Journal of Jilin University(Earth Science Edition) ›› 2018, Vol. 48 ›› Issue (2): 411-419.doi: 10.13278/j.cnki.jjuese.20170061

Previous Articles     Next Articles

3-D Forward Method for Geomagnetic Depth Sounding Based on Finite Difference Method in Spherical Coordinate

Li Jianping, Weng Aihua, Li Shiwen, Li Dajun, Li Sirui, Yang Yue, Tang Yu, Zhang Yanhui   

  1. Collegeof GeoExploration Sciences and Technology, Jilin University, Changchun 130026, China
  • Received:2017-02-07 Online:2018-03-26 Published:2018-03-26
  • Supported by:
    Supported by National Key Scientific Instrument and Equipment Development Projects of China (2011YQ05006010)

PDF (PC)

565

Abstract: In order to compute the global-scale electromagnetic induction responses, this paper introduces a 3-D forward method of the frequency domain geomagnetic depth sounding (GDS). The method is based on the Staggered-grid finite difference method (FDM) in spherical coordinate. The difference equations are derived from the integral form of Maxwell equations. The PARDISO Solver is used to solve the discrete equations to avoid the divergence correction of iterations. To validate our code, we compared the results to the solutions of the finite element method and FDM. The relative error between the finite difference numerical result of the three-dimensional staggered grid and the analytical solution is less than 5%. The accuracy of the two hemispheres model is also high enough. The calculation results of the three-dimensional checkerboard model show that the magnetic field components have a good resolution to the size and position of an abnormal body.

Key words: geomagnetic depth sounding, spherical coordinate, 3-D forward modeling, finite difference, geomagnetic response function

CLC Number: 

  • P631.2
[1] Karato S I. Remote Sensing of Hydrogen in Earth's Mantle[J]. Reviews in Mineralogy & Geochemistry, 2006, 62(1):343-375.
[2] Schultz A. On the Vertical Gradient and Associated Heterogeneity in Mantle Electrical Conductivity[J]. Phys Earth Planet Int,1990, 64(1):68-86.
[3] Utada H, Koyama T, Obayashi M, et al. A Joint Interpretation of Electromagnetic and Seismic Tomography Models Suggests the Mantle Transition Zone Below Europe is Dry[J]. Earth Planet Sci Lett, 2009, 281(3/4):249-257.
[4] Shimizu H, Utada H, Baba K, et al. Three-Dimen-sional Imaging of Electrical Conductivity in the Mantle Transition Zone Beneath the North Pacific Ocean by a Semi-Global Induction Study[J]. Phys Earth Planet Int, 2010, 183(1/2):252-269.
[5] Semenov A,Kuvshinov A. Global 3-D Imaging of Mantle Conductivity Based on Inversion of Observatory C-Responses:Ⅱ:Data Analysis and Results[J]. Geophysical Journal International,2012, 191(3):965-992.
[6] Kelbert A,Schultz A,Egbert G. Global Electromag-netic Induction Constraints on Transition-Zone Water Content Variations[J]. Nature, 2009, 460:1003-1006.
[7] Huang X,Xu Y,Karato S I. Water Content in the Transition Zone from Electrical Conductivity of Wadsleyite and Ringwoodite[J]. Nature, 2005, 434:746-749.
[8] Yoshino T,Manthilake G,Matsuzaki T,et al. Dry Mantle Transition Zone Inferred from the Conductivity of Wadsleyite and Ringwoodite[J]. Nature, 2008, 451:326-329.
[9] Sun J,Egbert G. A Thin-Sheet Model for Global Electromagnetic Induction[J]. Geophysical Journal International,2012, 189(1):343-356.
[10] Schmucker U. A Spherical Harmonic Analysis of Solar Daily Variations in the Years 1964-1965:Response Estimates and Source Fields for Global Induction:I:Methods[J]. Geophysical Journal International, 1999, 136(2):439-454.
[11] Koyama T, Khan A, Kuvshinov A. Three-Dimen-sional Electrical Conductivity Structure Beneath Australia from Inversion of Geomagnetic Observatory Data:Evidence for Lateral Variations in Transition-Zone Temperature, Water Content and Melt[J]. Geophysical Journal International, 2014, 196(3):1330.
[12] Kuvshinov A. 3-D Global Induction in the Oceans and Solid Earth:Recent Progress in Modeling Magnetic and Electric Fields from Sources of Magnetospheric, Ionospheric and Oceanic Origin[J]. Surveys in Geophysics, 2008, 29(2):139-186.
[13] Everett M E,Schultz A. Geomagnetic Induction in a Heterogeneous Sphere:Azimuthally Symmetric Test Computations and the Response of an Undulating 600-km Discontinuity[J]. J Geophys of Research Atmospheres, 1996, 101(B2):2765-2783.
[14] Yoshimura R,Oshiman N. Edge-Based Finite Element Approach to the Simulation of Geoelectromagnetic Induction on a 3-D Sphere[J]. Geophys Res Lett, 2002, 29(3):1-4.
[15] Ribaudo J T,Constable C G,Parker R L. Scripted Finite Element Tools for Global Electromagnetic Induction Studies[J]. Geophysical Journal International, 2012, 188(2):435-446.
[16] Uyeshima M,Schultz A. Geoelectromagnetic Induc-tion in a Heterogeneous Sphere:A New Three-Dimensional Forward Solver Using a Conservative Staggered-Grid Finite Difference Method[J]. Geophysical Journal International,2000, 140(3):636-650.
[17] Kelbert A, Egbert G D, Schultz A. Non-Linear Conjugate Gradient Inversion for Global EM Induction:Resolution Studies[J]. Geophysical Journal International, 2008, 173(2):365-381.
[18] Weiss C J. Triangulated Finite Difference Methods for Global-Scale Electromagnetic Induction Simulations of Whole Mantle Electrical Heterogeneity[J]. Geochemistry Geophysics Geosystems,2010,11(11):129-143.
[19] Tarits P, Mande A M. The Heterogeneous Electrical Conductivity Structure of the Lower Mantle[J]. Physics of the Earth & Planetary Interiors, 2010, 183(1/2):115-125.
[20] Martinec Z. Spectral-Finite Element Approach to Three-Dimensional Electromagnetic Induction in a Spherical Earth[J]. Geophysical Journal International, 1999, 136(1):229-250.
[21] Velímsk J, Martinec Z. Time-Domain, Spherical Harmonic-Finite Element Approach to Transient Three-Dimensional Geomagnetic Induction in a Spherical Heterogeneous Earth[J]. Geophysical Journal International, 2005, 161(1):81-101.
[22] Kelbert A, Kuvshinov A, Velímsk J, et al. Global 3-D Electromagnetic Forward Modelling:A Benchmark Study[J]. Geophysical Journal Internationa,2014, 197(2):785-814.
[23] 陈伯舫. 中国东南部地幔高导层的埋藏深度[J]. 地震学报, 1986,8(2):172-178. Chen Bofang. Buried Depth of the High Conductivity Layer Beneath the Region of South-East China[J]. Acta Seismologica Sinica,1986, 8(2):172-178.
[24] 杜兴信, 鲁秀玲. 用单台Z/H法研究陕西地区深部电导率[J]. 内陆地震, 1994,8(4):333-338. Du Xingxin, Lu Xiuling. Investigation on Deep Electroconductivity of Shaanxi Region by Means of Z/H Method with Single Station[J]. Inland Earthquake,1994, 8(4):333-338.
[25] 范国华, 姚同起, 顾左文,等. 利用磁梯度法研究我国地幔导电率[J]. 地震学报, 1997,19(2):164-173. Fan Guohua, Yao Tongqi, Gu Zuowen, et al. Research on Mantle Conductivity of China with Gradient Method[J]. Acta Seismologica Sinica, 1997, 19(2):164-173.
[26] 赵国泽,汤吉,梁竞阁,等. 用大地电磁网法在长春等地探测上地幔电导率结构[J]. 地震地质,2001, 23(2):143-152. Zhao Guoze,Tang Ji,Liang Jingge,et al. Measurement of Network-MT in Two Areas of NE China for Study of Upper Mantle Conductivity Structure of the Back-Arc Region[J]. Seismology and Geology,2001, 23(2):143-152.
[27] 徐光晶,汤吉,黄清华,等. 华北地区上地幔及过渡带电性结构研究[J]. 地球物理学报,2015, 58(2):566-575. Xu Guangjing,Tang Ji,Huang Qinghua,et al. Study on the Conductivity Structure of the Upper Mantle and Transition Zone Beneath North China[J]. Chinese Journal of Geophysics,2015, 58(2):566-575.
[28] Rokityansky I I. Geoelectromagnetic Investigation of the Earth's Crust and Mantle[M]. Berlin:Springer-Verlag,1982.
[29] 李大俊,翁爱华,杨悦,等. 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. Li Dajun, Weng Aihua, Yang Yue,et al. Three-Dimension Forward Modeling and Characteristics for Surface-Borehole Transient Electromagnetic by Using Staggered-Grid Finite Difference Method[J]. Journal of Jilin University (Earth Science Edition), 2017, 47(5):1552-1561.
[30] Smith J T. Conservative Modeling of 3-D Electromag-netic Fields:Part 1:Properties and Error Analysis[J]. Geophysics, 1996, 61(5):1308-1318.
[31] Schultz A,Larsen J C. On the Electrical Conductivity of the Mid-Mantle:I:Calculation of Equivalent Scalar Magnetotelluric Response Functions[J]. Geophysical Journal International, 1987, 88(3):733-761.
[32] Schmucker U. Substitute Conductors for Electromag-netic Response Estimates[J]. Pure and Applied Geophysics, 1987, 125(2):341-367.
[33] Fujii I, Schultz A. The 3D Electromagnetic Response of the Earth to Ring Current and Auroral Oval Excitation[J]. Geophysical Journal International, 2002, 151(3):689-709.
[34] Medin A E,Parker R L,Constable S. Making Sound Inferences from Geomagnetic Sounding[J]. Physics of the Earth & Planetary Interiors, 2007, 160(1):51-59.
[35] 李世文,翁爱华,李建平,等. 浅部约束的地磁测深C-响应一维反演[J]. 地球物理学报, 2017,60(3):1201-1210. Li Shiwen, Weng Aihua, Li Jianping, et al. 1-D Inversion of C-Response Data from Geomagnetic Depth Sounding with Shallow Resistivity Constraint[J]. Chinese Journal of Geophysics, 201760(3):1201-1210.
[36] Shimizu H, Koyama T, Baba K. Three-Dimensional Geomagnetic Response Functions for Global and Semi-Global Scale Induction Problems[J]. Geophysical Journal International, 2009, 178(1):123-144.
[1] Liu Mingchen, Sun Jianguo, Han Fuxing, Sun Zhangqing, Sun Hui, Liu Zhiqiang. Estimates of Seismic Reflector Dip by Adaptive Weighted Generalized Inverse Vector Direction Filter [J]. Journal of Jilin University(Earth Science Edition), 2018, 48(3): 881-889.
[2] Yang Haiyan, Yue Jianhua, Xu Zhengyu, Zhang Hua, Jiang Zhihai. Transient Electromagnetic Method Modeling in Ground-Borehole Model with Overburden Influence [J]. Journal of Jilin University(Earth Science Edition), 2016, 46(5): 1527-1537.
[3] Wang Weiping, Zeng Zhaofa, Li Jing, Wu Chengping. Topographic Effects and Correction for Frequency Airborne Electromagnetic Method [J]. Journal of Jilin University(Earth Science Edition), 2015, 45(3): 941-951.
[4] Yang Qingjie, Liu Cai, Geng Meixia, Feng Xuan, Guo Zhiqi, Liu Yang. Staggered Grid Finite Difference Scheme and Coefficients Deduction of Any Number of Derivatives [J]. Journal of Jilin University(Earth Science Edition), 2014, 44(1): 375-385.
[5] ZHOU Xiao-hua, CHEN Zu-bin, ZENG Xiao-xian, JIAO Jian. Simulation of Microtremor Using Staggered-Grid Finite Difference Method [J]. J4, 2012, 42(3): 852-857.
[6] MENG Qing-sheng, FAN Yu-qing, ZHANG Ke, ZHANG Meng. Tube Wave Propagation Numerical Simulation Based on High Order Finite-Difference Method [J]. J4, 2011, 41(1): 292-298.
[7] LIU Si-xin, ZHOU Jun-feng, WU Jun-jun, ZENG Zhao-fa, WAN Hong-xiang. Numerical Simulations of Borehole Radar for Metal Ore Detection [J]. J4, 2010, 40(6): 1479-1484.
[8] SUN Zhang-qing, SUN Jian-guo, ZHANG Dong-liang. 2.5-D DC Electric Field Numerical Modeling Including Surface Topography Based on Coordinate Transformation Method [J]. J4, 2010, 40(2): 425-431.
[9] YANG Hao, SUN Jian-guo, HAN Fu-xin, MA Shu-fang. Fast Algorithm of the Expanding Wavefronts Finite-Difference Traveltime Calculation Based on the Three Branch Tree Structure Heap Sorts [J]. J4, 2010, 40(1): 188-194.
[10] WU Guo-chen, LUO Cai-ming,LIANG Kai. Frequency-Space Domain Finite Difference Numerical Simulation of Elastic Wave in TTI Media [J]. J4, 2007, 37(5): 1023-1033.
[11] LIU Si-xin, ZENG Zhao-fa, XU Bo. FDTD Simulation of Ground Penetrating Radar Signal in 3-Dimensional Dispersive Medium [J]. J4, 2006, 36(01): 123-0127.
[12] LIU Si-xin, ZENG Zhao-fa, XU Bo. Realization of Absorbing Boundary Condition with Lossy Media for Ground Penetrating Radar Simulation [J]. J4, 2005, 35(03): 378-0381.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright © Journal of Jilin University(Earth Science Edition), All Rights Reserved.
Tel: +86-431-88502374；13756165364　E-mail: xuebao1956@jlu.edu.cn
Powered by Beijing Magtech Co. Ltd