大地电磁聚焦反演成像方法研究
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摘要
大地电磁测深法(MT)是在地面上观测具有区域性乃至全球性分布特征的天然交变电磁场来研究地下岩层的电学性质及其分布特征的一种探测方法。它通过研究大地对天然电磁场的频率响应，获得地下不同深度介质电阻率分布的信息。由于该方法不需要人工建场、成本低、勘探深度大等优点，已广泛应用于研究地壳和上地幔地质构造，同时也用来进行油气勘查、地热勘探及地震预报等研究工作。随着MT的广泛应用和对其理论研究的深入，许多问题也显现出来，特别是在高维、高精度大地电磁数据反演方法的研究方面进展较缓慢。本论文以中科院知识创新工程重大项目“环渤海(湾)地区前新生代海相油气资源研究”中的“环渤海(湾)地区前新生代残留盆地分布的综合地质地球物理研究”课题和中国石化西部新区勘探指挥部的科研项目“准南山前带非地震成像技术研究”为依托，分析了当前大地电磁数据反演的发展现状；鉴于传统的反演方法大都是基于最大平滑理论基础上，反演得出的地电图像都是渐变的，不能准确反映出电性突变时分界面的具体位置。针对这一问题，在前人工作的基础上，提出了大地电磁数据聚焦反演成像方法技术。根据聚焦反演方法固有的特点和需要，研究了基于计算二次场响应的MT模拟方法，构建了新的反演目标函数并对解反演目标函数的方法进行了优化，较好地实现了本次研究的目的。论文的主要内容与成果如下：
(1)当前二维大地电磁有限元正演模拟方法都是直接计算平行于走向的总场值，这种计算思路受网格密度的影响较大，而且在求取低频段的电磁场响应时解的精度偏低。针对这一问题，引入基于计算二次场响应的模拟方法。将非均匀地电结构中传播的大地电磁场分解为一次(电或磁)场与二次场之和，其中一次场为无异常体时的场，二次场为异常体产生的场。在使用有限元法解偏微分方程时，利用二次场偏微分方程与总场偏微分方程的相似性，直接引用总场法计算中的系数矩阵作为二次场方程的合成矩阵。与总场偏微分方程相比较，二次场方程只是在右端多了一个源项积分，因此总场法的有限元系数矩阵可直接用于求二次场的方程中。这种模拟方法受网格密度影响较低，而且较好地解决了总场法中低频场精度不高的缺点。根据上述原理所编制的二次场有限元法MT正演模拟软件，对几个典型模型进行了试算，并与传统总场模拟法进行了比较分析。结果表明直接计算二次场的结果精度更高、更接近真实解，这一方法的提出对提高大地电磁反演精度具有理论和实践意义。
(2)当前MT反演方法在构建目标函数时大都选择基于最大平滑稳定泛函作为模型目标函数，采用这种思路反演出的地电图像都是平滑的、渐变的，不能准确反映岩体电性突变时分界面的具体位置，这给后期的地质解释带来了一定的困难。本文分析了Oleg Portniaguine等人(1999)年提出的聚焦反演成像法，此方法是建立在一种全新的稳定器(如最小梯度支撑泛函等)的基础上，并结合惩罚泛函，将其作为反演模型目标函数。论文中简要说明了当前地球物理反演中几种常用的模型目标函数之后，根据聚焦反演成像方法的基本理论，并在大地电磁反演目标函数中引入一个新的稳定泛函一最小支撑泛函，代替传统最小构造或最大平滑准则下的模型目标函数。在构建新的目标函数后，编写了相应的程序并做了模型试验，反演出的结果比常规最大平滑类反演方法得到的地电图像更聚焦、清晰，对电性界面确定的更加准确。
(3)针对二维反演迭代过程中计算观测数据对于参数的灵敏度矩阵占用大量CPU时间的问题，提出利用互换定理、采用有限单元法计算灵敏度矩阵的思路。基本原理是根据源点与接收点可以互换的原理，将源点放到MT的测点处，这样做一次正演计算就可以求得测点上主场对研究区所有单元的偏导数，辅助场偏导数的计算方法也可采取相同的原理。采用这种思路，将计算灵敏度矩阵总共所需要的正演次数减少到了测点数，与差分法相比计算速度有很大提高。在第一次迭代后，引入Broyden公式更新灵敏度矩阵，大大减少了迭代周期。
(4)引入再加权的正则化思想，采用共轭梯度法求解最优化问题。在解目标函数极小值问题时，引入再加权正则化的思想，基本思路是在共轭梯度法的迭代过程中，根据目标的收敛情况更新正则化因子。这样有效地解决了迭代时目标函数发散的问题，保证了反演的稳定性并提高了目标函数的收敛速度。
(5)通过数值模型和实测资料的试验，证明了本论文研究算法的有效性和实用价值。应用编写的程序进行了典型模型的试算，并与传统反演算法的计算结果进行了对比分析；对徐闻地区多条实测MT资料进行聚焦反演成像处理，并与地震资料进行了对比分析，最后与综合地质解释进行了比较，结果表明了聚焦反演的准确性和实用性。
The magetotelluric sounding is an excellent geophysical tool by measuring thesurface electromagnetic response of earth and analyzing the character ofelectromagnetic field to study the rock electricity and character of conformation. Theprinciple of MT is deducing the geoelectrical structures by analysing theelectromagnetic frequency response of earth. MT is used to study the structuralfeature of earth crust and upper mantle for the excellence that needn't the artificialelectromagnetic field and can get the deep information of earth. However, with thewide practical application and in-depth theory research, lots of new problems arepresented and need to be solved. Sponsored by CAS and Sinopec, focusing inversionimages method is presented and advantage of the method is proved. The maincontents and achievements of the thesis are following:
(1) An efficient method named secondary finite element method (SFEM) ispresented to two-dimensional magnetotelluric numerical modeling, which solves forsecondary variations in the field. During deducing the rationle of the new procedurewe divide total field into primary and secondary field. Then we just need to solve thesecondary field equations for the primary field can get easily. The equations of thesecondary field are solved effortless by finite element method when the boundaryconditions are simple. The effect of resolution is analysed when we deal with theresponse of synthetic model by the secondary field and compare with the results usingtotal field FEM.
(2) Usually a maximum smoothness stabilizing functional is used to stabilize theinversion process. The obtained solution is a smooth image by the traditionalstabilizer, which in many practical situations does not describe the examined objectproperly. During narrating the procedure of the approach, we analyse the character ofseveral traditional model object functions firstly, then introduce a new stabilizingfunctional named minimum support stabilizer and the new parametric functional ispresented. The simulated results show the program is right and this approach helps togenerate much more "focused" and resolved images of blocky geoelectrical structures than conventional MT inversion.
(3) To speed up the calculation of the sensitivity matrix for 2-D magnetotelluricinversion using finite elements, the principle of electromagnetic reciprocity is applied.The governing relationship for the Jacobians of the field along strike is obtained bydifferentiating the Helmholtz equation with respect to the conductivity of each regionin the finite element mesh. According to the principle of electromagnetic reciprocity,the roles of sources and receivers are interchangeable. Utilizing reciprocity, the fieldvalues obtained from the original forward problem and for new unit sources imposedat the receivers are then utilized in the calculation of the Jacobian by simplemultiplication and summation with finite-element terms at each rectangle in the mesh.Reciprocity decreases the computational expense of Jacobians to the order of thenumber of stations of interest. After the first inversion, the sensitivities matrix isupdated by the Broyden updating formula, which saves the computational timegreatly.
(4) The approach of Reweighted Conjugate Gradient is based on regularizationtheory and adaptive regularized factor. Conjugate Gradient Algorithm is utilized tosearch for the minimum of the parametric functional. The optimal regularizationparameter is updated on subsequent iteration if the misfit does not decrease fastenough. This procedure insures the convergence of the inversion and enhances thespeed of inversion calculation.
(5) The simulated results of several synthetic data and imaging of field data inXuwen area are presented by focusing inversion, which are higher resolution thanusing conventional inversion method of MT data. All of these indicate the inversionapproach can describe the blocks structures correctly.
(1)当前二维大地电磁有限元正演模拟方法都是直接计算平行于走向的总场值，这种计算思路受网格密度的影响较大，而且在求取低频段的电磁场响应时解的精度偏低。针对这一问题，引入基于计算二次场响应的模拟方法。将非均匀地电结构中传播的大地电磁场分解为一次(电或磁)场与二次场之和，其中一次场为无异常体时的场，二次场为异常体产生的场。在使用有限元法解偏微分方程时，利用二次场偏微分方程与总场偏微分方程的相似性，直接引用总场法计算中的系数矩阵作为二次场方程的合成矩阵。与总场偏微分方程相比较，二次场方程只是在右端多了一个源项积分，因此总场法的有限元系数矩阵可直接用于求二次场的方程中。这种模拟方法受网格密度影响较低，而且较好地解决了总场法中低频场精度不高的缺点。根据上述原理所编制的二次场有限元法MT正演模拟软件，对几个典型模型进行了试算，并与传统总场模拟法进行了比较分析。结果表明直接计算二次场的结果精度更高、更接近真实解，这一方法的提出对提高大地电磁反演精度具有理论和实践意义。
(2)当前MT反演方法在构建目标函数时大都选择基于最大平滑稳定泛函作为模型目标函数，采用这种思路反演出的地电图像都是平滑的、渐变的，不能准确反映岩体电性突变时分界面的具体位置，这给后期的地质解释带来了一定的困难。本文分析了Oleg Portniaguine等人(1999)年提出的聚焦反演成像法，此方法是建立在一种全新的稳定器(如最小梯度支撑泛函等)的基础上，并结合惩罚泛函，将其作为反演模型目标函数。论文中简要说明了当前地球物理反演中几种常用的模型目标函数之后，根据聚焦反演成像方法的基本理论，并在大地电磁反演目标函数中引入一个新的稳定泛函一最小支撑泛函，代替传统最小构造或最大平滑准则下的模型目标函数。在构建新的目标函数后，编写了相应的程序并做了模型试验，反演出的结果比常规最大平滑类反演方法得到的地电图像更聚焦、清晰，对电性界面确定的更加准确。
(3)针对二维反演迭代过程中计算观测数据对于参数的灵敏度矩阵占用大量CPU时间的问题，提出利用互换定理、采用有限单元法计算灵敏度矩阵的思路。基本原理是根据源点与接收点可以互换的原理，将源点放到MT的测点处，这样做一次正演计算就可以求得测点上主场对研究区所有单元的偏导数，辅助场偏导数的计算方法也可采取相同的原理。采用这种思路，将计算灵敏度矩阵总共所需要的正演次数减少到了测点数，与差分法相比计算速度有很大提高。在第一次迭代后，引入Broyden公式更新灵敏度矩阵，大大减少了迭代周期。
(4)引入再加权的正则化思想，采用共轭梯度法求解最优化问题。在解目标函数极小值问题时，引入再加权正则化的思想，基本思路是在共轭梯度法的迭代过程中，根据目标的收敛情况更新正则化因子。这样有效地解决了迭代时目标函数发散的问题，保证了反演的稳定性并提高了目标函数的收敛速度。
(5)通过数值模型和实测资料的试验，证明了本论文研究算法的有效性和实用价值。应用编写的程序进行了典型模型的试算，并与传统反演算法的计算结果进行了对比分析；对徐闻地区多条实测MT资料进行聚焦反演成像处理，并与地震资料进行了对比分析，最后与综合地质解释进行了比较，结果表明了聚焦反演的准确性和实用性。
The magetotelluric sounding is an excellent geophysical tool by measuring thesurface electromagnetic response of earth and analyzing the character ofelectromagnetic field to study the rock electricity and character of conformation. Theprinciple of MT is deducing the geoelectrical structures by analysing theelectromagnetic frequency response of earth. MT is used to study the structuralfeature of earth crust and upper mantle for the excellence that needn't the artificialelectromagnetic field and can get the deep information of earth. However, with thewide practical application and in-depth theory research, lots of new problems arepresented and need to be solved. Sponsored by CAS and Sinopec, focusing inversionimages method is presented and advantage of the method is proved. The maincontents and achievements of the thesis are following:
(1) An efficient method named secondary finite element method (SFEM) ispresented to two-dimensional magnetotelluric numerical modeling, which solves forsecondary variations in the field. During deducing the rationle of the new procedurewe divide total field into primary and secondary field. Then we just need to solve thesecondary field equations for the primary field can get easily. The equations of thesecondary field are solved effortless by finite element method when the boundaryconditions are simple. The effect of resolution is analysed when we deal with theresponse of synthetic model by the secondary field and compare with the results usingtotal field FEM.
(2) Usually a maximum smoothness stabilizing functional is used to stabilize theinversion process. The obtained solution is a smooth image by the traditionalstabilizer, which in many practical situations does not describe the examined objectproperly. During narrating the procedure of the approach, we analyse the character ofseveral traditional model object functions firstly, then introduce a new stabilizingfunctional named minimum support stabilizer and the new parametric functional ispresented. The simulated results show the program is right and this approach helps togenerate much more "focused" and resolved images of blocky geoelectrical structures than conventional MT inversion.
(3) To speed up the calculation of the sensitivity matrix for 2-D magnetotelluricinversion using finite elements, the principle of electromagnetic reciprocity is applied.The governing relationship for the Jacobians of the field along strike is obtained bydifferentiating the Helmholtz equation with respect to the conductivity of each regionin the finite element mesh. According to the principle of electromagnetic reciprocity,the roles of sources and receivers are interchangeable. Utilizing reciprocity, the fieldvalues obtained from the original forward problem and for new unit sources imposedat the receivers are then utilized in the calculation of the Jacobian by simplemultiplication and summation with finite-element terms at each rectangle in the mesh.Reciprocity decreases the computational expense of Jacobians to the order of thenumber of stations of interest. After the first inversion, the sensitivities matrix isupdated by the Broyden updating formula, which saves the computational timegreatly.
(4) The approach of Reweighted Conjugate Gradient is based on regularizationtheory and adaptive regularized factor. Conjugate Gradient Algorithm is utilized tosearch for the minimum of the parametric functional. The optimal regularizationparameter is updated on subsequent iteration if the misfit does not decrease fastenough. This procedure insures the convergence of the inversion and enhances thespeed of inversion calculation.
(5) The simulated results of several synthetic data and imaging of field data inXuwen area are presented by focusing inversion, which are higher resolution thanusing conventional inversion method of MT data. All of these indicate the inversionapproach can describe the blocks structures correctly.
引文
[1] 石应骏，刘国栋，吴广耀等．大地电磁测深法教程．北京：地质出版社，1985
[2] 陈乐寿，刘任，王天生．大地电磁测深资料处理与解释．北京：石油工业出版社，1989
[3] 李金铭，罗延钟．电法勘探新进展．北京：地质出版社，1996
[4] 严良俊，胡文宝，杨绍芳等．电磁勘探方法及其在南方碳酸盐岩地区的应用．石油工业出版社，2001
[5] 王家映．石油电法勘探．北京：石油工业出版社，1993
[6] 魏文博．我国大地电磁测深新进展及瞻望．地球物理学进展，2002，Vol．17(2)：245～254
[7] 安四喜，陈秀儒．大地电磁测深法的现状、作用及发展趋势．石油地球物理勘探，1998，Vol．33(2)：164～168
[8] 朴化荣．电磁测深法原理．地质出版社，1990
[9] 米萨克N．纳比吉安．勘查地球物理电磁法．北京：地质出版社，1992
[10] 陈乐寿，王光锷．构造电法勘探．武汉：中国地质大学出版社，1991
[11] 刘国栋，邓前辉．电磁方法研究与勘探．北京：地震出版社，1993
[12] 王家映．我国大地电磁测深研究新进展．地球物理学报，1997，Vol．40(增刊)：308～316
[13] 文舸一，徐金平，漆一宏．电磁场数值计算的现代方法．河南：河南科学技术出版社，1994
[14] 欧阳联华．交错网格有限差分三维大地电磁场正演计算：[博士学位论文]．上海：同济大学，2003
[15] 谭捍东，余钦范等．大地电磁法三维交错采样有限差分数值模拟．地球物理学报，2003，Vol．46(5)：705～711
[16] 陈乐寿．有限元法在大地电磁正演计算中的应用及改进．石油物探，1981，Vol．20(3)：84～98
[17] 徐世浙．地球物理中的有限单元法．北京：科学出版社，1994
[18] 史明娟，徐世浙等．大地电磁二次函数插值的有限元法正演模拟．地球物理学报，1997，Vol．40(3)：421～430
[19] Zhdanov, M.S.. Continuation of nonstationary electromagnetic fields in geoeleetrical problems. Izv. Akad. Nauk SSSR, Fiz. Zemly, 1981, 12, 60～69
[20] Yuji Mitsuhata, roshihiro Uchida. 3D magnetotelluric modeling using the T-Ω finite-element method. Geophysics, 2004, 69(1): 108Φ119
[21] 陈小斌，赵国泽．基本结构有限元算法及大地电磁测深一维连续介质正演．地球物理学报，2004，Vol．47(3)：535～541
[22] Coggon, J. H.. Electromagnetic and electrical modeling by the finite element method. Geophysics, 1971, 36: 132～155
[23] Heise, W. , Pous, J. . Effects of undetected anisotropy in 2D inversion modelling. Deutsche Geophysikalische Gesellschaft e. V. Elektromagnetische Tiefenforschung. 18 Kolloquium, 2000, 1: 231—237
[24] Xueming Shi, Wang Jiaying. Three dimensional magnetotelluric forward modeling using vector finite element method combined with divergence corrections (VFE++), IAGA WG 1.2 on Electromagnetic Induction in the Earth Available at Proceedings of the 17th Workshop, Hyderabad, India, 2004
[25] Yuji Mitsuhata. 2-D electromagnetic modeling by finite-element method with a dipole source and topography. Geophysics, 2000, 65(2):465—475
[26] Weidelt, P. . Electromagnetic induction in three-dimensional structures. J. Geophys. , 1975, 41: 85—109
[27] Hursan, G. & M.S.Zhdanov. Contraction integral equation method in 3-D electromagnetic modeling. Radio Science, 2002, 37(6):1089
[28] Xiong Z. Modeling of three dimensional structures by the method of system iteration using integral equations. Geophysics, 1992, 57 (12):1556— 1561
[29] Wannamaker, P. E. . Advances in three-dimensional magnetotelluric modeling using integral equations. Geophysics, 1991, 56:1716—1728
[30] Michael S. Zhdanov & Sheng Fang. Quasi-linear approximation in 3-D electromagnetic modeling. Geophysics, 1996, 61(3):646—665
[31] Michael S. Zhdanov, Dmitriev V. I. & Fang Sh. Quasi-analytical approximations and series in electromagnetic modeling. Geophysics, 2000, 65(6) : 1746—1757
[32] Lee,K. H. , Liu,G. & Morrison, H. F. . A new approach to modeling the electromagnetic response of conductive media. Geophysics, 1989, 54:1180—1192
[33] Wannamaker, P. E. , Stodt, J. A. & Rijo, L. . A stable finite-element solution for two-dimensional magnetotelluric modeling. Geop. J. Roy. Astr, 1987, 88:277—296
[34] Kerry Key, Chester Weiss. Adaptive finite-element modeling using unstructured grids:The 2D magnetotelluric example. Geophysics, 2006, 71(6): G291—G299
[35] Badea, E. A. , Everett, M. E. et al. Finite-element analysis of controlled-source electromagnetic induction using Coulomb-gauged potentials. Geophysics, 2001, 66:786-799
[36] D. Livelybrooks, M. Mareschal. Magnetotelluric delineation of the Trillabelle massive sulfide body in Sudbury, Ontario. Geophysics, 1996, 61(4):971—986
[37] F. E. M. (Ted)Lilley. Magnetotelluric tensor decomposition: Part I, Theory for a basic procedure. Geophysics, 1998, 63(6): 1885—1897
[38] F. E. M. Lilley. Magnetotelluric tensor decomposition: Part II, Examples of a basic procedure. Geophysics, 1998, 63(6):1898—1907
[39] F. E. M. Lilley. Magnetotelluric analysis using Mohr circles. Geophysics, 1993, 58(10): 1498-1506
[40] McNeice, G.W. & A.G. Jones. Multisite, multifrequency tensor decomposition of magnetotelluric data. Geophysics, 2001, 66:158～173
[41] Silvester. P, Haslam. C.R.S. Magnetotelluric modelling by finite element method. Geophys. Prosp. 1972, 20:872～891
[42] Farquharson, C.G. & Oldenburg, D.W.. Approximate sensitivities for the electromagnetic inverse problem. Geophys. J. Internat, 1996, 127:235～252
[43] OLDENBURG D. W., MCGILLIVRAY P. R. & ELLIS R. G.. Generalized subspace methods for large-scale inverse problems. Geophys. J. Int, 1993, 114(1):12-20
[44] Portniaguine, O. & Zhdanov, M.S.. Focusing geophysical inversion images. Geophysics, 1999, 64:874～887
[45] C. deGroot-Hedlin & S. Constable. Occam's inversion to generate smooth, two～dimensional models from magnetotelluric data. Geophysics, 1990, 55(12):1613～1624
[46] Constable, S. C., Parker, R. L. and Constable, C. G.. Occam's inversion: A practical algorithm for generating smooth models from electromagnetic sounding data. Geophysics, 1987, 52:289～300
[47] Smith, J.T. & J.R. Booker. Rapid inversion of two- and three-dimensional magnetotelluric data. J. Geophys. Res., 1991, 96:3905～3922
[48] William Rodi, Randall L. Mackie. Nonlinear conjugate gradients algorithm for 2-D magnetotelluric inversion. Geophysics, 2001, 66(1):174～187
[49] Weerachai Siripunvaraporn & Gary Egbert. An efficient data-subspace inversion method for 2-D magnetotelluric data. Geophysics, 2000, 65(3):791～803
[50] Zhou, Q., Becker, A. & Morrison, H.F.. Audiofrequency electromagnetic tomography in 2-D. Geophysics, 1993, 58:482～495
[51] Garcia, X., Ledo, J. & Queralt, P.. 2D inversion of 3D magnetotelluric data: The Kayabe dataset. Earth Planets Space, 1999, 51:1135～1143
[52] Yuji Mitsuhata, Uchida T. & Amano H. 2.5-D inversion of frequency-domain electromagnetic data generated by a grounded-wire source. Geophysics, 2002, 67(6):1753～1768
[53] Eaton, P.A.. 3D Electromagnetic inversion using integral equations. Geophys. Prosp., 1989, 37:407～426
[54] Ganquan Xie, Jianhua Li, Majer, Ernest, et al. 3-D electromagnetic modeling and nonlinear inversion. Geophysics, 2000, 65(3):804～822
[55] Newman, G.A., S. Recher, B. Tezkan, & F.M. Neubauer. 3D inversion of a scalar radio magnetotelluric field data set. Geophysics, 2003, 68:791～802
[56] 欧东新．块状结构大地电磁综合反演方法研究：[博士学位论文]．上海：同济大学，2005
[57] 沈金松．用交错网格有限差分法计算三维频率域电磁响应．地球物理学报，2003，Vol．46(2)：281～288
[58] 于鹏，王家林，吴健生．有限差分法大地电磁多参数偏移成像．地球物理学报，2001， Vol．44(4)：552～562
[59] 谭捍东，余钦范，John Booker等．大地电磁法三维快速松弛反演．地球物理学报， 2003，Vol．46(6)：850～854
[60] 张翔，胡文宝．带地形的大地电磁测深联合二维反演．石油地球物理勘探，1999，Vol．34 (2)：190～196
[61] 王若，王妙月，底青云．二维大地电磁数据的整体反演．地球物理学进展，2001，Vol．16(4)：54～60
[62] 胡祖志，胡祥云．大地电磁二维反演方法对比研究．煤田地质与勘探，2005，Vol．33(1)：64～68
[63] Mackie, R. L. &Madden, T. R.. Three-dimensional magnetotelluric inversion using conjugate gradients. Geophys. J. Internat., 1993, 115: 215～229
[64] Madden, T. R. & Mackie, R. L.. Three-dimensional magnetotelluric modelling and inversion. Proc. IEEE, 1989, 77(2): 318～332
[65] 戴世坤，徐世浙．MT二维和三维连续介质快速反演．石油地球物理勘探，1997，Vol．32(3)：305～317
[66] 杨辉，王家林，吴健生等．大地电磁与地震资料仿真退火约束反演．地球物理学报，2002，Vol．45(5)：723～734
[67] 严良俊，胡文宝．大地电磁测深资料的二次函数逼近非线性反演．地球物理学报，2004，Vol．47(5)：935～940
[68] 胡祖志，胡祥云，何展翔．大地电磁非线性共轭梯度拟三维反演．地球物理学报，2006，Vol．49(4)：1226～1234
[69] Smith, J. T, &Booker, J.R.. Magnetotelluric inversion for minimum structure. Geophysics, 1988, 53: 1565～1576
[70] Santos, F. & Pous, J. et al. Magnetotelhric survey of the electrical conductivity of the crust across the Ossa Morena Zone and South Portuguese zone suture. Tectonophysics, 1999, 313: 449～462
[71] Zhdanov, M.S. & Traynin, P.. Migration versus inversion in electromagnetic imaging technique. J. Oeomag. Geoelec., 1997, 49: 1415～1437
[72] Berdichevsky, M. N., V. I. Dmitriev & E.E. Pozdnjakova. On two-dimensional interpretation of magnetotelluric soundings. Geophysical Journal International, 1998, 133: 585～606
[73] Christiansen A V, Auken E. Optimizing a layered and laterally constrained 2D inversion of resistivity data using Broyden' s update and ID derivatives. J. Appl. Geophys., 2004, 56: 247～261
[74] Hursan, G., & M. S. Zhdanov. Rapid 3-D magnetotelluric inversion. 2001, Proceedings of 2001 CEMI Annual Meeting
[75] hu, X., Unsworth, M. & Booker, J.. Rapid relaxation inversion of CSAMT data. Geophys. J. Internat., 1999, 138: 381～392
[76] L. B. Pedersenl & M. Engelsl. Routine 2D inversion of magnetotelluric data using the determinant of the impedance tensor. Geophysics, 2005, 70(2): G33～G41
[77] Takasugi S., Keisaku T., Noriaki K. & Shigeki, M.. High spatial resolution of the resistivity structure revealed by a dense network MT measurement-a case study in the Minamikayabe area, Hokkaido, Japan. J. Geomag. Geoelectr., 1992, 44: 289～308
[78] Eldad Haber U. Ascher & D. Oldenburg. Inversion of 3D electromagnetic data in frequency and time domain using an inexact all-at-once approach. Geophysics, 2004, 69(5): 1216～1228
[79] Madden, T.R.. Transmission systems and network analogies to geophysical forward and inversion problem: ONR Technical Report, 1972, 72～73
[80] Oldenburg, D. W., Eliss R G. Inversion of geophysical data using approximate inverse mapping. Geophys. J. Int., 1991, 105: 325～353
[81] Zhdanov, M.S.. Geophysical inverse theory and regularization problems. Elsevier, Amsterdam-New York-Tokyo, 2002
[82] Zhdanov, M.S., Ellis., R. &S. Mukherjee. Regularized focusing inversion of 3-D gravity tensor data. Proceedings of 2003 CEMI Annual Meeting, 2003, 57～84
[83] Zhdanov, M. S., Ellis., R. & S. Mukherjee. Three-D regularized focusing inversion of gravity gradient tensor data. Geophysics, 2004, 69: 925～937
[84] Portniaguine O. & M. S. Zhdanov. 3-D magnetic inversion with data compression and image focusing. Geophysics, 2002, 67(5): 1532～1541
[85] Salah, A. M. Multidimensional finite difference electromagnetic modeling and inversion based on the balance method: [Ph.D, thesis]. University of Utah. 2003
[86] de Groot-Hedlin C, Constable S. Inversion of magnetotelluric data for 2D structure with sharp resistivity contrasts. Geophysics, 2004, 69(1): 78～86
[87] 杨长福，徐世浙．国外大地电磁研究现状．物探与化探，2005，Vol．29(3)：243～247
[88] Oleg Portniaguine, Michael S. Zhdanov. New development of the parameter estimation method for 3-D electromagnetic inversion. 1996, SEG Technical Program Expanded Abstracts 15, 974～977
[89] 陈小斌．大地电磁正反演新算法研究及资料处理与解释的可视化集成系统开发：[博士学位论文]．北京：中国地震局地质研究所，2003
[90] 李学民．由大地电磁数据同时反演电阻率和磁化率参数的方法研究[博士学位论文]．成都：成都理工大学，2005
[91] Druskin, V. & Knizhnerman, L.. Spectral approach to solving three-dimensional Maxwell's equations in the time and frequency domains. Radio Science, 1994, 29: 937～953
[92] Hohmann, G.W.. Three-dimensional induced polarization and electromagneticmodeling. Geophysics, 1975, 40: 309～324
[93] Chan J., Haber E. & Oldenburg D.. Three-dimensional numerical modeling and inversion of magnetometric resistivity data. Geophys. J. Int., 2002, 149: 679～697
[94] Gunderson B. M., Newman G. A. & Hohmann, G.W.. Three-dimensional transient electromagnetic responses for a grounded source. Geophysics, 1986, 51:2117～2130
[95] 黄俊革，阮百尧，鲍光淑．三维地电断面激发极化法有限元数值模拟．地球科学，2003，Vol．28(3)：323～326
[96] Pedersen, L. B. & Rasmussen, T. M.. Inversion of magnetotelluric data: A non-linear least-squares approach. Geophys. Prosp., 1989, 37:669～695
[97] Xiaobo Li, Behrooz Oskooi & Laust B. Pedersen. Inversion of controlled-source tensor magnetotelluric data for a layered earth with azimuthal anisotropy. Geophysics, 2000, 65(2):452～464
[98] YANG Changfu, LIN Changyou & SUN Chong-chi, et al. Inversions for MT data in 2D symmetrical anisotropic media. ACTA SEISMOLOGICA SINICA, 2005, 18(3):361～367
[99] Haber E. and Oldenburg, D.. Joint inversion a structural approach. Inverse Problems, 1997, 13:63～77
[100] Maxwell A. Meju. Joint inversion of TEM and distorted MT soundings: Some effective practical considerations. Geophysics, 1996, 61(1):56～65
[101] Michael S. Zhdanov et al. Localized S-inversion of time-domain electromagnetic data. Geophysics, 2002, 67(4):1115～1125
[102] Vozoff, K.. The magnetotelluric method in the exploration of sedimentary basins. Geophysics, 1972, 37:98～141
[103] Wannamaker, P.E., G.W. Hohmann, & S.H. Ward. Magnetotelluric responses of three-dimensional bodies in layered earths. Geophysics, 1984, 49:1517～1534
[104] Pous, J., Ledo, J.J. & Marcuello, A., et al. On the Resolution of the Darai Limestones by Two-Dimensional MT Forward Modeling. Journal of Geomagnetism and Geoelectricity, 1997, 49:817～825
[105] Benjamin S. White & Werner E. Kohler. Random scattering in magnetotellurics. Geophysics, 2001, 66(1):188～204
[106] Larsen, J.C., Mackie, R.L. &Manzella, A., etal. Robust Smooth magnetotelluric Transfer Functions. Geophys. J. Int., 1996, 124:801～819
[107] Sasaki, Y.. 3-D inversion of electrical and electromagnetic data on PC. Proc. of 2rd International Symposium on Three-Dimensional Electromagnetics, 1999, 128～131
[108] Zhang, J., Mackie, R.L. & Madden, T. 3-D resistivity forward modeling and inversion using conjugate gradients. Geophysics, 1995, 60:1313～1325
[109] Zhdanov, M.S. & Hursan, G.. 3-D electromagnetic inversion based on quasi-analytical approximation. Inverse Problems, 2000, 16:1297～1322
[110] Zhdanov, M.S. & Fang, S.. 3-D quasi-linear electromagnetic inversion. Radio Sci., 1996, 31:741～754
[111] 杨文采．地球物理反演的理论与方法．北京：地质出版社，1997
[112] 王家映．地球物理反演理论．北京：高等教育出版社，2002
[113] 姚姚．地球物理反演基本理论与应用方法．武汉：中国地质大学出版社，2002
[114] Wu, F.T.. The inverse problem of magnetotelluric sounding. Geophysics, 1968, 33, 972～979
[115] Eaton P. A. & Hohmann G. W.. A rapid inversion technique for transient electromagnetic soundings. Phys. Earth Planet Inter., 1989, 53: 394～404
[116] J. C. Larsen. A new technique for layered earth magnetotelluric inversion. Geophysics, 1981, 46(9): 1247～1257
[117] Lee, K. H. & Xie, G.. A new approach to imaging with low frequency electromagnetic fields. Geophysics, 1993, 58: 780～796
[118] Laust B. Pedersen & Mehran Gharibi. Automatic 1-D inversion of magnetotelluric data: Finding the simplest possible model that fits the data. Geophysics, 2000, 65(3): 773～782
[119] 吴小平，徐果明．利用共轭梯度方法电阻率三维反演研究．地球物理学报，2000，Vol．43(3)：420～427
[120] Jacobs, D. A. H.. A generalization of the conjugate-gradient method to solve complex system. IMA J. Numerical Analysis, 1986, 6: 447～452
[121] Newman, G. A. & Alumbaugh, D. L.. Three-dimensional magnetotelluric inversion using non-linear conjugate gradients. Geophys. J. Int., 2000, 140: 410～424
[122] Zhdanov, M. S., Fang, S. and G. Hursan. Electromagnetic inversion using quasi-linear approximation: Geophysics, 2000, 65: 1501～1513
[123] Tartaras, E., Zhdanov, M. S. &Wada, K., et al. Fast imaging of TDEM data based on s-inversion. J. Appl. Geophys., 2000, 43: 115～132
[124] Oldenburg, D. W. & Y. Li. Inversion of induced polarization data. Geophysics, 1994, 59(9): 1327～1341
[125] Oristaglio, M., Wang, r. & Hohmann, G., etal. Resistivity imaging of transient electromagnetic data by conjugate-gradient method: 63rd Ann. Internat. Mtg., Soc. Expl. Geophys., 1993, Expanded Abstracts: 347～350
[126] Torres-Verdin, C. & Habashy, T. M.. Rapid 2.5-D forward modeling and inversion via a new nonlinear scattering approximation. Radio Sci., 1994, 29: 1051～1079
[127] Patricia, P. L. Fast and stable two-dimensional inversion of magnetotelluric data: [Ph.D, thesis]. The University of Utah. 1997
[128] Xinyou, Lu. Inversion of controlled-source audio-frequency magnetotelluric data: [Ph.D. thesis]. University of Washington, 1999
[129] Gabor Hursan. Rapic frequency domaion three-dimensional electromagnetic forward modeling and inversion: [Ph.D, thesis]. The University of Utah. 2001
[130] Zhang, Ge. Multidimensional electromagnetic inversion using the finite functions method: [Ph.D, thesis]. The University of Utah. 2004
[131] Barnett, C.T.. Simple inversion of time-domain electromagnetic data. Geophysics. 1984. 49: 925～933
[132] de Lugao P P, Wannamaker P E. Calculating the two dimensional magnetotelluric Jacobian in finite elements using reciprocity. Geophysical Journal International, 1996, 127:806～810
[133] McGillivray, P.R., Oldenburg, D.W. and Ellis, R.G.. Calculation of sensitivities for the frequency domain electromagnetic induction problem. Geophys. J. Internat., 1994, 116:1～4
[134] 何光渝，高永利．Visual Fortran常用数值算法集．北京：科学出版社，2002
[135] 谭浩强．Fortran程序设计．北京：清华大学出版社，1998
[136] Kevin L. Mickus. Case History:Magnetotelluric observations in the western Ouachita Mountains, southeastern Oklahoma. Geophysics, 1999, 64(6):1680～1688
[137] N.B. Boschetto, G. W. Hohmann. Controlled-source audiofrequency magnetotelluric responses of three-dimensional bodies. Geophysics, 1991, 56(2):255～264
[138] Pous, J., Ledo, J.J. & Queralt, P., et al. Constaintson the deep structure of the Pyrennes from new magnetotelluric data. Revista de la Sociedad Geologica de Espana, 1997, 8(4):395～400
[139] Lines, L.R. & S. Treitel. Tutorial: A review of least-squares inversion and its application to geophysical problems. Geophysical Prospecting, 1984, 32:159～186
[140] Heise, W., Pous, J.. Effects of the anisotropy on two dimensional inversion procedure. Geophysical Journal International, 2001, 147(3):610～622
[141] P.E. Wannamaker & P.M. Wright. Magnetotelluric transect of Long Valley caldera: Resistivity cross-section, structural implications, and the limits of a 2-D analysis. Geophysics, 1991, 56(7):926～940
[142] Hursan, G.. Storage reduction and fast matrix multiplication for integral-based geophysical problems. Proceedings of 2001 CEMI Annual Meeting, 2001
[143] Smith T, HoverstenM, GasperikovaE, et al. Sharp boundary inversion of 2D magnetotelluric data. Geophysical Prospecting, 1999, 47(2):469～486
[144] Wannamaker. P.E, Stodt. J.A & Rijo. L. Two-dimensional topographic responses in magnetotellurics modeled using finite elements. Geophysics, 1986, 51(11):2131～2144
[145] Kazunobu Yamanel & Kazumi Ohsato. Three-dimensional magnetotelluric investigation in Kakkonda geothermal area, Japan. Proceedings World Geothermal Congress 2000, Kyushu-Tohoku, Japan:1965～1968
[146] Newman G.A. & Alumbaugh, D.L.. Three-dimensional massively parallel electromagnetic inversion—I, Theory. Grophys. J. Int., 1997, 128:345～354
[147] Tripp, A.C. & Hohmann, G.W.. Three-dimensional electromagnetic crosswell inversion:IEEE Trans. on Geoscience and Remote Sensing, 1993, 31:121～126
[148] Yutaka Sasaki. Two-dimensional joint inversion of magnetotelluric and dipole-dipole resistivity data. Geophysics, 1989, 54(2): 254～262
[149] Zhdanov, M. S., Wannamaker, P. E..Three-dimensional electromagnetics. Elsevier, 2002, 153～171
[150] Zhdanov, M.S. & Frenkel, M.A.. The solution of the inverse problems on the basis of the analytical continuation of the transient electromagnetic field in reverse time. J. Geomag. Geoelectr., 1983, 35: 747～765
[151] Zhdanov, M. S. & N. G. Golubev. Use of the finite functions method for the solution of the 2D inverse problem. J. Geomag. Geoelectr., 1983, 35: 707～722
[152] Michael S. Zhdanov et al. Underground imaging by frequency-domain electromagnetic migration. Geophysics, 1996, 61(3): 666～682
[153] Paul, A. B. Electromagnetic imaging of active fault zones: [Ph. D, thesis]. University of Washington, 2002
[154] Umberto Spagnolini. Time-domain estimation of MT impedance tensor. Geophysics, 1994. 59(5): 712～721
[155] 王家林，吴健生，于鹏等．徐闻-纪家高精度重力和MT测量综合研究成果报告．同济大学，2004
[2] 陈乐寿，刘任，王天生．大地电磁测深资料处理与解释．北京：石油工业出版社，1989
[3] 李金铭，罗延钟．电法勘探新进展．北京：地质出版社，1996
[4] 严良俊，胡文宝，杨绍芳等．电磁勘探方法及其在南方碳酸盐岩地区的应用．石油工业出版社，2001
[5] 王家映．石油电法勘探．北京：石油工业出版社，1993
[6] 魏文博．我国大地电磁测深新进展及瞻望．地球物理学进展，2002，Vol．17(2)：245～254
[7] 安四喜，陈秀儒．大地电磁测深法的现状、作用及发展趋势．石油地球物理勘探，1998，Vol．33(2)：164～168
[8] 朴化荣．电磁测深法原理．地质出版社，1990
[9] 米萨克N．纳比吉安．勘查地球物理电磁法．北京：地质出版社，1992
[10] 陈乐寿，王光锷．构造电法勘探．武汉：中国地质大学出版社，1991
[11] 刘国栋，邓前辉．电磁方法研究与勘探．北京：地震出版社，1993
[12] 王家映．我国大地电磁测深研究新进展．地球物理学报，1997，Vol．40(增刊)：308～316
[13] 文舸一，徐金平，漆一宏．电磁场数值计算的现代方法．河南：河南科学技术出版社，1994
[14] 欧阳联华．交错网格有限差分三维大地电磁场正演计算：[博士学位论文]．上海：同济大学，2003
[15] 谭捍东，余钦范等．大地电磁法三维交错采样有限差分数值模拟．地球物理学报，2003，Vol．46(5)：705～711
[16] 陈乐寿．有限元法在大地电磁正演计算中的应用及改进．石油物探，1981，Vol．20(3)：84～98
[17] 徐世浙．地球物理中的有限单元法．北京：科学出版社，1994
[18] 史明娟，徐世浙等．大地电磁二次函数插值的有限元法正演模拟．地球物理学报，1997，Vol．40(3)：421～430
[19] Zhdanov, M.S.. Continuation of nonstationary electromagnetic fields in geoeleetrical problems. Izv. Akad. Nauk SSSR, Fiz. Zemly, 1981, 12, 60～69
[20] Yuji Mitsuhata, roshihiro Uchida. 3D magnetotelluric modeling using the T-Ω finite-element method. Geophysics, 2004, 69(1): 108Φ119
[21] 陈小斌，赵国泽．基本结构有限元算法及大地电磁测深一维连续介质正演．地球物理学报，2004，Vol．47(3)：535～541
[22] Coggon, J. H.. Electromagnetic and electrical modeling by the finite element method. Geophysics, 1971, 36: 132～155
[23] Heise, W. , Pous, J. . Effects of undetected anisotropy in 2D inversion modelling. Deutsche Geophysikalische Gesellschaft e. V. Elektromagnetische Tiefenforschung. 18 Kolloquium, 2000, 1: 231—237
[24] Xueming Shi, Wang Jiaying. Three dimensional magnetotelluric forward modeling using vector finite element method combined with divergence corrections (VFE++), IAGA WG 1.2 on Electromagnetic Induction in the Earth Available at Proceedings of the 17th Workshop, Hyderabad, India, 2004
[25] Yuji Mitsuhata. 2-D electromagnetic modeling by finite-element method with a dipole source and topography. Geophysics, 2000, 65(2):465—475
[26] Weidelt, P. . Electromagnetic induction in three-dimensional structures. J. Geophys. , 1975, 41: 85—109
[27] Hursan, G. & M.S.Zhdanov. Contraction integral equation method in 3-D electromagnetic modeling. Radio Science, 2002, 37(6):1089
[28] Xiong Z. Modeling of three dimensional structures by the method of system iteration using integral equations. Geophysics, 1992, 57 (12):1556— 1561
[29] Wannamaker, P. E. . Advances in three-dimensional magnetotelluric modeling using integral equations. Geophysics, 1991, 56:1716—1728
[30] Michael S. Zhdanov & Sheng Fang. Quasi-linear approximation in 3-D electromagnetic modeling. Geophysics, 1996, 61(3):646—665
[31] Michael S. Zhdanov, Dmitriev V. I. & Fang Sh. Quasi-analytical approximations and series in electromagnetic modeling. Geophysics, 2000, 65(6) : 1746—1757
[32] Lee,K. H. , Liu,G. & Morrison, H. F. . A new approach to modeling the electromagnetic response of conductive media. Geophysics, 1989, 54:1180—1192
[33] Wannamaker, P. E. , Stodt, J. A. & Rijo, L. . A stable finite-element solution for two-dimensional magnetotelluric modeling. Geop. J. Roy. Astr, 1987, 88:277—296
[34] Kerry Key, Chester Weiss. Adaptive finite-element modeling using unstructured grids:The 2D magnetotelluric example. Geophysics, 2006, 71(6): G291—G299
[35] Badea, E. A. , Everett, M. E. et al. Finite-element analysis of controlled-source electromagnetic induction using Coulomb-gauged potentials. Geophysics, 2001, 66:786-799
[36] D. Livelybrooks, M. Mareschal. Magnetotelluric delineation of the Trillabelle massive sulfide body in Sudbury, Ontario. Geophysics, 1996, 61(4):971—986
[37] F. E. M. (Ted)Lilley. Magnetotelluric tensor decomposition: Part I, Theory for a basic procedure. Geophysics, 1998, 63(6): 1885—1897
[38] F. E. M. Lilley. Magnetotelluric tensor decomposition: Part II, Examples of a basic procedure. Geophysics, 1998, 63(6):1898—1907
[39] F. E. M. Lilley. Magnetotelluric analysis using Mohr circles. Geophysics, 1993, 58(10): 1498-1506
[40] McNeice, G.W. & A.G. Jones. Multisite, multifrequency tensor decomposition of magnetotelluric data. Geophysics, 2001, 66:158～173
[41] Silvester. P, Haslam. C.R.S. Magnetotelluric modelling by finite element method. Geophys. Prosp. 1972, 20:872～891
[42] Farquharson, C.G. & Oldenburg, D.W.. Approximate sensitivities for the electromagnetic inverse problem. Geophys. J. Internat, 1996, 127:235～252
[43] OLDENBURG D. W., MCGILLIVRAY P. R. & ELLIS R. G.. Generalized subspace methods for large-scale inverse problems. Geophys. J. Int, 1993, 114(1):12-20
[44] Portniaguine, O. & Zhdanov, M.S.. Focusing geophysical inversion images. Geophysics, 1999, 64:874～887
[45] C. deGroot-Hedlin & S. Constable. Occam's inversion to generate smooth, two～dimensional models from magnetotelluric data. Geophysics, 1990, 55(12):1613～1624
[46] Constable, S. C., Parker, R. L. and Constable, C. G.. Occam's inversion: A practical algorithm for generating smooth models from electromagnetic sounding data. Geophysics, 1987, 52:289～300
[47] Smith, J.T. & J.R. Booker. Rapid inversion of two- and three-dimensional magnetotelluric data. J. Geophys. Res., 1991, 96:3905～3922
[48] William Rodi, Randall L. Mackie. Nonlinear conjugate gradients algorithm for 2-D magnetotelluric inversion. Geophysics, 2001, 66(1):174～187
[49] Weerachai Siripunvaraporn & Gary Egbert. An efficient data-subspace inversion method for 2-D magnetotelluric data. Geophysics, 2000, 65(3):791～803
[50] Zhou, Q., Becker, A. & Morrison, H.F.. Audiofrequency electromagnetic tomography in 2-D. Geophysics, 1993, 58:482～495
[51] Garcia, X., Ledo, J. & Queralt, P.. 2D inversion of 3D magnetotelluric data: The Kayabe dataset. Earth Planets Space, 1999, 51:1135～1143
[52] Yuji Mitsuhata, Uchida T. & Amano H. 2.5-D inversion of frequency-domain electromagnetic data generated by a grounded-wire source. Geophysics, 2002, 67(6):1753～1768
[53] Eaton, P.A.. 3D Electromagnetic inversion using integral equations. Geophys. Prosp., 1989, 37:407～426
[54] Ganquan Xie, Jianhua Li, Majer, Ernest, et al. 3-D electromagnetic modeling and nonlinear inversion. Geophysics, 2000, 65(3):804～822
[55] Newman, G.A., S. Recher, B. Tezkan, & F.M. Neubauer. 3D inversion of a scalar radio magnetotelluric field data set. Geophysics, 2003, 68:791～802
[56] 欧东新．块状结构大地电磁综合反演方法研究：[博士学位论文]．上海：同济大学，2005
[57] 沈金松．用交错网格有限差分法计算三维频率域电磁响应．地球物理学报，2003，Vol．46(2)：281～288
[58] 于鹏，王家林，吴健生．有限差分法大地电磁多参数偏移成像．地球物理学报，2001， Vol．44(4)：552～562
[59] 谭捍东，余钦范，John Booker等．大地电磁法三维快速松弛反演．地球物理学报， 2003，Vol．46(6)：850～854
[60] 张翔，胡文宝．带地形的大地电磁测深联合二维反演．石油地球物理勘探，1999，Vol．34 (2)：190～196
[61] 王若，王妙月，底青云．二维大地电磁数据的整体反演．地球物理学进展，2001，Vol．16(4)：54～60
[62] 胡祖志，胡祥云．大地电磁二维反演方法对比研究．煤田地质与勘探，2005，Vol．33(1)：64～68
[63] Mackie, R. L. &Madden, T. R.. Three-dimensional magnetotelluric inversion using conjugate gradients. Geophys. J. Internat., 1993, 115: 215～229
[64] Madden, T. R. & Mackie, R. L.. Three-dimensional magnetotelluric modelling and inversion. Proc. IEEE, 1989, 77(2): 318～332
[65] 戴世坤，徐世浙．MT二维和三维连续介质快速反演．石油地球物理勘探，1997，Vol．32(3)：305～317
[66] 杨辉，王家林，吴健生等．大地电磁与地震资料仿真退火约束反演．地球物理学报，2002，Vol．45(5)：723～734
[67] 严良俊，胡文宝．大地电磁测深资料的二次函数逼近非线性反演．地球物理学报，2004，Vol．47(5)：935～940
[68] 胡祖志，胡祥云，何展翔．大地电磁非线性共轭梯度拟三维反演．地球物理学报，2006，Vol．49(4)：1226～1234
[69] Smith, J. T, &Booker, J.R.. Magnetotelluric inversion for minimum structure. Geophysics, 1988, 53: 1565～1576
[70] Santos, F. & Pous, J. et al. Magnetotelhric survey of the electrical conductivity of the crust across the Ossa Morena Zone and South Portuguese zone suture. Tectonophysics, 1999, 313: 449～462
[71] Zhdanov, M.S. & Traynin, P.. Migration versus inversion in electromagnetic imaging technique. J. Oeomag. Geoelec., 1997, 49: 1415～1437
[72] Berdichevsky, M. N., V. I. Dmitriev & E.E. Pozdnjakova. On two-dimensional interpretation of magnetotelluric soundings. Geophysical Journal International, 1998, 133: 585～606
[73] Christiansen A V, Auken E. Optimizing a layered and laterally constrained 2D inversion of resistivity data using Broyden' s update and ID derivatives. J. Appl. Geophys., 2004, 56: 247～261
[74] Hursan, G., & M. S. Zhdanov. Rapid 3-D magnetotelluric inversion. 2001, Proceedings of 2001 CEMI Annual Meeting
[75] hu, X., Unsworth, M. & Booker, J.. Rapid relaxation inversion of CSAMT data. Geophys. J. Internat., 1999, 138: 381～392
[76] L. B. Pedersenl & M. Engelsl. Routine 2D inversion of magnetotelluric data using the determinant of the impedance tensor. Geophysics, 2005, 70(2): G33～G41
[77] Takasugi S., Keisaku T., Noriaki K. & Shigeki, M.. High spatial resolution of the resistivity structure revealed by a dense network MT measurement-a case study in the Minamikayabe area, Hokkaido, Japan. J. Geomag. Geoelectr., 1992, 44: 289～308
[78] Eldad Haber U. Ascher & D. Oldenburg. Inversion of 3D electromagnetic data in frequency and time domain using an inexact all-at-once approach. Geophysics, 2004, 69(5): 1216～1228
[79] Madden, T.R.. Transmission systems and network analogies to geophysical forward and inversion problem: ONR Technical Report, 1972, 72～73
[80] Oldenburg, D. W., Eliss R G. Inversion of geophysical data using approximate inverse mapping. Geophys. J. Int., 1991, 105: 325～353
[81] Zhdanov, M.S.. Geophysical inverse theory and regularization problems. Elsevier, Amsterdam-New York-Tokyo, 2002
[82] Zhdanov, M.S., Ellis., R. &S. Mukherjee. Regularized focusing inversion of 3-D gravity tensor data. Proceedings of 2003 CEMI Annual Meeting, 2003, 57～84
[83] Zhdanov, M. S., Ellis., R. & S. Mukherjee. Three-D regularized focusing inversion of gravity gradient tensor data. Geophysics, 2004, 69: 925～937
[84] Portniaguine O. & M. S. Zhdanov. 3-D magnetic inversion with data compression and image focusing. Geophysics, 2002, 67(5): 1532～1541
[85] Salah, A. M. Multidimensional finite difference electromagnetic modeling and inversion based on the balance method: [Ph.D, thesis]. University of Utah. 2003
[86] de Groot-Hedlin C, Constable S. Inversion of magnetotelluric data for 2D structure with sharp resistivity contrasts. Geophysics, 2004, 69(1): 78～86
[87] 杨长福，徐世浙．国外大地电磁研究现状．物探与化探，2005，Vol．29(3)：243～247
[88] Oleg Portniaguine, Michael S. Zhdanov. New development of the parameter estimation method for 3-D electromagnetic inversion. 1996, SEG Technical Program Expanded Abstracts 15, 974～977
[89] 陈小斌．大地电磁正反演新算法研究及资料处理与解释的可视化集成系统开发：[博士学位论文]．北京：中国地震局地质研究所，2003
[90] 李学民．由大地电磁数据同时反演电阻率和磁化率参数的方法研究[博士学位论文]．成都：成都理工大学，2005
[91] Druskin, V. & Knizhnerman, L.. Spectral approach to solving three-dimensional Maxwell's equations in the time and frequency domains. Radio Science, 1994, 29: 937～953
[92] Hohmann, G.W.. Three-dimensional induced polarization and electromagneticmodeling. Geophysics, 1975, 40: 309～324
[93] Chan J., Haber E. & Oldenburg D.. Three-dimensional numerical modeling and inversion of magnetometric resistivity data. Geophys. J. Int., 2002, 149: 679～697
[94] Gunderson B. M., Newman G. A. & Hohmann, G.W.. Three-dimensional transient electromagnetic responses for a grounded source. Geophysics, 1986, 51:2117～2130
[95] 黄俊革，阮百尧，鲍光淑．三维地电断面激发极化法有限元数值模拟．地球科学，2003，Vol．28(3)：323～326
[96] Pedersen, L. B. & Rasmussen, T. M.. Inversion of magnetotelluric data: A non-linear least-squares approach. Geophys. Prosp., 1989, 37:669～695
[97] Xiaobo Li, Behrooz Oskooi & Laust B. Pedersen. Inversion of controlled-source tensor magnetotelluric data for a layered earth with azimuthal anisotropy. Geophysics, 2000, 65(2):452～464
[98] YANG Changfu, LIN Changyou & SUN Chong-chi, et al. Inversions for MT data in 2D symmetrical anisotropic media. ACTA SEISMOLOGICA SINICA, 2005, 18(3):361～367
[99] Haber E. and Oldenburg, D.. Joint inversion a structural approach. Inverse Problems, 1997, 13:63～77
[100] Maxwell A. Meju. Joint inversion of TEM and distorted MT soundings: Some effective practical considerations. Geophysics, 1996, 61(1):56～65
[101] Michael S. Zhdanov et al. Localized S-inversion of time-domain electromagnetic data. Geophysics, 2002, 67(4):1115～1125
[102] Vozoff, K.. The magnetotelluric method in the exploration of sedimentary basins. Geophysics, 1972, 37:98～141
[103] Wannamaker, P.E., G.W. Hohmann, & S.H. Ward. Magnetotelluric responses of three-dimensional bodies in layered earths. Geophysics, 1984, 49:1517～1534
[104] Pous, J., Ledo, J.J. & Marcuello, A., et al. On the Resolution of the Darai Limestones by Two-Dimensional MT Forward Modeling. Journal of Geomagnetism and Geoelectricity, 1997, 49:817～825
[105] Benjamin S. White & Werner E. Kohler. Random scattering in magnetotellurics. Geophysics, 2001, 66(1):188～204
[106] Larsen, J.C., Mackie, R.L. &Manzella, A., etal. Robust Smooth magnetotelluric Transfer Functions. Geophys. J. Int., 1996, 124:801～819
[107] Sasaki, Y.. 3-D inversion of electrical and electromagnetic data on PC. Proc. of 2rd International Symposium on Three-Dimensional Electromagnetics, 1999, 128～131
[108] Zhang, J., Mackie, R.L. & Madden, T. 3-D resistivity forward modeling and inversion using conjugate gradients. Geophysics, 1995, 60:1313～1325
[109] Zhdanov, M.S. & Hursan, G.. 3-D electromagnetic inversion based on quasi-analytical approximation. Inverse Problems, 2000, 16:1297～1322
[110] Zhdanov, M.S. & Fang, S.. 3-D quasi-linear electromagnetic inversion. Radio Sci., 1996, 31:741～754
[111] 杨文采．地球物理反演的理论与方法．北京：地质出版社，1997
[112] 王家映．地球物理反演理论．北京：高等教育出版社，2002
[113] 姚姚．地球物理反演基本理论与应用方法．武汉：中国地质大学出版社，2002
[114] Wu, F.T.. The inverse problem of magnetotelluric sounding. Geophysics, 1968, 33, 972～979
[115] Eaton P. A. & Hohmann G. W.. A rapid inversion technique for transient electromagnetic soundings. Phys. Earth Planet Inter., 1989, 53: 394～404
[116] J. C. Larsen. A new technique for layered earth magnetotelluric inversion. Geophysics, 1981, 46(9): 1247～1257
[117] Lee, K. H. & Xie, G.. A new approach to imaging with low frequency electromagnetic fields. Geophysics, 1993, 58: 780～796
[118] Laust B. Pedersen & Mehran Gharibi. Automatic 1-D inversion of magnetotelluric data: Finding the simplest possible model that fits the data. Geophysics, 2000, 65(3): 773～782
[119] 吴小平，徐果明．利用共轭梯度方法电阻率三维反演研究．地球物理学报，2000，Vol．43(3)：420～427
[120] Jacobs, D. A. H.. A generalization of the conjugate-gradient method to solve complex system. IMA J. Numerical Analysis, 1986, 6: 447～452
[121] Newman, G. A. & Alumbaugh, D. L.. Three-dimensional magnetotelluric inversion using non-linear conjugate gradients. Geophys. J. Int., 2000, 140: 410～424
[122] Zhdanov, M. S., Fang, S. and G. Hursan. Electromagnetic inversion using quasi-linear approximation: Geophysics, 2000, 65: 1501～1513
[123] Tartaras, E., Zhdanov, M. S. &Wada, K., et al. Fast imaging of TDEM data based on s-inversion. J. Appl. Geophys., 2000, 43: 115～132
[124] Oldenburg, D. W. & Y. Li. Inversion of induced polarization data. Geophysics, 1994, 59(9): 1327～1341
[125] Oristaglio, M., Wang, r. & Hohmann, G., etal. Resistivity imaging of transient electromagnetic data by conjugate-gradient method: 63rd Ann. Internat. Mtg., Soc. Expl. Geophys., 1993, Expanded Abstracts: 347～350
[126] Torres-Verdin, C. & Habashy, T. M.. Rapid 2.5-D forward modeling and inversion via a new nonlinear scattering approximation. Radio Sci., 1994, 29: 1051～1079
[127] Patricia, P. L. Fast and stable two-dimensional inversion of magnetotelluric data: [Ph.D, thesis]. The University of Utah. 1997
[128] Xinyou, Lu. Inversion of controlled-source audio-frequency magnetotelluric data: [Ph.D. thesis]. University of Washington, 1999
[129] Gabor Hursan. Rapic frequency domaion three-dimensional electromagnetic forward modeling and inversion: [Ph.D, thesis]. The University of Utah. 2001
[130] Zhang, Ge. Multidimensional electromagnetic inversion using the finite functions method: [Ph.D, thesis]. The University of Utah. 2004
[131] Barnett, C.T.. Simple inversion of time-domain electromagnetic data. Geophysics. 1984. 49: 925～933
[132] de Lugao P P, Wannamaker P E. Calculating the two dimensional magnetotelluric Jacobian in finite elements using reciprocity. Geophysical Journal International, 1996, 127:806～810
[133] McGillivray, P.R., Oldenburg, D.W. and Ellis, R.G.. Calculation of sensitivities for the frequency domain electromagnetic induction problem. Geophys. J. Internat., 1994, 116:1～4
[134] 何光渝，高永利．Visual Fortran常用数值算法集．北京：科学出版社，2002
[135] 谭浩强．Fortran程序设计．北京：清华大学出版社，1998
[136] Kevin L. Mickus. Case History:Magnetotelluric observations in the western Ouachita Mountains, southeastern Oklahoma. Geophysics, 1999, 64(6):1680～1688
[137] N.B. Boschetto, G. W. Hohmann. Controlled-source audiofrequency magnetotelluric responses of three-dimensional bodies. Geophysics, 1991, 56(2):255～264
[138] Pous, J., Ledo, J.J. & Queralt, P., et al. Constaintson the deep structure of the Pyrennes from new magnetotelluric data. Revista de la Sociedad Geologica de Espana, 1997, 8(4):395～400
[139] Lines, L.R. & S. Treitel. Tutorial: A review of least-squares inversion and its application to geophysical problems. Geophysical Prospecting, 1984, 32:159～186
[140] Heise, W., Pous, J.. Effects of the anisotropy on two dimensional inversion procedure. Geophysical Journal International, 2001, 147(3):610～622
[141] P.E. Wannamaker & P.M. Wright. Magnetotelluric transect of Long Valley caldera: Resistivity cross-section, structural implications, and the limits of a 2-D analysis. Geophysics, 1991, 56(7):926～940
[142] Hursan, G.. Storage reduction and fast matrix multiplication for integral-based geophysical problems. Proceedings of 2001 CEMI Annual Meeting, 2001
[143] Smith T, HoverstenM, GasperikovaE, et al. Sharp boundary inversion of 2D magnetotelluric data. Geophysical Prospecting, 1999, 47(2):469～486
[144] Wannamaker. P.E, Stodt. J.A & Rijo. L. Two-dimensional topographic responses in magnetotellurics modeled using finite elements. Geophysics, 1986, 51(11):2131～2144
[145] Kazunobu Yamanel & Kazumi Ohsato. Three-dimensional magnetotelluric investigation in Kakkonda geothermal area, Japan. Proceedings World Geothermal Congress 2000, Kyushu-Tohoku, Japan:1965～1968
[146] Newman G.A. & Alumbaugh, D.L.. Three-dimensional massively parallel electromagnetic inversion—I, Theory. Grophys. J. Int., 1997, 128:345～354
[147] Tripp, A.C. & Hohmann, G.W.. Three-dimensional electromagnetic crosswell inversion:IEEE Trans. on Geoscience and Remote Sensing, 1993, 31:121～126
[148] Yutaka Sasaki. Two-dimensional joint inversion of magnetotelluric and dipole-dipole resistivity data. Geophysics, 1989, 54(2): 254～262
[149] Zhdanov, M. S., Wannamaker, P. E..Three-dimensional electromagnetics. Elsevier, 2002, 153～171
[150] Zhdanov, M.S. & Frenkel, M.A.. The solution of the inverse problems on the basis of the analytical continuation of the transient electromagnetic field in reverse time. J. Geomag. Geoelectr., 1983, 35: 747～765
[151] Zhdanov, M. S. & N. G. Golubev. Use of the finite functions method for the solution of the 2D inverse problem. J. Geomag. Geoelectr., 1983, 35: 707～722
[152] Michael S. Zhdanov et al. Underground imaging by frequency-domain electromagnetic migration. Geophysics, 1996, 61(3): 666～682
[153] Paul, A. B. Electromagnetic imaging of active fault zones: [Ph. D, thesis]. University of Washington, 2002
[154] Umberto Spagnolini. Time-domain estimation of MT impedance tensor. Geophysics, 1994. 59(5): 712～721
[155] 王家林，吴健生，于鹏等．徐闻-纪家高精度重力和MT测量综合研究成果报告．同济大学，2004
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