Journal of Jilin University(Earth Science Edition) ›› 2016, Vol. 46 ›› Issue (5): 1538-1549.doi: 10.13278/j.cnki.jjuese.201605302

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Vector Finite Element Method

Yan Jiabin, Huang Xiangyu   

  1. School of Geosciences and Info-Physics, Central South University, Changsha 410083, China
  • Received:2016-01-15 Online:2016-09-26 Published:2016-09-26
  • Supported by:

    Supported by the National Nature Science Foundation of China (40874055) and the Natural Science Foundation of Hunan Province, China (14JJ2012)

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Abstract:

Based on the vector basis function,the generalized variational principle was adopted to deduce the discrete equations of magnetotelluric field.In order to increase the accuracy and efficiency of calculation, the direct method is used to impose boundary conditions, improving condition number of generalco efficient matrix. At the same time, the complex, symmetric,large sparselinear systems was solved by symmetric successive over relaxation preconditioned BICGSTAB method. The international standard model had been calculated,and the contrast with the results in related references had validated the accuracy of the algorithm. The forward modeling on a typical low resistivity model had been carried out, the response of apparent resistivity and phase had been got, and the results of 3D model and 2D model were compared.The results showed that in x direction, the change range of ρyx is less than that of ρxy. The response of both ρyx and ρxy for 3D model in thecentral survey line is similar to the 2D TM mode.

Key words: magnetotelluric method, generalized variational principle, vector finite element method, SSOR precondition, imposition of boundary conditions

CLC Number: 

  • P631.3

[1] Avdeev D B. Three-Dimensional Electromagnetic Modelling and Inversion from Theory to Application[J]. Surveys in Geophysics,2005,26(6):767-799.

[2] Hohmann G W. Three-Dimensional Induced Polarization and Electromagnetic Modeling[J]. Geophysics,1975,40(2):309-324.

[3] Xiong Z,Raiche A,Sugeng F. Efficient Solution of Full Domain 3D Electromagnetic Modelling Problems[J]. Exploration Geophysics,2000,31(1/2):158-161.

[4] Smith J T. Conservative Modeling of 3-D Electromagnetic Fields:Part I:Properties and Error Analysis[J]. Geophysics,1996,61(5):1308-1318.

[5] 谭捍东,余钦范,John Booker,等. 大地电磁法三维交错采样有限差分数值模拟[J]. 地球物理学报,2003,46(5):705-711. Tan Handong,Yu Qinfan,Booker J,et al. Magnetotelluric Three-Dimensional Modeling Using the Staggered-Grid Finite Difference Method[J]. Chinese Journal of Geophysics,2003,46(5):705-711.

[6] 陈辉,邓居智,谭捍东,等. 大地电磁三维交错网格有限差分数值模拟中的散度校正方法研究[J]. 地球物理学报,2011,54(6):1649-1659. Chen Hui,Deng Juzhi,Tan Handong,et al. Study on Divergence Correction Method in Three-Dimensional Magnetotelluric Modeling with Staggered-Grid Finite Difference Method[J]. Chinese Journal of Geophysics,2011,54(6):1649-1659.

[7] Badea E A,Everett M E,Newman G A,et al. Finite-Element Analysis of Controlled-Source Electromagnetic Induction Using Coulomb-Gauged Potentials[J]. Geophysics,2001,66(3):786-799.

[8] Um E S,Harris J M,Alumbaugh D L. A Lorenz-Gauged Finite-Element Solution for Transient CSEM Modeling[C]//2010 SEG Annual Meeting. Denver:Society of Exploration Geophysicists,2010.

[9] Mitsuhata Y,Uchida T. 3D Magnetotelluric Modeling Using the T-Ω Finite-Element Method[J]. Geophysics,2004,69(1):108-119.

[10] 徐志锋,吴小平. 可控源电磁三维频率域有限元模拟[J]. 地球物理学报,2010,53(8):1931-1939. Xu Zhifeng,Wu Xiaoping.Controlled Source Electro-magnetic 3-D Modeling in Frequency Domain by Finite Element Method[J]. Chinese Journal of Geophysics,2010,53(8):1931-1939.

[11] 王若,王妙月,底青云,等. CSAMT三维单分量有限元正演[J]. 地球物理学进展,2014,29(2):839-845. Wang Ruo,Wang Miaoyue,Di Qingyun,et al. 3D1C Modeling Using Finite Element Method[J]. Progress in Geophysics,2014,29(2):839-845.

[12] 张继锋. 基于电场双旋度方程的三维可控源电磁法有限单元法数值模拟[D]. 长沙:中南大学,2008. Zhang Jifeng. Three Dimensional Controlled Source Electromagnetic Numerical Simulation Based on Electric Field Double Curl Equation Using Finite Element Method[D]. Changsha:Central South University,2008.

[13] 徐凌华,童孝忠,柳建新,等. 基于有限单元法的二维/三维大地电磁正演模拟策略[J]. 物探化探计算技术,2009,31(5):421-425+407. Xu Linghua,Tong Xiaozhong,Liu Jianxin,et al. Solution Strategies For 2D and 3D Magnetotelluric Forward Modeling Based on the Finite Element Method[J]. Computing Techniques for Geophysical and Geochemical Exploration,2009,31(5):421-425.

[14] 童孝忠. 大地电磁测深有限单元法正演与混合遗传算法正则化反演研究[D].长沙:中南大学,2008. Tong Xiaozhong. Research of Forward Using Finite Element Method and Regularized Inversion Using Hybrid Genetic Algorithm in Magnetotelluric Sounding[D]. Changsha:Central South University,2008.

[15] 金建铭.电磁场有限元方法[M]. 西安:西安电子科技大学出版社,1998:164-190. Jin Jianming. Finite Element Method of Electromagnetic Field[M]. Xi'an:Xi'an Electronic University Press,1998:164-190.

[16] Nam M J,Kim H J,Song Y,et al. 3D Magne-totelluric Modelling Including Surface Topography[J]. Geophysical Prospecting,2007,55(2):277-287.

[17] 王烨. 基于矢量有限元的高频大地电磁法三维数值模拟[D].长沙:中南大学,2008. Wang Ye. A Study of 3D High Frequency Magnetotelluric Modeling by Edge-Based Finite Element Method[D]. Changsha:Central South University,2008.

[18] 刘长生. 基于非结构化网格的三维大地电磁自适应矢量有限元数值模拟[D]. 长沙:中南大学,2009. Liu Changsheng. Three-Dimensional Magnetotellurics Adaptive Edge Finite-Element Numerical Simulation Based on Unstructured Meshes[D]. Changsha:Central South University,2009.

[19] 顾观文,吴文鹂,李桐林. 大地电磁场三维地形影响的矢量有限元数值模拟[J]. 吉林大学学报(地球科学版),2014,44(5):1678-1686. Gu Guanwen,Wu Wenli,Li Tonglin. Modeling for the Effect of Magnetotelluric 3D Topography Based on the Vector Finite-Element Method[J]. Journal of Jilin University (Earth Science Edition),2014,44(5):1678-1686.

[20] 陈乐寿,王光锷.大地电磁测深法[M].北京:地质出版社,1990. Chen Leshou,Wang Guang'e. Magnetotelluric Sounding Method[M]. Beijing:Geological Publishing House,1990.

[21] 徐世浙. 地球物理中的有限单元法[M].北京:科学出版社,1994. Xu Shizhe. Finite Element Method in Geophysics[M]. Beijing:Science Press,1994.

[22] 曾攀. 有限元分析基础教程[M]. 北京:清华大学出版社,2008. Zeng Pan. Fundamentals of Finite Element Analysis[M]. Beijing:Tsinghua University Press,2008.

[23] 李建慧. 基于矢量有限单元法的大回线源瞬变电磁法三维数值模拟[D].长沙:中南大学,2011. Li Jianhui.3D Numerical Simulation for Transient Electromagnetic Field Excited by Large Source Loop Based on Vector Finite Element Method[D]. Changsha:Central South University,2011.

[24] Weiss C,Newman G. Electromagnetic Induction in a Generalized 3D Anisotropic Earth:Part 2:The LIN Preconditioner[J]. Geophysics,2003,68(3):922-930.

[25] Zhdanov M S,Varentsov I M,Weaver J T,et al. Methods for Modelling Electromagnetic Fields Results from COMMEMI:The International Project on the Comparison of Modelling Methods for Electromagnetic Induction[J]. Journal of Applied Geophysics,1997,37(3/4):133-271.

[26] 肖调杰,王赟,宋滔,等. 大地电磁法的理论探测深度[J]. 地球物理学进展,2015,30(5):2100-2106. Xiao Tiaojie,Wang Yun,Song Tao,et al. Depth of Investigation in Magnetotelluric Method[J]. Progress in Geophysics,2015,30(5):2100-2106.
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