吉林大学学报(地球科学版) ›› 2017, Vol. 47 ›› Issue (5): 1552-1561.doi: 10.13278/j.cnki.jjuese.201705303

• 地球探测与信息技术 • 上一篇    下一篇

地-井瞬变电磁三维交错网格有限差分正演及响应特性

李大俊, 翁爱华, 杨悦, 李斯睿, 李建平, 李世文   

  1. 吉林大学地球探测科学与技术学院, 长春 130026
  • 收稿日期:2016-12-23 出版日期:2017-09-26 发布日期:2017-09-26
  • 通讯作者: 翁爱华(1969),男,教授,博士生导师,主要从事电磁勘探方法技术与应用研究,E-mail:wengah@jlu.edu.cn E-mail:wengah@jlu.edu.cn
  • 作者简介:李大俊(1990),男,博士研究生,主要从事瞬变电磁方法正反演理论与应用研究,E-mail:lidj14@mails.jlu.edu.cn
  • 基金资助:
    国家重大科技仪器专项（2011YQ05006010）

Three-Dimension Forward Modeling and Characteristics for Surface-Borehole Transient Electromagnetic by Using Staggered-Grid Finite Difference Method

Li Dajun, Weng Aihua, Yang Yue, Li Sirui, Li Jianping, Li Shiwen   

  1. College of GeoExploration Science and Technology, Jilin University, Changchun 130026, China
  • Received:2016-12-23 Online:2017-09-26 Published:2017-09-26
  • Supported by:
    Supported by the Chinese Science and Technology Major Instrument Project (2011YQ05006010)

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摘要： 为了研究地-井瞬变电磁响应特征，获得不同井位低阻薄板异常体的响应规律：首先采用交错网格有限差分技术离散二次场满足的频率域赫姆霍兹方程；然后结合虚框叠加等效和虚拟界面法将发射源和接收位置扩展到任意层位，解决了全空间背景格林函数的计算问题；之后利用MUMPS求解器求解频率域二次场，再经过余弦变换，获得井中任意位置的瞬变电磁响应；最后采用三维模型对本文算法的正确性进行验证，设计了均匀半空间和嵌入低阻薄板的三维模型，获得垂直磁场的三维分布，分析均匀导电半空间中低阻薄板对地-井瞬变电磁三维响应的影响特点。结果表明：本文三维地-井瞬变电磁计算方案的计算精度与前人基本相同；水平导电薄板的存在主要影响板体附近及穿过薄板的井中瞬变响应，最大的特点是在异常体位置附近的中期时间道响应出现变号现象。本文的研究为定性解释地-井瞬变电磁法异常提供一个技术手段，也为地-井瞬变电磁三维反演奠定基础。

关键词: 地-井瞬变电磁, 三维正演, 有限差分, 余弦变换, 虚拟界面法

Abstract: In this study, we developed three-dimension forward modeling for surface-borehole transient electromagnetic (TEM) by using staggered-grid finite difference method, and obtained transient electromagnetic response characteristics from different borehole positions for a conductive thin plate. The Helmholtz function is discreted by staggered-grid finite difference method in frequency domain, then the abnormal-field is quickly processed using MUMPS package. Background Green function can be efficiently computed by equivalent fictitious square overlay method and virtual interface method, which extending the transmitter and receiver to anywhere in full space. The cosine-transformation was performed for borehole transient electromagnetic response in any position, then the mentioned algorithm was validated by three-dimension model. We designed two three-dimension conductive models, one is the homogeneous half-space, the other is an embedded conductive plate, to get the three-dimension distribution of vertical magnetic field in the time domain, and then we analyzed the influence of the conductive body on transient electromagnetic response. It is shown that the solution of three-dimension transient electromagnetic in this study is comparable to those of the predecessors'. The existence of a conductive plate influences mainly on borehole TEM near the plate body and through the conductive thin plate; and TEM symbol change occurs in the middle time channels near the abnormal body. The proposed research provides a technical method for qualitative interpretation of surface-borehole transient electromagnetic data, and lays the foundation for three-dimension inversion of surface-borehole transient electromagnetic

Key words: surface-borehole transient electromagnetic, three-dimensional forward, finite-difference, cosine-transformation, virtual-surface method

中图分类号: 

  • P631.3
[1] 蒋邦远. 实用近区磁源瞬变电磁法勘探[M]. 北京:地质出版社, 1998. Jiang Bangyuan. Applied near Zone Magnetic Source Transient Electromagnetic Exploration[M].Beijing:Geological Publishing House, 1998.
[2] 牛之琏. 时间域电磁法原理[M]. 长沙:中南大学出版社, 2007. Niu Zhilian. Theory of Time Domain Electromagentic Method[M].Changsha:Central South University of Technology Press, 2007.
[3] Dyck A V, West G F. The Role of Simple Computer Models in Interpretations of Wide-Band, Drill-Hole Electromagnetic Surveys in Mineral Exploration[J]. Geophysics, 1984, 49(7):957-980.
[4] Swidinsky A, Nabighian M. On Smoke Rings Produ-ced by a Loop Buried in a Conductive Half-Space[J]. Geophysics, 2015, 80(4):E225-E236.
[5] Nabighian M N. Quasi-Static Transient Response of a Conducting Half-Space:An Approximate Representation[J]. Geophysics, 1979, 44(10):1700-1705.
[6] West R C, Ward S H. The Borehole Transient Elec-tromagnetic Response of a Three-Dimensional Fracture Zone in a Conductive Half-Space[J]. Geophysics, 1988, 53(11):1469-1478.
[7] 李建慧, 刘树才, 焦险峰, 等. 地-井瞬变电磁法三维正演研究[J]. 石油地球物理勘探, 2015, 50(3):556-564. Li Jianhui, Liu Shucai, Jiao Xianfeng, et al. Three-Dimensional Forward Modeling for Surface-Borehole Transient Electromagnetic Model[J]. Oil Geophysical Prospecting, 2015, 50(3):556-564.
[8] 徐正玉, 杨海燕, 邓居智, 等. 基于异常场的地-井瞬变电磁法正演研究[J]. 物探与化探, 2015, 39(6):1176-1182. Xu Zhengyu, Yang Haiyan, Deng Juzhi, et al. Research on Forward Simulation of Down-Hole TEM Based on the Abnormal Filed[J]. Geophysical and Geochemical Exploration, 2015, 39(6):1176-1182.
[9] 杨海燕, 岳建华. 巷道影响下三维全空间瞬变电磁法响应特征[J]. 吉林大学学报(地球科学版), 2008, 38(1):129-134. Yang Haiyan, Yue Jianhua. Response of Characteristics of the 3D Whole-Space TEM Disturbed by Roadway[J]. Journal of Jilin University (Earth Science Edition),2008, 38(1):129-134.
[10] 杨海燕, 徐正玉, 岳建华, 等. 覆盖层下三维板状体地-井瞬变电磁响应[J]. 物探与化探, 2016, 40(1):190-196. Yang Haiyan, Xu Zhengyu, Yue Jianhua, et al. 3D Inclined Conductor Behavior of Down-Hole Transient Electromagnetic Method with Overburden Layer[J]. Geophysical and Geochemical Exploration, 2016, 40(1):190-196.
[11] 杨海燕, 邓居智, 汤洪志, 等. 全空间瞬变电磁法资料解释方法中的平移算法[J]. 吉林大学学报(地球科学版), 2014, 44(3):1012-1017. Yang Haiyan, Deng Juzhi, Tang Hongzhi, et al. Translation Algorithm of Data Interpretation Technique in Full-Space Transient Electromagnetic Method[J]. Journal of Jilin University (Earth Science Edition), 2014, 44(3):1012-1017.
[12] 翁爱华, 刘云鹤, 贾定宇, 等. 地面可控源频率测深三维非线性共轭梯度反演[J]. 地球物理学报, 2012, 55(10):3506-3515. Weng Aihua, Liu Yunhe, Jia Dingyu, et al. Three-Dimensional Controlled Source Electromagnetic Inversion Using Non-Linear Conjugate Gradient[J]. Chinese Journal of Geophysics, 2012, 55(10):3506-3515.
[13] 贲放, 刘云鹤, 黄威, 等. 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. Ben Fang, Liu Yunhe, Huang Wei, et al.MCSEM Responses for Anisotropic Media in Shallow Water[J]. Journal of Jilin University (Earth Science Edition), 2016, 46(2):581-593.
[14] Alumbaugh D L, Newman G A, Prevost L, et al. Three-Dimensional Wideband Electromagnetic Modeling on Massively Parallel Computers[J]. Radio Science, 1996, 31(1):1-23.
[15] Yee K S. Numerical Solution of Initial Value Prob-lems of Maxwells Equations in Isotropic Media[J]. IEEE Transactions on Antennas and Propagation, 1966, AP-14:302-307.
[16] Sasaki Y, Yi M J,Choi J, et al. Frequency and Time Domain Three-Dimensional Inversion of Electromagnetic Data for a Grounded-Wire Source[J]. Journal of Applied Geophysics, 2015, 112:106-114.
[17] Kelbert A, Meqbel N, Egbert G D, et al. ModEM:A Modular System for Inversion of Electromagnetic Geophysical Data[J]. Computers & Geosciences, 2014, 66:40-53.
[18] Egbert G D, Kelbert A. Computational Recipes for Electromagnetic Inverse Problems[J]. Geophysical Journal International, 2012, 189(1):251-267.
[19] Mackie R L, Smith J T, Madden T R. Three-Di-mensional Electromagnetic Modeling Using Finite Difference Equations:The Magnetotelluric Example[J]. Radio Science, 1994, 29(4):923-935.
[20] Oldenburg D W, Haber E, Shekhtman R. Three Di-mensional Inversion of Multisource Time Domain Electromagnetic Data[J]. Geophysics, 2013, 78(1):E47-E57.
[21] Weng A H, Liu Y H, Chen Y L, et al. Computation of Transient Electromagnetic Field from a Rectangular Loop over Stratified Earths[J]. Chinese Journal of Geophysics, 2010, 53(3):646-650.
[22] Weng A H, Liu Y H, Yin C C, et al. Singularity-Free Green's Function for EM Sources Embedded in a Stratified Medium[J]. Applied Geophysics, 2016, 13(1):25-36.
[23] 张成范, 翁爱华, 孙世栋, 等. 计算矩形大定源回线瞬变电磁测深全区视电阻率[J]. 吉林大学学报(地球科学版), 2009, 39(4):755-758. Zhang Chengfan, Weng Aihua, Sun Shidong, et al. Computation of Whole-Time Apparent Resistivity of Large RectangularLoop[J]. Journal of Jilin University (Earth Science Edition), 2009, 39(4):755-758.
[24] 李建平, 李桐林, 张辉, 等. 不规则回线源层状介质瞬变电磁场正反演研究及应用[J]. 吉林大学学报(地球科学版), 2005, 35(6):790-795. Li Jianping, Li Tonglin, Zhang Hui, et al. Study and Application of the TEM Forward and Inversion Problem of Irregular Loop Source over the Layered Medium[J]. Journal of Jilin University (Earth Science Edition), 2005, 35(6):790-795.
[25] Das U C, de Hoop A T. Efficient Computation of Apparent Resistivity Curves for Depth Profiling of a Layered Earth[J]. Geophysics, 1995, 60(6):1691-1697.
[26] Chave A D. Numerical Integration of Related Hankel Transforms by Quadrature and Continued Fraction Expansion[J]. Geophysics, 1983, 48(12):1671-1686.
[27] Newman G A, Hohmann G W. Transient Electro-magnetic Responses of High-Contrast Prisms in a Layered Earth[J]. Geophysics, 1988, 53(5):691-706.
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