Journal of Jilin University(Earth Science Edition) ›› 2016, Vol. 46 ›› Issue (3): 884-892.doi: 10.13278/j.cnki.jjuese.201603302

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3D Finite Element Forward Modeling of Five-Pole Longitude Induced Polarization Sounding

Liu Haifei1,2, Liu Jie2, Gao Han2, Guo Rongwen1,2, Tong Xiaozhong1,2, Ma Changying2   

  1. 1. Hunan Key Laboratory of Nonferrous Resources and Geological Hazard Detection, Changsha 410083, China;
    2. School of Geosciences and InfoPhysics, Central South University, Changsha 410083, China
  • Received:2015-10-10 Online:2016-05-26 Published:2016-05-26
  • Supported by:

    Supported by the National Natural Science Foundation of China (41174102)

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Abstract:

The authors develop a three-dimensional(3D) finite element forward modeling method for five-pole longitude induced polarization (IP) soundingin this paper. Boundary value problems of the secondary potential field are derived from that of the primary potential field with the three-point current sources, it also proves the corresponding variation equation saccording to the boundary value problem of the secondary potential field. Then we solved the variation equations of the secondary potential field using a finite element method (FEM) based on a 3D continuous model of the electrical conductivity, specifically for five-pole longitude array. Finally, we calculate the induced polarization sounding curve with the five-pole longitude array based on the horizontal layered medium, the results show that the maximum relative error is less than 0.25% and the total computational time is about 18 seconds. Three examples indicate the accuracy and efficiency of the proposed algorithm, which will facilitate the application of the five-pole longitude IP sounding for complex geoelectrical structure, understanding of the IP sounding curve anomaly, and further carrying out the inversion.

Key words: five-pole longitude induced polarization sounding, 3D FEM forward modeling, boundary value problem, variation problem, secondary potential

CLC Number: 

  • P631.3

[1] 黄兰珍,方兴付.五极纵轴直流电测深法的理论研究及应用[J].物探化探计算技术,1980,2(1):2-26. Huang Lanzhen, Fang Xingfu. The Study and Application About the Theory of Five Poles Electrical Sounding[J]. Computing Techniques for Geophysical and Geochemical Exploration, 1980, 2(1):2-26.

[2] 杨庆镰.五极纵轴测深法在龙岩灰岩地区寻找岩溶水的应用[J].山东国土资源,2010,26(9):43-45. Yang Qinglian. Surveying the Underground Water Using the Five Poles Electrical Sounding Method in the Karst Area of Longyan[J]. Shandong Land and Resources, 2010, 26(9):43-45.

[3] 徐宜芽.双频激电五极纵轴测深法在铀金勘查中的应用[J].华东铀矿地质,1997,4(3):14-20. Xu Yiya. The Uranium Exploration Using the Five Poles Sounding Method of Dual-Frequency Induced Polarization[J]. Uranium Geology of East China, 1997, (3):14-20.

[4] 张金广,张宗岭.五极纵轴测深法在岩溶地区的应用原理与实践[J].地质与勘探,1997,33(5):46-49. Zhang Jinguang, Zhang Zongling. The Principle and Pratice of the Five Poles Electrical Sounding Applied to Survey of the Karst Area[J]. Geology and Exploration, 1997, 33(5):46-49.

[5] 曹平华,黄文清.五极纵轴测深法在溶洞探测中的应用[J].物探与化探,2003,27(4):323-325. Cao Pinghua, Huang Wenqing. The Application of the Five Poles Electrical Sounding on the Survey of Karst[J].Geophysical and Geochemical Exploration, 2003, 27(4):323-325.

[6] Dey A, Morrison H F. Resistivity Modeling for Arbitrarily Shaped Three-Dimensional Structures[J]. Geophysics, 1979, 44(4):753-780.

[7] Scriba H. Computation of the Electrical Potential in Three-Dimensional Structures[J]. Geophysical Prospecting, 1981, 29(5):790-802.

[8] Spitzer K. A 3-D Finite-Difference Algorithm for DC Resistivity Modeling Using Conjugate Gradient Methods[J]. Geophys J Internat, 1995, 123(3):903-914.

[9] 吴小平,徐果明,李时灿.利用不完全Cholesky共轭梯度法求解点源三维地电场[J].地球物理学报,1998, 41(6):848-855. Wu Xiaoping, Xu Guoming, Li Shican. The Calculation of 3D Geoelectric Field of Point Source by Incomplete Cholesky Conjugate Gredient Method[J]. Chinese Journal of Geophysics, 1998, 41(6):848-855.

[10] 徐世浙,倪逸.复杂地电条件下点源三维电阻率模拟的新方法[J].物探化探计算技术,1991, 13(1):13-20. Xu Shizhe, Ni Yi. New Method of 3D Resistivity Modeling for Point Dicrect Current Source with Complex Earth Model[J]. Computing Techniques for Geophysical and Geochemical Exploration, 1991, 13(1):13-20.

[11] Ma Qinzhong. The Boundary Element Method for 3-D DC Resistivity Modeling in Layered Earth[J].Geophysics, 2002, 67(2):610-617.

[12] Rucker C, Gunther T, Spitzer K. Three-Dimensional Modelling and Inversion of DC Resistivity Data Incorporating Topography:I:Modelling[J]. Geophys J Internat, 2006, 166(3):495-505.

[13] Zhou B, Greenhalgh M, Greenhalgh S A. 2.5-D/3-D Resistivity Modelling in Anisotropic Media Using Gaussian Quadrature Grids[J]. Geophys J Internat, 2009, 176(1):63-80.

[14] Plattner A, Maurer H R, Vorloeper J, et al. Three-Dimensional Geoelectric Modelling with Optimal Work/Accuracy Rate Using an Adaptive Wavelet Algorithm[J]. Geophys J Internat, 2010, 182(4):741-752.

[15] 阮百尧,熊彬.电导率连续变化的三维电阻率测深有限元模拟[J].地球物理学报,2002,45(1):131-138. Ruan Baiyao, Xiong Bin. A Finite Element Modeling of 3D Resistivity Sounding with Continuous Conductivity[J]. Chinese Journal of Geophysics, 2002, 45(1):131-138.

[16] 刘海飞,阮百尧,柳建新,等.起伏地形电导率连续变化的三维激电数据有限元数值模拟[J].物探化探计算技术,2008,30(4):308-313. Liu Haifei, Ruan Baiyao, Liu Jianxin, et al. The 3D Finite Element Numerical Modeling of Direct Current Induced Polarization Data for Continuous Conductivity Model with Rolling Terrain[J]. Computing Techniques for Geophysical and Geochemical Exploration, 2008, 30(4):308-313.

[17] 徐世浙.地球物理中的有限单元法[M].北京:科学出版社,1994:183-189. Xu Shizhe. Finite Element Method in Geophysics[M]. Beijing:Science Press, 1994:183-189.

[18] Saad Y. Iterative Methods for Sparse Linear Systems[M]. 2nd Ed. Philadelphia:Society for Industrial and Applied Mathematics, 2003:266-267.

[19] 胡家赣.线性代数方程组的迭代解法[M].北京:科学出版社,1991:185-192. Hu Jiagan. Iterative Solving Method for Algebraic Equations[M]. Beijing:Science Press, 1991.

[20] 武汉地质学院金属物探教研室.电法勘探教程[M].北京:地质出版社,1991:186-187. Research Team of Metal Geophysical Exploration, Wuhan Institute of Geology. Electrical Prospecting Tutorial[M]. Beijing:Geology Publishing House, 1991:186-187.
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