|
|
|
| Analysis of 3D finite-element forward modeling of CSEM data using three different formulas and unstructured grids |
| ZHOU Feng1,2,3,4, ZHANG Zhiyong1,2, CHEN Huang3, TANG Jingtian3, DENG Juzhi1,2, LI Yong4 |
1. Fundamental Science on Radioactive Geology and Exploration Technology Laboratory, East China University of Technology, Nanchang, Jiangxi 330013, China;
2. School of Geophysics and Measurement-control Technology, East China University of Technology, Nanchang, Jiangxi 330013, China;
3. School of Geosciences and Info-physics, Central South University, Changsha, Hunan 410083, China;
4. Key Laboratory of Geophysical Electromagnetic Probing Technologies of Ministry of Natural Resources, Institute of Geophysical and Geochemical Exploration, Chinese Academy of Geological Sciences, Langfang, Hebei 065000, China |
|
|
|
|
Abstract High-precision and efficient 3D CSEM forward modeling algorithms have always been one of the key and hot issues in the study of electromagnetic forward modeling. Currently, one electric field equation and two A-Φ coupling potential equations with different structures are often used to solve 3D CSEM forward modeling problems. In this paper, the application effects of these three equations were analyzed by a finite element method. Firstly, in view of the CSEM boundary value problem, an electric field equation and two A-Φ coupling potential equations with a curl-curl structure and a Laplacian structure, respectively, were derived. Secondly, for elimination of field source singularity, the computational regions were discretized with unstructured tetrahedral grids. A local refinement technique for the field source was also applied for an accurate solution to the unified field source integration. Lastly, the three equations were fast solved through a Krylov subspace iterative algorithm and the PARDISO solver. The correctness of the algorithms developed in this paper was verified by calculation of the electromagnetic responses of the magnetic dipole source and the electric dipole source via the three equations, respectively, with a homogeneous half-space geoelectric model. The convergence, memory consumption and solution accuracy of the three CSEM forward equations were analyzed with a geoelectric model of low-resistance anomalous bodies. The results show that within a small computational region, the electric field equation based on vector finite elements has higher solution accuracy and higher solution efficiency. Otherwise, the A-Φ coupling potential equation with a Laplacian structure is more suitable than the other two equations for 3D CSEM forward modeling studies.
|
|
Received: 05 March 2021
|
|
|
|
|
|
| [1] |
何继善.可控源音频大地电磁法[M]. 湖南长沙:中南工业大学出版社, 1990.
|
| [2] |
汤井田, 何继善.可控源音频大地电磁法及其应用[M]. 湖南长沙:中南大学出版社, 2005.
|
| [3] |
底青云, 王若.可控源音频大地电磁数据正反演及方法应用[M]. 北京:科学出版社, 2008.
|
| [4] |
Hou J, Mallan R K, Torresverdín C.Finite-difference simulation of borehole EM measurements in 3D anisotropic media using coupled scalar-vector potentials[J]. Geophysics, 2006, 71(5):G225-G233.
|
| [5] |
蔡红柱, 熊彬, Michael Zhdanov.电导率各向异性的海洋电磁三维有限单元法正演[J]. 地球物理学报, 2015, 58(8):2839-2850.CAI Hongzhu, XIONG Bin, Michael Z.Three-dimensional marine controlled-source electromagnetic mode-lling in anisotropic medium using finite element me-thod[J]. Chinese Journal of Geophysics, 2015, 58(8):2839-2850.
|
| [6] |
张林成, 汤井田, 任政勇, 等.基于二次场的可控源电磁法三维有限元-无限元数值模拟[J]. 地球物理学报, 2017, 60(9):3655-3666.ZHANG Lincheng, TANG Jingtian, REN Zhengyong, et al.Forward modeling of 3D CSEM with the coupled finite-infinite element method based on the second field[J]. Chinese Journal of Geophysics, 2017, 60(9):3655-3666.
|
| [7] |
汤文武, 柳建新, 叶益信, 等.基于节点有限元与矢量有限元的可控源电磁三维正演对比[J]. 石油地球物理勘探, 2018, 53(3):617-624.TANG Wenwu, LIU Jianxin, YE Yixin, et al.Comparison of 3D controlled-source electromagnetic forward modeling based on the nodal finite element and the edge-based finite element[J]. Oil Geophysical Prospecting, 2018, 53(3):617-624.
|
| [8] |
严波, 李予国, 韩波, 等.任意方位电偶源的MCSEM电磁场三维正演[J]. 石油地球物理勘探, 2017, 52(4):859-868.YAN Bo, LI Yuguo, HAN Bo, et al.3D marine controlled-source electromagnetic forward modeling with arbitrarily orientated dipole source[J]. Oil Geophysical Prospecting, 2017, 52(4):859-868.
|
| [9] |
李勇, 吴小平, 林品荣, 等.基于二次场电导率分块连续变化的三维可控源电磁有限元数值模拟[J]. 地球物理学报, 2015, 58(3):1072-1087.LI Yong, WU Xiaoping, LIN Pinrong, et al.Three-dimensional controlled source electromagnetic finite element simulation using the secondary field for continuous variation of electrical conductivity within each block[J]. Chinese Journal of Geophysics, 2015, 58(3):1072-1087.
|
| [10] |
Mitsuhata Y.2-D electromagnetic modeling by finite-element method with a dipole source and topography[J]. Geophysics, 2000, 65(2):465-475.
|
| [11] |
闫述.基于三维有限元数值模拟的电和电磁探测研究[D]. 陕西西安:西安交通大学, 2003.
|
| [12] |
阎述, 陈明生.电偶源频率电磁测深三维地电模型有限元正演[J]. 煤田地质与勘探, 2000, 28(3):50-56.YAN Shu, CHEN Mingsheng.Finite-element solution of three-dimensional geoelctric models in frequency electromagnetic sounding excited by a horizontal electric dipole[J]. Coal Geology & Exploration, 2000, 28(3):50-56.
|
| [13] |
Weiss C J.Project APhiD:A Lorenz-gauged A-Φ decomposition for parallelized computation of ultra-broadband electromagnetic induction in a fully heterogeneous earth[J]. Computers & Geosciences, 2013, 58(1):40-52.
|
| [14] |
Schwarzbach C, Börner R U, Spitzer K.Three-dimensional adaptive higher order finite element simulation for geo-electromagnetics:a marine CSEM example[J]. Geophysical Journal International, 2011, 187(1):63-74.
|
| [15] |
李建慧, 胡祥云, 陈斌, 等.复杂形态回线源激发电磁场的矢量有限元解[J]. 石油地球物理勘探, 2017, 52(6):1324-1332.LI Jianhui, HU Xiangyun, CHEN Bin, et al.3D electromagnetic modeling with vector finite element for a complex-shaped loop source[J]. Oil Geophysical Prospecting, 2017, 52(6):1324-1332.
|
| [16] |
杨军, 刘颖, 吴小平.海洋可控源电磁三维非结构矢量有限元数值模拟[J]. 地球物理学报, 2015, 58(8):2827-2838.YANG Jun, LIU Ying, WU Xiaoping.3D simulation of marine CSEM using vector finite element method on unstructured grids[J]. Chinese Journal of Geophy-sics, 2015, 58(8):2827-2838.
|
| [17] |
李建慧, 胡祥云, 曾思红.基于电场总场矢量有限元法的接地长导线源三维正演[J]. 地球物理学报, 2016, 59(4):1521-1534.LI Jianhui, HU Xiangyun, ZENG Sihong.A vector finite element solver of three-dimensional modelling for a long grounded wire source based on total electric field[J]. Chinese Journal of Geophysics, 2016, 59(4):1521-1534.
|
| [18] |
Yin C.A goal-oriented adaptive finite-element method for 3D scattered airborne electromagnetic method modeling[J]. Geophysics, 2016, 81(5):E337-E346.
|
| [19] |
张继锋, 汤井田, 喻言, 等.基于电场矢量波动方程的三维可控源电磁法有限单元法数值模拟[J]. 地球物理学报, 2009, 52(12):3132-3141.ZHANG Jifeng, TANG Jingtian, YU Yan, et al.Three dimensional controlled source electromagnetic numerical simulation based on electric field vector wave equation using finite element method[J]. Chinese Journal of Geophysics, 2009, 52(12):3132-3141.
|
| [20] |
陈辉, 殷长春, 邓居智.基于Lorenz规范条件下磁矢势和标势耦合方程的频率域电磁法三维正演[J]. 地球物理学报, 2016, 59(8):3087-3097.CHEN Hui, YIN Changchun, DENG Juzhi.A finite-volume solution to 3D frequency-domain electromagnetic modelling using Lorenz-gauged magnetic vector and scalar potentials[J]. Chinese Journal of Geophy-sics, 2016, 59(8):3087-3097.
|
| [21] |
叶益信, 李予国, 刘颖, 等.基于局部加密非结构网格的海洋可控源电磁法三维有限元正演[J]. 地球物理学报, 2016, 59(12):4747-4758.YE Yixin, LI Yuguo, LIU Ying, et al.3D finite element modeling of marine controlled-source electromagnetic fields using locally refined unstructured meshes[J]. Chinese Journal of Geophysics, 2016, 59(12):4747-4758.
|
| [22] |
Jahandari H C, Farquharson G.A finite-volume solution to the geophysical electromagnetic forward problem using unstructured grids[J]. Geophysics, 2014, 79(6):E287-E302.
|
| [23] |
Ansari S C, Farquharson G.3D finite-element forward modeling of electromagnetic data using vector and scalar potentials and unstructured grids[J]. Geophy-sics, 2014, 79(4):E149-E165.
|
| [24] |
Puzyrev V, Koldan J, de la Puente J, et al.A parallel finite-element method for three-dimensional controlled-source electromagnetic forward modelling[J]. Geophysical Journal International, 2013, 193(2):678-693.
|
| [25] |
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 electromagnetic 3-D modeling in frequency domain by finite element method[J]. Chinese Journal of Geophysics, 2010, 53(8):1931-1939.
|
| [26] |
Franke A, Börner R U, and Spitzer K.Adaptive unstructured grid finite element simulation of two-dimensional magnetotelluric fields for arbitrary surface and seafloor topography[J]. Geophysical Journal of the Royal Astronomical Society, 2007, 171(1):71-86.
|
| [27] |
Schenk O and Gärtner K.Solving unsymmetric sparse systems of linear equations with PARDISO[C]. International Conference on Computational Science.Springer, Berlin, Heidelberg, 2002.
|
| [28] |
Mitsuhata Y.3D magnetotelluric modeling using the t-ω finite-element method[J]. Geophysics, 2004, 69(1):108-119.
|
| [29] |
Jin J.The Finite Element Method in Electromagnetics[M]. John Wiley & Sons, New York, 2002.
|
| [30] |
Saad Y.Iterative Methods for Sparse Linear Systems[M]. Society for Industrial and Applied Mathematics, Philadelphia, 2003.
|
|
|
|
2021, Vol. 56 
