三维磁场有限元—无限元耦合数值模拟

doi:10.11720/wtyht.2021.1539

摘要
图/表
参考文献
相关文章
Metrics

全文: PDF(7208 KB) HTML
输出: BibTeX | EndNote (RIS)

摘要

利用传统有限单元法在有限空间范围内开展三维地球物理场正演模拟时,由于截断边界的影响,会引起局部异常的畸变,影响数值模拟的精度,对该问题通常采用扩边的办法加以解决,但需要的范围较大,从而大大增加运算成本,影响正演模拟效率。本文基于COMSOL Multiphysics软件,在求解域外部边界设置无限元以替代传统边界条件,达到减小计算区域目的。通过孤立球体和组合模型磁场正演模拟,考虑退磁、剩磁及地表起伏条件,与传统有限元方法相比,有限元—无限元耦合算法能够有效克服边界效应,提高计算精度,降低运算量,从而提高了有限单元法正演数值模拟效率。

	服务

	把本文推荐给朋友
	加入引用管理器
	E-mail Alert
	RSS
	作者相关文章
	郭楚枫
	张世晖
	刘天佑

关键词 ：有限元—无限元, 三维正演, 磁法勘探, COMSOL

Abstract：

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.

Key words： finite-infinite 3D forward modeling magnetic prospecting COMSOL

收稿日期: 2020-12-01 修回日期: 2021-01-13 出版日期: 2021-06-20

ZTFLH:

P631

基金资助:雄安新区深层地热资源探测评价技术示范项目(2018YFC0604303);深部资源预测系统技术研究与示范项目(2017YFC0601504)

通讯作者: 张世晖

作者简介: 郭楚枫(1996-),男,在读硕士研究生,研究方向为重磁勘探。Email: gcf2013@cug.edu.cn

引用本文:

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.

链接本文:

https://www.wutanyuhuatan.com/CN/10.11720/wtyht.2021.1539 或 https://www.wutanyuhuatan.com/CN/Y2021/V45/I3/726

Fig.1 非均匀介质分布(改自徐世浙,1994)

Fig.2 三维无限元映射(改自汤井田等,2010)

Fig.3 球体模型及网格剖分示意(蓝色为球体模型,红色直线代表测线,黄色为观测平面范围)

Fig.4 不同方法正演的球体平面ΔT磁异常及其平面误差分布

Fig.5 不同方法正演的球体磁异常曲线

Fig.6 绝对误差分布曲线

Table 1 不同算法模型计算效率及误差对比

Fig.7 组合形体模型及网格剖分示意(红色直线代表测线,黄色为观测平面范围)

Fig.8 有限元数值模拟结果及平面误差分布

Table 2 组合形体计算效率及误差对比

Fig.9 起伏地表模型(黄色为观测面范围)

Fig.10 起伏地形下有限元数值模拟结果及平面误差分布

[1]	徐世浙. 地球物理中的有限单元法[M]. 北京: 科学出版社, 1994.
[1]	Xu S Z. The finite element method in geophysics [M]. Beijing: Science Press, 1994.
[2]	Coggon J H. Electromagnetic and electrical modeling by the finite element method[J]. Geophysics, 1971, 36(1):132-132. doi: 10.1190/1.1440151
[3]	赵宁, 王绪本, 余刚, 等. 面向目标自适应海洋可控源电磁三维矢量有限元正演[J]. 地球物理学报, 2019, 62(2):779-788.
[3]	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
[6]	曹晓月, 殷长春, 张博, 等. 面向目标自适应有限元法的带地形三维大地电磁各向异性正演模拟[J]. 地球物理学报, 2018, 61(6):2618-2628.
[6]	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.
[7]	刘云鹤, 殷长春, 蔡晶, 等. 电磁勘探中各向异性研究现状和展望[J]. 地球物理学报, 2018, 61(8):3468-3487.
[7]	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.
[8]	李勇, 吴小平, 林品荣, 等. 电导率任意各向异性海洋可控源电磁三维矢量有限元数值模拟[J]. 地球物理学报, 2017, 60(5):1955-1978.
[8]	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.
[9]	蒋甫玉, 谢磊磊, 常文凯, 等. 三度体重力矢量的有限单元法正演计算[J]. 吉林大学学报:地球科学版, 2015, 45(4):1217-1226.
[9]	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
[12]	朱自强, 曾思红, 鲁光银, 等. 二度体的重力张量有限元正演模拟[J]. 物探与化探, 2010, 34(5):668-671.
[12]	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.
[13]	朱自强, 邢泽峰, 鲁光银. 有限元重力任意复杂地形校正方法研究[J]. 物探化探计算技术, 2019, 41(6):768-773.
[13]	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.
[14]	王书惠. 磁各向异性条件下的磁法勘探正问题及其解法[J]. 地球物理学报, 1983, 26(1):58-69.
[14]	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.
[15]	刘双, 刘天佑, 高文利, 等. 基于FlexPDE考虑退磁作用的有限元法磁场正演[J]. 物探化探计算技术, 2013, 35(2):134-141.
[15]	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.
[16]	刘双, 刘天佑, 高文利, 等. 退磁作用对磁测资料解释的影响[J]. 物探与化探, 2012, 36(4):602-606.
[16]	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.
[17]	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.
[17]	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
[25]	史贵才. 脆塑性岩石破坏后区力学特性的面向对象有限元与无界元耦合模拟研究[D]. 武汉:中国科学院研究生院(武汉岩土力学研究所), 2005.
[25]	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.
[26]	李录贤, 国松直, 王爱琴. 无限元方法及其应用[J]. 力学进展, 2007, 37(2):161-174.
[26]	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
[29]	朱军, 唐章宏, 顿月芹, 等. 无限元法在三维电测井计算中的应用[J]. 天然气工业, 2008, 28(11):59-61.
[29]	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.
[30]	汤井田, 公劲喆. 三维直流电阻率有限元—无限元耦合数值模拟[J]. 地球物理学报, 2010, 53(3):717-728.
[30]	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.
[31]	欧洋, 冯杰, 赵勇, 等. 同时考虑退磁和剩磁的有限体积法正演模拟[J]. 地球物理学报, 2018, 61(11):4635-4646.
[31]	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.

[1]	周钟航, 张莹莹. 山峰对电性源地面瞬变电磁响应的影响及校正方法[J]. 物探与化探, 2023, 47(5): 1236-1249.
[2]	吴国培, 张莹莹, 赵华亮, 周钟航, 李医滨. 基于横向约束的中心回线瞬变电磁一维反演[J]. 物探与化探, 2023, 47(4): 1024-1032.
[3]	赵友超, 张军, 范涛, 姚伟华, 杨洋, 孙怀凤. 地—井瞬变电磁三维响应特征分析与异常体快速定位方法研究[J]. 物探与化探, 2022, 46(2): 383-391.
[4]	田郁, 乐彪. 复杂异常体模型下的三维MT倾子正演模拟[J]. 物探与化探, 2021, 45(4): 1021-1029.
[5]	智庆全, 武军杰, 王兴春, 孙怀凤, 杨毅, 张杰, 邓晓红, 陈晓东, 杜利明. 在瞬变电磁三维正演中的应用[J]. 物探与化探, 2021, 45(4): 1037-1042.
[6]	顾观文, 武晔, 石砚斌. 基于矢量有限元的大地电磁快速三维正演研究[J]. 物探与化探, 2020, 44(6): 1387-1398.
[7]	王昊, 严加永, 孟贵祥, 吕庆田, 王栩. 地磁梯度测量及其在金属矿勘查中的试验——以拉依克勒克铜铁矿为例[J]. 物探与化探, 2019, 43(6): 1173-1181.
[8]	朱裕振, 强建科, 王林飞, 张文艳, 戴世坤. 深埋铁矿磁测数据三维反演分析与找矿靶区预测[J]. 物探与化探, 2019, 43(6): 1182-1190.
[9]	马炳镇. 起伏地形下地面瞬变电磁法三维正演数值模拟研究[J]. 物探与化探, 2018, 42(4): 777-784.
[10]	任志平, 李貅, 戚志鹏, 赵威, 智庆全, 刘磊. 地面核磁共振三维响应影响因素[J]. 物探与化探, 2017, 41(1): 92-97.
[11]	武军杰, 王兴春, 杨毅, 张杰, 邓晓红, 杨启安. 偶极TEM三分量曲线特征分析及应用试验[J]. 物探与化探, 2015, 39(5): 973-977.
[12]	廉西猛, 张睿璇. 基于GPU集群的大规模三维有限差分正演模拟并行策略[J]. 物探与化探, 2015, 39(3): 615-620.
[13]	宋双, 张恒磊. 向下延拓在深部矿产勘探中的应用——以青海某矿区为例[J]. 物探与化探, 2014, 38(6): 1195-1199.
[14]	郭莹, 曲赞, 范志雄, 王传雷. 关于磁测工作质量检查方式的实验及讨论[J]. 物探与化探, 2014, 38(4): 781-786.
[15]	张天龙, 张维, 王忠义, 张福斌, 李斌, 杨立伟. 冀东滦南一带重磁异常特征及找矿意义[J]. 物探与化探, 2014, 38(4): 641-648.

Viewed

Full text

Abstract

Cited

Shared

Discussed