吉林大学学报(地球科学版) ›› 2017, Vol. 47 ›› Issue (1): 215-223.doi: 10.13278/j.cnki.jjuese.201701301

• 地球探测与信息技术 • 上一篇    下一篇

复杂电性结构大地电磁二维响应特征

罗天涯1, 熊彬1, 蔡红柱2, 陈欣1, 刘云龙1, 兰怀慷1, 李祖强1, 梁卓1   

  1. 1. 桂林理工大学地球科学学院, 广西 桂林 541006;
    2. 犹他大学矿产和地球科学学院, 美国 犹他州 盐湖城 84112
  • 收稿日期:2016-05-08 出版日期:2017-01-26 发布日期:2017-01-26
  • 通讯作者: 熊彬(1974-),男,教授,博士,主要从事电磁场理论及反演成像方面的教学与科研工作,E-mail:xiongbin@msn.com E-mail:xiongbin@msn.com
  • 作者简介:罗天涯(1989-),男,博士研究生,主要从事电磁场数值模拟研究,E-mail:tianyaluo@aliyun.com
  • 基金资助:
    国家自然科学基金项目（40974077,41164004,41674075）；广西自然科学基金项目（2016GXNSFA380004,2013GXNSFAA019277）；桂林市“漓江学者”专项经费资助项目（2013005）；桂林理工大学研究生创新项目（BS201601）

Magnetotelluric Responses of Two-Dimensional Complex Conductivity Structures

Luo Tianya1, Xiong Bin1, Cai Hongzhu2, Chen Xin1, Liu Yunlong1, Lan Huaikang1, Li Zuqiang1, Liang Zhuo1   

  1. 1. College of Earth Sciences, Guilin University of Technology, Guilin 541006, Guangxi, China;
    2. College of Mines & Earth Sciences, University of Utah, Salt Lake City 84112, UT, USA
  • Received:2016-05-08 Online:2017-01-26 Published:2017-01-26
  • Supported by:
    Supported byNational Natural Science Foundation of China (40974077,41164004, 41674075), Natural Science Foundation of Guangxi Province (2016GXNSFA380004, 2013GXNSFAA019277), Lijiang Scholars Special Expenditure Grant (2013005)and Innovation Project of GLUT Graduate Education (BS201601)

PDF (PC)

601

摘要： 为了改进计算区域离散化问题,本文利用自适应非结构化网格有限单元法求解二维地电结构下大地电磁场满足的加权余量表达式。在有限元求解电磁场的过程中,网格剖分越精细、计算精度越高,计算量也会越大。此外,结构化网格难以适应任意地形以及复杂地质构造。而自适应非结构化网格在电性变化剧烈的区域会自动加密,在电性缓变的区域则生成粗疏的网格,从而优化网格质量与数量。因此,文中引入COMSOL Multiphysics软件,以实现若干地电模型的构建及非结构化自由四边形单元网格化。将网格数据信息导入本文算法,计算大地电磁场响应,并与解析解及数值解对比。结果表明,基于非结构化网格的正演模拟精度高、适应性强,为计算区域网格化提供了新的方法。

关键词: 非结构化网格, 大地电磁, 有限单元法, 正演

Abstract: To improve the discretization technique, adaptive unstructured quadrilateral grid finite element (FE) procedure is presented for solving weighted residual formulation of magnetotelluric (MT) fields in 2-D conductivity structures. The finer the meshes are, the more accurate the numerical solutions are. However, this is at the cost of time-consuming and large memory requirement. Adaptive mesh refinement generally provides an optimization of both run time and accuracy since in the method meshes are only refined where the electrical parameters vary intensely, while coarsen in the slow electrical resistivity change region. Due to the fact that regular grids have no potential to incorporate arbitrary topography and complex geologic structures, we introduced COMSOL Multiphysics software package to build arbitrary geometries and subdivide them with free quadrilaterals, then apply meshes information to our algorithm. Comparison with analytical solutions and previous numerical solutions demonstrate a high-accuracy and flexibility of numerical simulations based on unstructured grid, a new technology to discretize the computating domain.

Key words: unstructured grid, magnetotelluric(MT), finite element method, forward

中图分类号: 

  • P631.3
[1] 赵广茂,李桐林,王大勇,等. 基于二次场二维起伏地形MT有限元数值模拟[J]. 吉林大学学报(地球科学版),2008,38(6):1055-1059. Zhao Guangmao, Li Tonglin, Wang Dayong, et al. Secondary Field-Based Two-Dimensional Topographic Numerical Simulation in Magnetotellurics by Finite Element Method[J]. Journal of Jilin University (Earth Science Edition), 2008, 38(6):1055-1059.
[2] 顾观文,吴文鹂,李桐林. 大地电磁场三维地形影响的矢量有限元数值模拟[J]. 吉林大学学报(地球科学版),2014,44(5):1678-1686. Gu Guanwen, Wu Wenli, Li Tonglin. Modeling for the Effect of Magnetotelluric 3D Topography Based on the Vector Finite-Element Method[J]. Journal of Jilin University (Earth Science Edition), 2014, 44(5):1678-1686.
[3] 李桐林,张镕哲,朴英哲.大地电磁测深与地震初至波走时交叉梯度反演[J].吉林大学学报(地球科学版),2015,45(3):952-961. Li Tonglin, Zhang Rongzhe, Pak Yongchol. Joint Inversion of Magnetotelluric and First-Arrival Wave Seismic Traveltime with Cross-Gradient Constraints[J]. Journal of Jilin University (Earth Science Edition), 2015, 45(3):952-961.
[4] Zhdanov M S, Lee S K, Yoshioka K. Integral Equa-tion Method for 3D Modeling of Electromagnetic Fields in Complex Structures with Inhomogeneous Background Conductivity[J]. Geophysics, 2006, 71(6):333-345.
[5] Newman G A, Alumbaugh D L. Frequency-Domain Modelling of Airborne Electromagnetic Responses Using Staggered Finite Differences[J]. Geophysical Prospecting, 1995, 43(8):1021-1042.
[6] Aprea C, Booker J R, Smith J T. The Forward Pro-blem of Electromagnetic Induction:Accurate Finite-Difference Approximations for Two Dimensional Discrete Boundaries with Arbitrary Geometry[J]. Geophys J Int, 1997, 129(1):29-40.
[7] Cai H Z, Xiong B, Han M, et al. 3D Controlled-Source Electromagnetic Modeling in Anisotropic Medium Using Edge-Based Finite Element Method[J]. Computers & Geosciences, 2014, 73:164-176.
[8] Key K, Weiss C. Adaptive Finite-Element Modeling Using Unstructured Grids:The 2D Magnetotelluric Example[J]. Geophysics, 2006, 71(6):G291-G299.
[9] Fox R C, Hohmann G W, Killpack T J, et al.Topo-graphic Effects in Resistivity and Induced-Polarization Surveys[J]. Geophysics, 1980, 45(1):75-93.
[10] Wannamaker P E, Stodt J A, Rijo L. A Stable Finite Element Solution for Two-Dimensional Magneto-telluric Modelling[J]. Geophys J Int, 1987, 88(1):277-296.
[11] Reddy I K, Rankin D. Magnetotelluric Response of Laterally Inhomogeneous and Anisotropic Media[J]. Geophysics, 1975, 40(6):1035-1045.
[12] Franke A, B rner R U, Spitzer K. Adaptive Unstru-ctured Grid Finite Element Simulation of Two-Dimensional Magnetotelluric Fields for Arbitrary Surface and Seafloor Topography[J]. Geophys J Int, 2007, 171(1):71-86.
[13] McFee S, Giannacopoulos D. Optimal Discretizations in Adaptive Finite Element Electromagnetics[J]. Int J Numer Methods Eng, 2001, 52(9):939-978.
[14] Badea E A, Everett M E, Newman G A, et al.Finite-Element Analysis of Controlled-Source Electro-magnetic Induction Using Coulomb-Gauged Potentials[J]. Geophysics, 2001, 66(3):786-799.
[15] Li Y, Pek J.Adaptive Finite Element Modelling of Two-Dimensional Magnetotelluric Fields in General Anisotropic Media[J]. Geophys J Int, 2008, 175(3):942-954.
[16] Puzyrev V, Koldan J, Puente J, et al.A Parallel Finite-Element Method for Three-Dimensional Controlled-Source Electromagnetic Forward Modelling[J]. Geophys J Int, 2013, 193(2):678-693.
[17] Lee S K, Kim H J, Song Y, et al. MT2D Inv Matlab:A Program in MATLAB and FORTRAN for Two-Dimensional Magnetotelluric Inversion[J]. Computers & Geosciences, 2009, 35(8):1722-1734.
[18] Rodi W L. A Technique for Improving the Accuracy of Finite Element Solutions for Magnetotelluric Data[J]. Geophys J Int, 1976, 44(2):483-506.
[19] 陈乐寿. 有限元法在大地电磁场正演计算中的应用及改进[J]. 石油勘探,1981(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(3):84-103.
[20] 邓建辉,熊文林,葛修润. 复杂区域非结构化四边形网格全自动生成方法[J]. 计算结构力学及应用,1995,12(2):196-204. Deng Jianhui, Xiong Wenlin, Ge Xiurun. Automatic Generation of Unstructured Quadrilateral Mesh for Complex Domain[J]. Computational Structural Mechanics and Application, 1995, 12(2):196-204.
[21] 陈建军,郑耀,陈立岗,等. 非结构化四边形网格生成新算法[J]. 中国图像图形学报,2008,13(9):1796-1803. Chen Jianjun, Zheng Yao,Chen Ligang, et al. A New Unstructured Quadrilateral Mesh Generation Algorithm[J]. Journal of Image and Graphics, 2008, 13(9):1796-1803.
[22] Jin J M.The Finite Element Method in Electroma-gnetics[M]. New Jersey:Wiley-IEEE Press, 2002:1-780.
[23] Wannamaker P E, Stodt J A, Rijo L. Two-Dimen-sional Topographic Responses in Magnetotellurics Modeled Using Finite Elements[J]. Geophysics, 1986, 51(11):2131-2144.
[24] 李磊. 湘南骑田岭锡铅锌多金属矿区岩矿石电性研究[J]. 物探与化探,2007,31(增刊1):77-80. Li Lei. Researches on Rock Electrical Properties in the Qitianling Tin,Lead and Zinc Polymetallic Ore Deposit,Southern Hunan[J]. Geophysical and Geochemical Exploration,2007, 31(Sup. 1):77-80.
[25] Chouteau M, Bouchard K. Two-Dimensional Terrain Correction in Magnetotelluric Surveys[J]. Geophysics, 1988, 53(6):854-862.
[26] Jiracek G R. Near-Surface and Topographic Distor-tions in Electromagnetic Induction[J]. Surveys in Geophysics, 1990, 11:163-203.
[1] 张聪, 石砥石, 张子亚, 陈科, 苑坤, 乔计花, 彭芳苹. 云南楚雄盆地西部高精度重磁电特征及基底特征[J]. 吉林大学学报(地球科学版), 2018, 48(3): 863-871.
[2] 李建平, 翁爱华, 李世文, 李大俊, 李斯睿, 杨悦, 唐裕, 张艳辉. 基于球坐标系下有限差分的地磁测深三维正演[J]. 吉林大学学报(地球科学版), 2018, 48(2): 411-419.
[3] 殷长春, 卢永超, 刘云鹤, 张博, 齐彦福, 蔡晶. 多重网格准线性近似技术在三维航空电磁正演模拟中的应用[J]. 吉林大学学报(地球科学版), 2018, 48(1): 252-260.
[4] 陈辉, 尹敏, 殷长春, 邓居智. 大地电磁三维正演聚集多重网格算法[J]. 吉林大学学报(地球科学版), 2018, 48(1): 261-270.
[5] 安振芳, 张进, 张建中. 海洋三维VC观测系统优化设计[J]. 吉林大学学报(地球科学版), 2018, 48(1): 271-284.
[6] 李大俊, 翁爱华, 杨悦, 李斯睿, 李建平, 李世文. 地-井瞬变电磁三维交错网格有限差分正演及响应特性[J]. 吉林大学学报(地球科学版), 2017, 47(5): 1552-1561.
[7] 蔡剑华, 肖晓. 基于组合滤波的矿集区大地电磁信号去噪[J]. 吉林大学学报(地球科学版), 2017, 47(3): 874-883.
[8] 韩松, 刘国兴, 韩江涛. 华南地区进贤-柘荣剖面深部电性结构[J]. 吉林大学学报(地球科学版), 2016, 46(6): 1837-1846.
[9] 杨海燕, 岳建华, 徐正玉, 张华, 姜志海. 覆盖层影响下典型地-井模型瞬变电磁法正演[J]. 吉林大学学报(地球科学版), 2016, 46(5): 1527-1537.
[10] 严家斌, 皇祥宇. 大地电磁三维矢量有限元正演[J]. 吉林大学学报(地球科学版), 2016, 46(5): 1538-1549.
[11] 刘海飞, 柳杰, 高寒, 郭荣文, 童孝忠, 麻昌英. 五极纵轴激电测深三维有限元正演模拟[J]. 吉林大学学报(地球科学版), 2016, 46(3): 884-892.
[12] 李庆洋, 李振春, 黄建平, 李娜, 苏在荣. 基于贴体全交错网格的起伏地表正演模拟影响因素[J]. 吉林大学学报(地球科学版), 2016, 46(3): 920-929.
[13] 贲放, 刘云鹤, 黄威, 徐驰. 各向异性介质中的浅海海洋可控源电磁响应特征[J]. 吉林大学学报(地球科学版), 2016, 46(2): 581-593.
[14] 王丹丹, 李世臻, 周新桂, 李爱勇, 温泉波, 林燕华. 大兴安岭地区突泉盆地高精度重磁电特征及其构造格架[J]. 吉林大学学报(地球科学版), 2016, 46(1): 240-253.
[15] 殷长春, 邱长凯, 刘云鹤, 蔡晶. 时间域航空电磁数据加权横向约束反演[J]. 吉林大学学报(地球科学版), 2016, 46(1): 254-261.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 《吉林大学学报(地球科学版)》编辑部
地址：长春市西民主大街938号(130026)　电话：+86-431-88502374；13756165364　E-mail: xuebao1956@jlu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发