耦合势有限体积法高效模拟各向异性地层中海洋可控源的三维电磁响应

周建美; 张烨; 汪宏年; 杨守文; 殷长春

doi:10.7498/aps.63.159101

摘要

本文基于电场矢势与标势分解的耦合势有限体积法研究建立一套各向异性地层中海洋可控源电磁法的三维响应的高效数值模拟技术. 首先引入电场的矢势和标势，将电场分解为无散场和无旋场之和，Maxwell方程转换为关于矢势与标势的混合Helmholtz方程，克服低感应数问题. 在此基础上，借助Yee氏交错网格和有限体积法以及非均质单元中等效电导率公式，建立混合Helmholtz方程的离散方程. 并采用直接法求解器PARDISO求解离散方程，有效保证在大的求解空间中仍然能够获得电磁场稳定可靠的数值解. 此外，在数值模拟中利用差异场技术，克服源的奇异性问题，尽可能提高近场的计算精度. 与解析解的对比证明了该算法的有效性. 数值模拟结果表明，海洋可控源电磁法沿测线方向的电场，对油气藏的纵向电阻率敏感，对横向电阻率不敏感；对油气藏上方的覆盖层的纵向电阻率和横向电阻率都敏感.

关键词:

Abstract

A coupled potential finite volume method for simulation of three-dimensional marine controlled-source electromagnetic (CSEM) response in anisotropic formation is developed. To circumvent ill-conditioning and convergence problems, Maxwell's equations are reformulated into coupled scalar-vector potentials with Coulomb gauge and its complement by applying a Helmholtz decomposition to the electric field. Yee's staggered girds, finite volume averaging and interpolation techniques are used to make the Helmholtz equations discrete. The resulting sparse and complex linear system in large-scale models is solved by a direct solver PARDISO. In order to improve the accuracy of the near field results without significantly reducing the computational efficiency, a method using difference fields is proposed to reduce the source singularity effect of anisotropic formation. The anisotropic modeling examples show that marine CSEM response is predominantly sensitive to reservoir vertical resistivity, not to reservoir horizontal resistivity, provided that the reservoir are thin and high-resistive; but the marine CSEM response is sensitive to both horizontal and vertical resistivity of the overburden on top of the reservoir.

Keywords:

marine controlled-source electromagnetic method /
anisotropy /
finite volume method /
direct method

作者及机构信息

1.
吉林大学物理学院, 长春 130012;

2.
长春理工大学理学院, 长春 130022;

3.
吉林大学地球探测科学与技术学院, 长春 130026

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 Physics, Jilin University, Changchun 130012, China;

2.
School of Science, Changchun University of Science and Technology, Changchun 130022, China;

3.
College of Geo-exploration Science and Technology, Jilin University, Changchun 130026, China

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

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施引文献

[1]	Constable S 2010 Geophysics 75 75A67
[2]
[3]
[4]	Eidesmo T, Ellingsrud S, MacGregor L M, Constable S, Sinha M C, Johansen S, Kong F N, Westerdahl H 2002 First Break 20 144
[5]	Chimedsurong Z, Wang H N 2003 Chin. J. Comput. Phys. 20 161 (in Chinese) [Z其木苏荣, 汪宏年 2003 计算物理 20 161]
[6]
[7]	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]
[8]
[9]
[10]	Li Y G, Constable S 2010 Chin. J. Geophys. 53 737
[11]
[12]	Wang J X, Wang H N, Zhou J M, Yin C C 2013 Acta Phys. Sin. 62 224101 (in Chinese) [汪建勋, 汪宏年, 周建美, 殷长春 2013 62 224101]
[13]
[14]	Hong D C, Yang S D 2011 Acta Phys. Sin. 60 109101 (in Chinese) [洪德成, 杨善德 2011 60 109101]
[15]
[16]	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]
[17]
[18]	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]
[19]	Yin C C 2006 Geophysics 71 G115
[20]
[21]
[22]	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]
[23]
[24]	Li F Y, Wen H, Fang Z Y 2013 Chin. Phys. B 22 120402
[25]
[26]	Wang R, Gui L X, Ma J 2009 Chin. Phys. B 18 3422
[27]
[28]	Zhou J M, Wang H N, Yao J J, Yang S W, Ma Y Z 2012 Acta Phys. Sin. 61 089101 (in Chinese) [周建美, 汪宏年, 姚敬金, 杨守文, 马寅芝 2012 61 089101]
[29]	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]
[30]
[31]	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]
[32]
[33]	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]
[34]
[35]
[36]	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]
[37]
[38]	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]
[39]
[40]	Wang H N, Tao H G, Yao J J, Zhang Y 2012 IEEE Trans. Geosci. Remote Sens. 50 3383
[41]
[42]	Börner R 2010 Surv. Geophys. 31 225
[43]	Yee K S 1966 IEEE Trans. Antenn. Propag. 14 302
[44]
[45]	Streich R 2009 Geophysics 74 F95
[46]
[47]
[48]	Schwarzbach C, Börner R, Spitzer K 2011 Geophys. J. Int. 187 63
[49]
[50]	Newman G A, Alumbaugh D L 2002 Geophysics 67 484
[51]
[52]	Kong F N, Johnstad S, RØsten T, Westerdahl H 2008 Geophysics 73 F9
[53]
[54]	Schenk O, Gärtner K 2006 Electron. T. Numer. Ana. 23 158
[55]	Schenk O, Gärtner K 2004 Future Gener. Comp. Sy. 20 475

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