用改进的传输线算法计算水平层状横向同性地层中海洋可控源电磁响应

汪建勋; 汪宏年; 周建美; 杨守文; 刘晓军; 殷长春

doi:10.7498/aps.62.224101

摘要

利用二维Fourier变换与电磁场分解技术将层状横向同性地层中Maxwell方程转化成两个独立的关于横磁(TM)波和横电(TE)波的传输线方程; 借助传输线理论与叠加原理, 仅利用电流源传输线Green函数得到TM波和TE波的解, 改进传输线算法, 建立横向同性地层中频率-波数域电流源电场和磁场并矢Green函数的新算法与新的解析表达式, 提高海洋可控源电磁响应数值模拟效率. 在此基础上, 利用传输线Green函数的基本解以及边界条件, 推导出广义反射系数与振幅递推公式, 得到各个地层中传输线Green函数的解析解; 然后利用Fourier逆变换与Bessel公式将海洋可控源电磁响应表示为Sommerfeld形式的积分, 借助三次样条插值与Lommel积分公式快速计算其数值解. 通过数值模拟结果考察工作频率以及地层各向异性电阻率变化等对海洋电磁响应的影响.

关键词:

Abstract

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.

Keywords:

transmission line method /
transversely isotropic formation /
marine controlled-source electromagnetic system /
Sommerfeld integral

作者及机构信息

1.
吉林大学电子科学与技术学院, 长春 130012;

2.
吉林大学物理学院, 长春 130012;

3.
吉林大学地球探测技术学院, 长春 130026;

4.
齐齐哈尔大学理学院物理系, 齐齐哈尔 161006

基金项目: 国家高技术研究发展计划(批准号: 2012AA09A20103)资助的课题.

Authors and contacts

1.
College of Electronic Science and Engineering, Jilin University, Changchun 130012, China;

2.
College of Physics, Jilin University, Changchun 130012, China;

3.
College of Geoexploration Science and Technology, Jilin University, Changchun 130026, China;

4.
Department of Physics, Nature Science College, Qiqihar University, Qiqihar 161006, China

Funds: Project supported by the National High Technology Research and Development Program of China (Grant No. 2012AA09A20103).

参考文献

[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)

施引文献

[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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