有限元法作为一种高效的数值模拟方法，广泛用于地球物理的正演计算。网格剖分的合适与否是有限元求解的先决条件。在满足剖分区域大小一致，且满足边界条件，进行稀疏与加密网格比较的前提下，讨论了二维介质理想模型的网格剖分对大地电磁正演精度的影响。研究表明，在低频阶段，TE 和TM 两种极化模式从整体上看，粗网格比细网格模拟精度高，但是在近地表开始阶段，TM 模式下，粗网格模拟精度不及细网格；整体变化幅度粗网格比细网格缓和，曲线尾部粗网格与细网格波动幅度都较大，脱离了正常值。结果表明，正确的网格剖分能有效地提高电磁有限元正演的精度，且对后续反演同样有意义。
As a highly efficient numerical simulation method, finite element method is widely used in geophysical forward calculation. Whether grid subdivision is suitable or not is the prerequisite for finite element solution. From the aspect of ideal twodimensional medium model, this paper discusses the effect of grid subdivision on magnetotelluric forward modeling precision, under the conditions that the subdivision areas have the same size, the boundary conditions are satisfied, and the sparse and dense mesh are compared. In low frequency phase, two polarization modes were taken as a whole, the coarse grid has higher simulation accuracy than the fine grid, but at the beginning of the near-surface phase under TM mode, the simulation accuracy of the coarse grid is not as high as that of the fine grid. Overall, the coarse grid has more moderate change than the fine grid, and the fluctuation amplitude of the coarse grid and fine grid is higher in the tail of the curve, both of which deviate from the normal value. The results show that proper grid subdivision can effectively improve the accuracy of electromagnetic finite element forward modeling, and it is significant for the subsequent inversion as well.
[1] Coggon G H. Electromagnetic and electrical modeling by the finite element [J]. Geophysics, 1971, 36: 132-155.
[2] 陈乐寿. 有限元法在大地电磁场正演计算中的应用与改进[J]. 石油物 探, 1981, 20(3): 84-103. Chen Leshou. Application and improvement of finite-element method in forward calculation of geo-electromagnetic field[J]. Geophysical Prospecting for Petroleum, 1981, 20(3): 84-103.
[3] 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.
[4] 王绪本, 李永年, 高永才. 大地电磁测深二维地形影响及其校正方法 研究[J]. 物探化探计算技术, 1999, 21(4): 327-332. Wang Xuben, Li Yongnian, Gao Yongcai. Two dimensional topographic responses in magneto telluric sounding and its correction methods[J]. Computing Techniques for Giophysical and Geochenical Exploration, 1999, 21(4): 327-332.
[5] 阮百尧, 徐世浙. 电导率分块线性变化二维地电断面电阻率测深有限 元数值模拟[J]. 中国地质大学学报, 1998, 23(3): 303-307. Ruan Baiyao, Xu Shizhe. FEM for modeling resistivity sounding on 2D geoelectric model with line variation of conductivity within each block[J]. Journal of China University of Geosciences, 1998, 23(3): 303-307.
[6] 陈小斌, 张翔, 胡文宝. 有限元直接迭代算法在MT二维正演计算中的 应用[J]. 石油地球物理勘探, 2000, 35(4): 487-496. Chen Xiaobin, Zhang Xiang, Hu Wenbao. Application of finite-element direct iteration algorithm to MT 2D forward computation[J]. Oil Geophysical Prospecting, 2000, 35(4): 487-496.
[7] 马为, 陈小斌, 赵国泽. 大地电磁测深二维正演中辅助场的新算法[J]. 地震地质, 2008, 30(2): 525-533. Ma Wei, Chen Xiaobin, Zhao Guoze. A new algorithm for the calculation of auxiliary field in MT 2D forward modeling[J]. Seismology and Geology, 2008, 30(2): 525-533.
[8] 柳建新, 蒋鹏飞, 童孝忠, 等. 不完全LU分解预处理的BICGSTAB算 法在大地电磁二维正演模拟中的应用[J]. 中南大学学报, 2009, 40(2): 484-491. Liu Jianxin, Jiang Pengfei, Tong Xiaozhong, et al. Application of BICGSTAB algorithm with incomplete LU decomposition preconditioning to two- dimensional magnetotelluric forward modeling[J]. Journal of Central South University, 2009, 40(2) : 484-491.
[9] 欧东新. 计算机精度和网格大小对大地电磁有限单元法正演的影响[J]. 桂林工学院学报, 2007, 27(3): 329-332. Ou Dongxin. Effect of computer precision and grid length on MT simulating using FEM[J]. Journal of Guilin University of Technology, 2007, 27(3): 329-332.
[10] Wannamaker P E, Stodt J A, Rijo L. A stable finite element solution for two- dimensional magnetotelluric modelling[J]. Geophys Journal of the Intermational, 1987, 88: 277-296.
[11] 吴娟, 席振铢, 王鹤. 网格尺寸及边界对大地电磁有限元正演精度的 影响[J]. 物探化探计算技术, 2012, 34(1): 27-32. Wu Juan, Xi Zhenzhu, Wang He. Effects of grid size and boundary on MT forward modeling using finite element method[J]. Computing Techniques for Geophysical and Geochemical Exploration, 2012, 34 (1): 27-32.
