Due to the influence of the artificial boundary condition, when the conventional finite element method is used to carry out the forward simulation of the three-dimensional geophysical field in a limited space, local abnormal distortion may occur, which affects the accuracy of the numerical simulation. This problem is usually solved by expanding the edge, but this requires a larger range, which greatly increases the computational cost and affects the efficiency of forward simulation. In this paper, on the basis of COMSOL Multiphysics software, infinite elements are set on the external boundary to replace the traditional boundary conditions so as to reduce the calculation area. Compared with the traditional finite element method, the finite element infinite element coupling method, by setting the isolated sphere and the combined body model and considering the conditions of demagnetization, remanence and surface undulation, can effectively overcome the boundary effect, improve the calculation accuracy and reduce the amount of calculation, thus improving the forward numerical simulation efficiency of the finite element method.
郭楚枫, 张世晖, 刘天佑. 三维磁场有限元—无限元耦合数值模拟[J]. 物探与化探, 2021, 45(3): 726-736.
GUO Chu-Feng, ZHANG Shi-Hui, LIU Tian-You. 3D magnetic field forward modeling by finite-infinite element coupling method. Geophysical and Geochemical Exploration, 2021, 45(3): 726-736.
Zhao N, Wang X B, Yu G, et al. 3D MCSEM parallel goal-oriented adaptive vector finite element modeling[J]. Chinese Journal of Geophysics, 2019, 62(2):779-788.
[4]
Kordy M, Wannamaker P, Maris V, et al. 3-D magnetotelluric inversion including topography using deformed hexahedral edge finite elements and direct solvers parallelized on SMP computers - Part I: forward problem and parameter Jacobians[J]. Geophysical Journal International, 2016, 204(1):74-93.
doi: 10.1093/gji/ggv410
[5]
Ren Z, Kalscheuer T, Greenhalgh S, et al. A goal-oriented adaptive finite-element approach for plane wave 3-D electromagnetic modelling[J]. Geophysical Journal International, 2013, 194(2):700-718.
doi: 10.1093/gji/ggt154
Cao X Y, Yin C C, Zhang B, et al. A goal-oriented adaptive finite-element method for 3D MT anisotropic modeling with topography[J]. Chinese Journal of Geophysics, 2018, 61(6):2618-2628.
Liu Y H, Yin C C, Cai J, et al. Review on research of electrical anisotropy in electromagnetic prospecting[J]. Chinese Journal of Geophysics, 2018, 61(8):3468-3487.
Li Y, Wu X P, Ling P R, et al. Three-dimensional modeling of marine controlled-source electromagnetism using the vector finite element method for arbitrary anisotropic media[J]. Chinese Journal of Geophysics, 2017, 60(5):1955-1978.
Jiang F Y, Xie L L, Chang W K, et al. Forward calculation of three dimensional gravity vector using finite element method[J]. Journal of Jilin University:Earth Science Edition, 2015, 45(4):1217-1226.
[10]
May D A, Knepley M G. Optimal, scalable forward models for computing gravity anomalies[J]. Geophysical Journal International, 2011, 187(1):161-177.
doi: 10.1111/gji.2011.187.issue-1
[11]
Cai Y, Wang C. Fast finite-element calculation of gravity anomaly in complex geological regions[J]. Geophysical Journal International, 2005, 162(3):696-708.
doi: 10.1111/gji.2005.162.issue-3
Zhu Z Q, Zeng S H, Lu G Y, et al. Finite element forward simulation of the two-dimensional gravity gradient tensor[J]. Geophysical and Geochemical Exploration, 2010, 34(5):668-671.
Zhu Z Q, Xing Z F, Lu G Y. Research on the gravity arbitrarily complex terrain correction method based on FEM[J]. Computing Techniques for Geophysical and Geochemical Exploration, 2019, 41(6):768-773.
Wang S H. The direct problem of magnetic prospecting under anisotropic condition and the solution to solve it[J]. Chinese Journal of Geophysics, 1983, 26(1):58-69.
Liu S, Liu T Y, Gao W L, et al. Magnetic forward modeling considering demagnetization effect using finite element method based on FlexPDE[J]. Computing Techniques for Geophysical and Geochemical Exploration, 2013, 35(2):134-141.
Liu S, Liu T Y, Gao W L, et al. The Influence of demagnetization on magnetic data interpretation[J]. Geophysical and Geochemical Exploration, 2012, 36(4):602-606.
Zhang L C, Tang J T, Ren Z Y, 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.
[18]
Ungless R F. An infinite finite element[D]. Prince George:University of British Columbia, 1973.
[19]
Bettess P, Zienkiewicz O C. Diffraction and refraction of surface waves using finite and infinite elements[J]. International Journal for Numerical Methods in Engineering, 1977, 11(8):1271-1290.
doi: 10.1002/(ISSN)1097-0207
[20]
Astley R J, Bettess P, Clark P J. Mapped infinite elements for exterior wave problems[J]. International Journal for Numerical Methods in Engineering, 1991, 32(1):207-209.
doi: 10.1002/(ISSN)1097-0207
[21]
Astley R J, Macaulay G J. Mapped wave envelope elements for acoustical radiation and scattering[J]. Journal of Vibration and Acoustics, 1994, 170(1):207-209.
[22]
Astley R J, Macaulay G J, Coyette J, et al. Three-dimensional wave-envelope elements of variable order for acoustic radiation and scattering. Part I. Formulation in the frequency domain[J]. The Journal of the Acoustical Society of America, 1998, 103(1):49-63.
doi: 10.1121/1.421106
[23]
Burnett D S. A three‐dimensional acoustic infinite element based on a prolate spheroidal multipole expansion[J]. The Journal of the Acoustical Society of America, 1994, 96(5):2798-2816.
doi: 10.1121/1.411286
[24]
Burnett D S, Holford R L. Prolate and oblate spheroidal acoustic infinite elements[J]. Computer Methods in Applied Mechanics and Engineering, 1998, 158(1):117-141.
doi: 10.1016/S0045-7825(97)00251-X
Shi G C. Research on post-failure mechanical properties of Brittle-plastic rocks by OOFEM coupled with IEM[D]. Wuhan:Wuhan Institute of Rock and Soil Mechanics, The Chinese Academy of Sciences,P.R. China, 2005.
Li L X, Guo S Z, Wang A Q. The infinite element method and its application[J]. Advances in Mechanics, 2007, 37(2):161-174.
[27]
Wu S, Xiang Y, Yao J, et al. An element-free galerkin coupled with improved infinite element method for exterior acoustic problem[J]. Journal of Theoretical and Computational Acoustics, 2019, 27(2):411-454.
[28]
Fu L Y, Wu R S. Infinite boundary element absorbing boundary for wave propagation simulations[J]. Geophysics, 2000, 65(2):596-602.
doi: 10.1190/1.1444755
Zhu J, Tang Z H, Dun Y Q, et al. Application of infinite element method in 3D electric logging calculation[J]. Natural Gas Industry, 2008, 28(11):59-61.
Tang J T, Gong J Z. 3D DC resistivity forward modeling by finite-infinite element coupling method[J]. Chinese Journal of Geophysics, 2010, 53(3):717-728.
Ou Y, Feng J, Zhao Y, et al. Forward modeling of magnetic data using finite volume method with a simultaneous consideration of demagnetization and remanence[J]. Chinese Journal of Geophysics, 2018, 61(11):4635-4646.
[32]
刘鹏飞. 岩石磁性特征及考虑退磁影响的正反演研究[D]. 武汉:中国地质大学(武汉), 2019.
[32]
Liu P F. Magnetic behavior of rocks and forward and inverse models incorporating demagnetization[D]. Wuhan:China University of Geosciences(Wuhan), 2019.