, Zhao Z W, Zhang Y S, Wang B 2012 Chin. Phys. B 21 109202
[8] Sun B, Wang H, Sun X B, Hong J, Zhang Y J 2012 Chin. Phys. B 21 129501
[9] Hong D C, Yang S D 2011 Acta Phys. Sin. 60 109101 (in Chinese) [洪德成, 杨善德 2011 60 109101]
[10] Chen G B, Wang H N, Yao J J, Han Z Y, Yang S W 2009 Acta Phys. Sin. 58 1608 (in Chinese) [陈桂波, 汪宏年, 姚敬金, 韩子夜, 杨守文 2009 58 1608]
[11] Chen G B, Bi J, Wang J B, Chen X Y, Sun G C, Lu J 2011 Acta Phys. Sin. 60 094102 (in Chinese) [陈桂波, 毕娟, 汪剑波, 陈新邑, 孙贯成, 卢俊 2011 60 094102]
[12] Yin C C 2006 Geophysics 71 G115
[13] Wang H N, Yang S D, Wang Y 1999 Oil Geophys. Prospect. 34 649 (in Chinese) [汪宏年, 杨善德, 王艳 1999 石油地球物理勘探 34 649]
[14] Yao D H, Wang H N, Yang S W, Yang H L 2010 Chin. J. Geophys. 53 3026 (in Chinese) [姚东华, 汪宏年, 杨守文, 杨海亮 2010 地球 53 3026]
[15] Xu Z F, Wu X P 2010 Chin. J. Geophys. 53 1931 (in Chinese) [徐志锋, 吴小平 2010 地球 53 1931]
[16] Zhang Y, Wang H N, Tao H G, Yang S W 2012 Chin. J. Geophys. 55 2141 (in Chinese) [张烨, 汪宏年, 陶宏根, 杨守文 2012 地球 55 2141]
[17] Yang B, Xu Y X, He Z X, Sun W B 2011 Chin. J. Geophys. 54 1649 (in Chinese) [杨波, 徐义贤, 何展翔, 孙卫斌 2011 地球 54 1649]
[18] Chen G B, Wang H N, Yao J J, Han Z Y 2009 Acta Phys. Sin. 58 3848 (in Chinese) [陈桂波, 汪宏年, 姚敬金, 韩子夜 2009 58 3848]
[19] Chen G B, Wang H N, Yao J J, Han Z Y, Yang S W 2009 Chin. J. Geophys. 52 2174 (in Chinese)[陈桂波, 汪宏年, 姚敬金, 韩子夜, 杨守文 2009 地球 52 2174]
[20] Wang H N, Tao H G, Yao J J, Zhang Y 2012 IEEE Trans. on Geosci. Remote Sens. 50 3383
[21] Wang H N, Tao H Gg, Yao J J, Chen G B, Yang S W 2008 Chin. J. Geophys. 50 1591 (in Chinese) [汪宏年, 陶宏根, 姚敬金, 陈桂波, 杨守文 2008 地球 50 1591]
[22] Zhou J M, Wang H N, Yao J J, Yang S W, Ma Y Z 2012 Acta Phys. Sin. 61 0891011 (in Chinese) [周建美, 汪宏年, 姚敬金, 杨守文, 马寅芝 2012 61 0891011]
[23] Zhou J M, Wang J X, Shang Q L, Wang H N, Yin C C 2013 J. Geophys. Eng. (in Review)
[24] Michalski K A, Mosig J R 1997 IEEE Trans. Anten. Propag. 45 508
[25] Yang S W, Wang J X, Zhou J M, Zhu T Z, Wang H N 2013 IEEE Trans. On Geosci. Remote Sens. (in press)
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