基于背景分离的被动源电磁测深双模联合反演
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摘要
被动源电磁测深法以其特有的优势,已经越来越多地被应用于实际工作中。然而,其反演解释技术相对落后,限制了其资料解释的水平。本文在国家高技术研究发展计划(863计划)“被动源电磁测深的多尺度自适应双模联合反演研究(2006AA06Z105)”的资助下,进行了基于背景分离的被动源电磁测深双模联合反演研究,具有重要的理论和实际意义。
本文基于最小构造的思想,对被动源电磁测深法双模联合快速反演展开研究,重点研究了灵敏度矩阵的快速计算和基于多分辨小波分解理论的背景分离反演方法。论文通过理论分析、数值模拟、模型试验以及实际应用等手段,研究了如何有效地利用被动源电磁测深两种模式的数据联合反演提高反演的精度,同时在加快反演速度方面做了一定的研究工作。
首先,论文研究了带模型约束的被动源电磁测深双模联合反演的目标函数,对模型参数和各种数据残差进行不同的权重的单独约束,能有效地利用各种数据相互约束反演获得光滑的地电模型；针对被动源电磁测深反演的实际情况,设计了正演与反演的双重网格方案,在保证正演精度的同时,提高了反演速度,且实际操作简单,管理方便。在此基础上,编程实现了被动源电磁测深TE与TM双模联合最小构造反演,并针对七种典型电磁模型,系统分析了视电阻率与相位差四种观测数据及其联合反演的效果,总结出具有指导意义的规律,并应用于内蒙某矿区的实际数据反演。
接着,论文在进行一维大地电磁灵敏度分析的基础上,以高频大地电磁测深法为例,利用数值模拟方法,分析了二维情况下各种观测资料的灵敏度随模型电阻率、频率以及空间坐标的变化和衰减规律,得出了二维灵敏度在趋肤深度一定的情况下随空间坐标迅速衰减的结论；在此基础上,提出了利用趋肤深度限定范围进行快速灵敏度矩阵计算,并应用于被动源电磁测深双模联合反演中,进行了模型试验,结果表明,该方法大大加快了反演的速度。
然后,论文利用Mallat小波多分辨分析,分离出被动源电磁测深法地表电磁响应中的背景电磁响应信息和异常电磁响应信息,并进行模型试验验证了方法的应用效果。在此基础上,提出了基于背景分离的二维被动源电磁测深反演方案,对背景电磁响应进行快速反演,并用该反演结果约束异常区域的反演,达到了背景分离反演的目的。模型试验表明,基于背景分离的被动源电磁测深双模联合反演的结果,冗余构造少,反演速度快。
最后,总结了全文的主要内容和创新工作,并指出了研究工作的不足之处和今后工作的建议。
Passive source electromagnetic sounding method has increasingly been used in practical work for its unique advantages. However, the inversion method is lag behind which restricts the level of data interpretation results. With the support of National High Technology Development "863" Project-"Multi-scale Self-adapting Two-mode Joint Inversion of Passive Source Electromagnetic Sounding", This article researched a two-mode joint inversion method of the passive source electromagnetic sounding data based on background subtraction.
This paper studied a rapid two-mode joint inversion of the passive source electromagnetic sounding data based on the idea of minimum structure. The main focus is the fast computing of the sensitivity matrix and the background subtraction inversion method based on the theory of wavelet multi-resolution decomposition. By theoretical analysis, numerical simulation, model test and practical application, the method of improving the inversion accuracy with making effective use of joint two-mode data is researched; meanwhile, speed is also discussed.
Firstly, the objective function of the joint inversion of the two-mode passive source sounding with model constraints is built. Model parameters and data residual errors are restricted individually with different weights which can use various kinds of data effectively to get a smoother model. For the practical situation of the passive source sounding, a double grid of forward and inversion is designed which accelerate the inversion speed without loss of forward significance, moreover, it's easy for operation and management. On this basis, the two-mode joint inversion of passive source electromagnetic sounding data based on minimum structure is implemented by programming. The effects of individual and joint inversion with four kind of sounding data is analysed by inversion test to seven typical geoelectricity model, which lead to some significative conclusions. The inversion method is applied to real data of a mining area in Inner Mongolia in the following part.
Secondly, on the basis of the analysis of one-dimensional magnetotelluric sensitivity function, by using numerical simulation method, high-frequency magnetotelluric sounding on two-dimensional model is taken for example to show the relationships between the sensitivity of various observational data and model resistivities, frequency and spatial coordinates, and the conclusion summarized is that the sensitivity will decay fast when spatial coordinates changed in the condition of a constant skin depth. With this conclusion, a method of fast computing the sensitivity matrix by limiting the rang with skin depth is presented and applied to the passive source electromagnetic sounding two-mode joint inversion and proved by model test that it can greatly accelerated the inversion speed.
Thirdly, based on the theory of Mallat wavelet multi-resolution decomposition, a discussion and computing formula of obtaining background information from the surface electromagnetic response of the passive source electromagnetic sounding method is provided and verified by test. On this Basis a two-mode joint inversion method of passive source sounding based on the background subtraction is presented. The inversion of the background electromagnetic response is done individually while the result resistivity is imposed on the background outside the abnormal regions of the model for restricting the inversion, only the abnormal regions changes will be calculated. Model tests show that this method can effectively reduce the redundant structure and the elapsed time.
Finally, the main work and innovations involved and some limitations in current research are pointed out and recommendations for future research are given in the conclusion part.
本文基于最小构造的思想,对被动源电磁测深法双模联合快速反演展开研究,重点研究了灵敏度矩阵的快速计算和基于多分辨小波分解理论的背景分离反演方法。论文通过理论分析、数值模拟、模型试验以及实际应用等手段,研究了如何有效地利用被动源电磁测深两种模式的数据联合反演提高反演的精度,同时在加快反演速度方面做了一定的研究工作。
首先,论文研究了带模型约束的被动源电磁测深双模联合反演的目标函数,对模型参数和各种数据残差进行不同的权重的单独约束,能有效地利用各种数据相互约束反演获得光滑的地电模型；针对被动源电磁测深反演的实际情况,设计了正演与反演的双重网格方案,在保证正演精度的同时,提高了反演速度,且实际操作简单,管理方便。在此基础上,编程实现了被动源电磁测深TE与TM双模联合最小构造反演,并针对七种典型电磁模型,系统分析了视电阻率与相位差四种观测数据及其联合反演的效果,总结出具有指导意义的规律,并应用于内蒙某矿区的实际数据反演。
接着,论文在进行一维大地电磁灵敏度分析的基础上,以高频大地电磁测深法为例,利用数值模拟方法,分析了二维情况下各种观测资料的灵敏度随模型电阻率、频率以及空间坐标的变化和衰减规律,得出了二维灵敏度在趋肤深度一定的情况下随空间坐标迅速衰减的结论；在此基础上,提出了利用趋肤深度限定范围进行快速灵敏度矩阵计算,并应用于被动源电磁测深双模联合反演中,进行了模型试验,结果表明,该方法大大加快了反演的速度。
然后,论文利用Mallat小波多分辨分析,分离出被动源电磁测深法地表电磁响应中的背景电磁响应信息和异常电磁响应信息,并进行模型试验验证了方法的应用效果。在此基础上,提出了基于背景分离的二维被动源电磁测深反演方案,对背景电磁响应进行快速反演,并用该反演结果约束异常区域的反演,达到了背景分离反演的目的。模型试验表明,基于背景分离的被动源电磁测深双模联合反演的结果,冗余构造少,反演速度快。
最后,总结了全文的主要内容和创新工作,并指出了研究工作的不足之处和今后工作的建议。
Passive source electromagnetic sounding method has increasingly been used in practical work for its unique advantages. However, the inversion method is lag behind which restricts the level of data interpretation results. With the support of National High Technology Development "863" Project-"Multi-scale Self-adapting Two-mode Joint Inversion of Passive Source Electromagnetic Sounding", This article researched a two-mode joint inversion method of the passive source electromagnetic sounding data based on background subtraction.
This paper studied a rapid two-mode joint inversion of the passive source electromagnetic sounding data based on the idea of minimum structure. The main focus is the fast computing of the sensitivity matrix and the background subtraction inversion method based on the theory of wavelet multi-resolution decomposition. By theoretical analysis, numerical simulation, model test and practical application, the method of improving the inversion accuracy with making effective use of joint two-mode data is researched; meanwhile, speed is also discussed.
Firstly, the objective function of the joint inversion of the two-mode passive source sounding with model constraints is built. Model parameters and data residual errors are restricted individually with different weights which can use various kinds of data effectively to get a smoother model. For the practical situation of the passive source sounding, a double grid of forward and inversion is designed which accelerate the inversion speed without loss of forward significance, moreover, it's easy for operation and management. On this basis, the two-mode joint inversion of passive source electromagnetic sounding data based on minimum structure is implemented by programming. The effects of individual and joint inversion with four kind of sounding data is analysed by inversion test to seven typical geoelectricity model, which lead to some significative conclusions. The inversion method is applied to real data of a mining area in Inner Mongolia in the following part.
Secondly, on the basis of the analysis of one-dimensional magnetotelluric sensitivity function, by using numerical simulation method, high-frequency magnetotelluric sounding on two-dimensional model is taken for example to show the relationships between the sensitivity of various observational data and model resistivities, frequency and spatial coordinates, and the conclusion summarized is that the sensitivity will decay fast when spatial coordinates changed in the condition of a constant skin depth. With this conclusion, a method of fast computing the sensitivity matrix by limiting the rang with skin depth is presented and applied to the passive source electromagnetic sounding two-mode joint inversion and proved by model test that it can greatly accelerated the inversion speed.
Thirdly, based on the theory of Mallat wavelet multi-resolution decomposition, a discussion and computing formula of obtaining background information from the surface electromagnetic response of the passive source electromagnetic sounding method is provided and verified by test. On this Basis a two-mode joint inversion method of passive source sounding based on the background subtraction is presented. The inversion of the background electromagnetic response is done individually while the result resistivity is imposed on the background outside the abnormal regions of the model for restricting the inversion, only the abnormal regions changes will be calculated. Model tests show that this method can effectively reduce the redundant structure and the elapsed time.
Finally, the main work and innovations involved and some limitations in current research are pointed out and recommendations for future research are given in the conclusion part.
引文
[1]Tiknonov AN. On determining electrical characteristics of the deep layers of the earth's crust [J]. Deki Akud Nuck,1950,73:295-297.
[2]Cagniard L. Basic theory of the magnetotelluric methods of geophysical prospecting [J]. Geophysics,1953,18:605-635.
[3]A.A考夫曼,GV凯勒.频率域和时间域电磁测深[M].地质出版社,1987.08
[4]石应骏,刘国栋等.大地电磁测深法教程[M].地震出版社,1985.09
[5]A.A考夫曼,GV凯勒.大地电磁测深法[M].地震出版社,1987.08
[6]陈乐寿,刘任,王天生等.大地电磁测深资料处理与解释[M]石油工业出版社,1989.01
[7]傅良魁.应用地球物理学教程.[M]北京：地质出版社,1990.8
[8]汤井田,何继善.可控源音频大地电磁法及其应用.[M]长沙：中南大学出版社,2005
[9]Coggon J H. Electromagnetic and electrical modeling by the finite element method [J]. Geophysics,1971,36(2):132-151.
[10]Silvester P, Haslam C R S. Magnetotelluric modeling by the finite element method [J]. Geophysical Prospect,1972,20:872-891.
[11]Reddy I K, Rankin D. Magnetotelluric response of a two-dimensional sloping contact by the finite element method [J]. Geophysics,1973,38:847-857.
[12]William L, Rodi. A technique for improving the accuracy of finite element solution for magnetotelluric data [J]. Geophysics,1976,44:483-506.
[13]Rijo L. Modeling of electric and electromagnetic data [D]. Ph.D dissertation, University of Utah,1977.
[14]陈乐寿.有限元法在大地电磁测深正演计算中的应用与改进[J].石油物探,1981,20(3)：84-103.
[15]陈乐寿,孙必俊.有限元法在大地电磁测深中正演计算的改进[J].石油地球物理勘探,1982,17(3)：69-72.
[16]胡建德,王光锷,陈乐寿等.大地电磁二维正演计算中若干问题的讨论[J].石油地球物理勘探,1982,17(6)：47-55.
[17]胡建德,蔡刚.用三角形二次插值法计算二维大地电磁测深曲线[J].石油地球物理勘探,1984,19(4)：358-367.
[18]Wannamaker P E, Stodt J A, Rijo L. Two-dimensional topographic responses in magnetotelluric model using finite elements [J]. Geophysics,1986,51:2131-2144.
[19]Wannamaker P E, Stodt J A, Rijo L. A stable finite element solution for two-dimensional magnetotelluric modeling [J]. Geophysics,1987,88:277-296.
[20]徐世浙,刘斌.电导率分层连续变化的水平层的大地电磁正演[J].地球物理学报,1995,38(2)：262-268.
[21]徐世浙,于涛,李予国等.电导率连续变化的MT有限元正演(Ⅰ)[J].高校地质学报,1995,1(2)：65-73.
[22]李予国,徐世浙,刘斌等.电导率连续变化的MT有限元正演(Ⅱ)[J].高校地质学报,1996,2(4)：448-452.
[23]胡建德,闫述等.线电流源声频大地电磁测深的二维正演计算及响应特点[J].现代地质,1997,11(2)：203-210.
[24]史明娟,徐世浙,刘斌.大地电磁测深二次函数插值的有限元法的正演模拟[J].地球物理学报,1997,40(3)：421-430.
[25]陈小斌.有限元直接迭代算法[J].物探化探计算技术,1999,21(2)：165-171.
[26]陈小斌,张翔,胡文宝.有限元直接迭代算法在MT二维正演中的应用[J].石油地球物理勘探,2000,35(4)：487-496.
[27]陈小斌,胡文宝.有限元直接迭代法及其在线源频率域电磁响应中应用[J].地球物理学报,2002,45(1)：119-130.
[28]底青云,Martyn Unsworth,王妙月.复杂介质有限元法2.5维可控源音频大地电磁法数值模拟[J].地球物理学报,2004,47(4)：723-730.
[29]Kerry Key, Chester Weiss, Adaptive finite-element modeling using unstructured grids:The 2D magnetotelluric example[J]. GEOPHYSICS,2006.71(6).291-299.
[30]刘小军,王家林,于鹏.基于二次场的二维大地电磁有限元数值模拟[J].同济大学学报,2007,35(8)：1113-1117.
[31]Reddy I K. Three-dimensional modeling in magnetotelluric and magnetic variational sounding [J]. Geophysics,1977,51:313-325.
[32]Mogi T. Three-dimensional modeling of magnetotelluric data using finite-element method [J]. Journal of Applied Geophysics,1996,35:185-189.
[33]Zyserman F I, Santos J E. Parallel finite element algorithm with domain decomposition for three-dimensional magnetotelluric modeling [J]. Journal of Applied Geophysics,2000,44:337-351.
[34]Son J S, Song y, Suh J H. High-Frequency Three-Dimensional Electromagnetic Modeling Using Vector Finite Elements [J]. Three-Dimensional Electromagnetics Ⅲ, Adelaide, Australia, February,2003:20-21.
[35]Mitsuhata Y, Uchida T.3D magnetotelluric modeling using the T-Ω finite-element method [J]. Geophysics,2004,69,108-119.
[36]闫述,陈明生.电偶源频率电磁测深三维地电模型有限元正演[J].煤田地质与勘探,2000,28(3)：50-56.
[37]黄临平,戴世坤.复杂条件下3D电磁场有限元计算方法[J].中国地质大学学报,2002,27(6)：775-779.
[38]王若,王妙月,卢元林.三维三分量CASMT法有限元正演模拟研究初探[J].地球物理学进展,2007,22(2)：579-585.
[39]王烨.基于矢量有限元的高频大地电磁法三维数值模拟[D].长沙,中南大学.2008.
[40]张继峰.基于电场双旋度方程的三维可控源电磁法有限单元法数值模拟[D].长沙,中南大学.2008.
[41]Dey A, Morrison H F. Electromagnetic response of two-dimensional inhomogeneities in a dissipative half-space for Turam interpretation [J]. Geophysical Prospecting,1973,21(2):441-450.
[42]Hohmann G W. Three-dimensional induced polarization and electromagnetic modeling [J]. Geophysics,1975,40:309-324.
[43]Ting S C, Hohmann G W. Integral equation modeling of three-dimensional magnetotelluric response [J]. Geophysics,1981,46:182-197.
[44]Wannamaker P E. Hohmann G W, SanFilipo W A. Electromagnetic modeling of three-dimensional bodies in layered earths using integral equation [J]. Geophysics, 1984,49:60-74.
[45]Wannamaker P E. Advances in three-dimensional magnetotelluric modeling using integral equations [J]. Geophysics,1991,56,1716-1728.
[46]Zhdanov M S, Fand S. Quasi-linear approximation in 3-D EM modeling [J]. Geophysics,1996a,61:623-665.
[47]Avdeev D B, Kuvshinov A V, Pankratov O V. High performance three dimensional electromagnetic modeling using modified Neumann series, wide-band numerical solution and examples[J]. Journal of Geomagnetism and Geoelectricity, 1997,49,338-347.
[48]Xiong Z. EM modeling of three-dimensional structures by the method of system iteration using integral equations [J]. Geophysics,1992,57:1556-1561.
[49]Xiong Z. Domain decomposition for 3D electromagnetic modeling [J]. Earth Planets Space,1999,51:1013-1018.
[50]毛先进,鲍光淑,宋守根.半空间中多个三维电阻率响应的边界积分方程模 拟[J].地球物理学报,1996,39(6)：823-834.
[51]曹建章,唐天同,宋建平.三维电磁模拟的积分方程法[J].西安石油学院学报,1998,13(3)：65-68.
[52]鲍光淑,张碧星,敬荣中等.三维电磁响应积分方程法数值模拟[J].中南工业大学学报,1999,30(5)：472-474.
[53]徐凯军,李桐林,张辉等.利用积分方程法的大地电磁三维正演[J].西北地震学报,2006,28(2)：104-107.
[54]徐世浙.地球物理中的有限单元法[M].北京：科学出版社,1994.
[55]Yee.K.S. Numerical solution of initial boundary value problems involving maxwells equations in isotropic media [J]. IEEETrans.Ant.Prop.1966,14:302-307. Lamontagne, Y.and West, G.F. EM response of a rectangular thin plate. [J] Geophysics, 1971,36:26-30
[56]Jepsen,A.F. Numerical modeling in resistivity prospecting. [D] University of California. Berkeley.1975.
[57]Gldman, M.M., Stoyert, C.H. Finite-difference calculations of the transient field of an axiallvsvmmetric earth for vertical magnetic dipole excitation. [J] Geophysics, 1983,48:953-957.
[58]Leppin. M., Electromagnetic modeling of 3-D sources over 2-D inhomo-geneties in the time domain. [J] Geophysics,1992,57:994-1003.
[59]Smith.J.T, Booker.J.R. Rapid inversion of two and three dimensional magnetotelluric data [J].J Geophys Res,1991,96 (B3):3905-3922.
[60]Mackie.R.L, Madden.T.R, Wannamaker.P.E. Three dimensional magnetotelluric modeling using difference equations Theory and comparisons to integral equation solutions. [J]Geophysics,1993,58:215-226.
[61]Wang.T, Hohmann.G.W.A. Finite difference time domain solution for three dimensional electromagnetic modeling [J]. Geophysics,1993,58:797-809.
[62]Mackie.R.L, Smith.T.J, Madden.T.R.3-D electromagnetic modeling using difference equations [J]. The Magnetotelluric Example, RadioSci.1994,29:923-935.
[63]吴小平,徐果明.利用不完全Cholesky共轭梯度法求解点源三维电场.[J]地球物理学报,1998,41(6)：848-858.
[64]段红伟.基于模拟退火算法的实现及应用.计算机与网络[J].1999,40(5)：543-545.
[65]Spitzer. Magnetotelluric static shift and direct current sensitivity [J]. Geophys. J. Int.,2001, 144:289-299
[66]Fomenko.E.Y, Mogi.T.A new computation method for a staggeredgrid of 3D EM field conservative modeling [J]. Earth Planets Space,2002,54:499-509.
[67]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[J].地球物理学报,2003,46(5)：705-711
[68]徐凯军,李桐林.垂直有限线源三维地电场有限差分正演研究[J].吉林大学学报(地球科学版),2006,36(1)：137-147
[69]王彦飞.反演问题的计算方法及其应用[M].高等教育出版社：北京,2007
[70]王家映.地球物理反演理论[M].高等教育出版社：北京,2002.
[71]姚姚.地球物理反演基本理论与应用方法[M].中国地质大学出版社：武汉,2002.
[72]Bostick F X. A simple almost exact method of MT analysis [J]. Workshop on Electrical Methods in Geothermal Exploration,1977,175-177.
[73]Coen, S., Quercia, F., Mackiewicz, M. Direct inversion of one-dimensional MT data. JGR.1983, V.88, No. B3
[74]王家映,周一强.一维大地电磁资料的直接反演法[J].地质科技情报,1987,6(4)：104-114
[75]Gupta, P. K., Sri Niwas, V. K. Gaur. Straightforward inversion scheme (SIS) for one-dimensional magnetotelluric data [J]. Proceedings of the Indian Academy of Sciences (Earth and Planetary Sciences),1996,105:413-429
[76]Sri Niwas, P. K. Gupta, V. K. Gaur. Straightforward inversion of MT data using a normalized impedance function [J]. Geophysics,2007,72(1):F19-F24.
[77]Weidelt P. The inverse problem of geomagnetic induction [J]. Geophysics,1972, 38:257-289.
[78]Oldenburg D W. One-dimensional inversion of natural source magnetotelluric observations [J]. Geophysics,1979,44(7):1218-1244.
[79]Constable S C, Parker R L, Constable C G. Occam's inversion:a practical algorithm for generating smooth models from electromagnetic sounding data [J]. Geophysics,1987,52(3):289-300.
[80]Weaver J T, Agarwal A K. Automatic 1-D inversion of magnetotelluric data by the method of modeling [J]. Geopysics,1993,112:115-123.
[81]Parker R L, Booker J R. One-dimensional inversion and bounding of magnetotelluric apparent resistivity and phase measurements [J]. Phy.Earth Planet.Int, 1996,98:269-282.
[82]Pedersen L B, Gharibi M. Automatic 1-D inversion of magnetotelluric data: Finding the simplest possible model that fits the data[J]. Geophysics,2000, 65(3):773-782.
[83]Santos A B, Sampaio E S, Porsani M J. A robust two-step inversion of complex magnetotelluric apparent resistivity data [J]. Geophyseics,2005,49:109-125.
[84]Haber E. Quasi-Newton methods for large-scale electromagnetic inverse problems [J]. Inverse Problem,2005,21:305-323.
[85]晋光文.大地电磁相位资料的一维反演[J].地震地质,1986,10(4)：159-168.
[86]晋光文.大地电磁视电阻率和阻抗相位资料的联合反演方法研究[J].地震地质,1987,9(4)：81-86.
[87]徐世浙,刘斌.大地电磁一维连续介质反演的曲线对比法[J].地球物理学报,1995,38(5)：676-682.
[88]徐义贤,王家映.大地电磁的多尺度反演[J].地球物理学报,1998,41(5)：704-711.
[89]吴小平,徐果明.大地电磁数据的Occam反演改进[J].地球物理学报,1998,41(4)：547-554.
[90]杨振武,王家映,张胜业,高仕谦.一维大地电磁和地震数据联合反演方法研究[J].石油地球物理勘探,1998,33(1)：78-88.
[91]张大海,徐世浙.带相位信息的一维大地电磁曲线对比反演法.地震地质,2001,23(2)：227-231.
[92]苏朱刘,罗延钟,胡文宝.大地电磁测深“正演修正法”一维反演.石油地球物理勘探,2002,37(2)：138-145.
[93]严良俊、胡文宝
[94]陈小斌,赵国泽,汤吉等.大地电磁自适应正则化反演算法.地球物理学报,2005,48(4)：937-946.
[95]师学明,肖敏,范建柯等.大地电磁阻尼粒子群优化反演法研究[J].地球物理学报,2009,52(4)：1114-1120.
[96]Zhdanov M S, Fang S.3-D quasi-linear electromagnetic inversion [J]. Radio Science,1996,31:741-754.
[97]Zhdanov M S, Fang S, Hursan G. Electromagnetic inversion using quasi-linear approximation [J]. Geophysics,2000,65:1501-1513.
[98]Zhdanov M S, Hursan G 3-D electromagnetic inversion based on quasi-analytical approximation [J]. Inverse Problems,2000,16:1297-1322.
[99]Zhdanov M S, Golubev N, Hursan G. Rapid 3-D inversion of the array magnetotelluric data [J]. PEPI,2003.
[100]Mackie R L, Rieven R, Rodi W. Users manual and software documentation for two-dimensional inversion of magnetotelluric data [M]. Department of Geological Sciences, Indiana University,1997.
[101]de Lugao P, Wannamaker P E. Calculating the two-dimensional magnetotelluric Jacobian in finite elements using reciprocity[J]. Geophysics,1996,127:806-810.
[102]Newman G A, Alumbaugh D L. Three-dimensional massively parallel inversion [J]. Geophysics,1997,128:355-363.
[103]Newman G A, Alumbaugh D L. Three-dimensional magnetotelluric inversion using non-linear conjugate gradients [J]. Geopysics,2000,140:410-424.
[104]Haber E, Oldenburg D. A GCV based method for nonlinear ill-posed problems [J]. Computational Geosciences,2000,4:41-63.
[105]Oldenburg D W. One-dimensional inversion of natural source magnetotelluric observations [J]. Geophysics,1979,44(7):1218-1244.
[106]Oldenburg, D.W. Inversion of electromagnetic data:An overview of new techniques [J]. Surveys in Geophysics,1990,11:231-270.
[107]Oldenburg, D.W.& Ellis, R.G. Efficient inversion of magnetotelluric data in two dimensions, Phys. Earth planet [J]. Inter.,1993,81:177-200
[108]Oldenburg, D.W., McGillivray, P.R.& Ellis, R.G. Generalised subspace methods for large scale inverse problems, Geophys.[J]. J. Int.,1993,114:12-20
[109]Ellis R.G, Oldenburg D.W. Applied geophysical inversion [J]. Geophys.J.Int., 1994,116:5-11
[110]Aruliah D, AscherU, Haber E, et al. A method for the forward modelling of 3D electromagnetic quasi-static problems [J]. Math Modelling Applied Sciences,2001, 11(1):1-21.
[111]Sasaki Y.. Two-dimensional joint inversion of magnetotelluric and dipole-dipole resistivity data [J]. Geophysics,1989,54(2):254-262
[112]Sasaki Y. Full 3-D inversion of electromagnetic data on PC [J]. Journal of Applied Geophysics,2001,45-54.
[113]DeGroot-Hedlin C., Constable S C. Occam's inversion to generate smooth, two-dimensional models from electromagnetic sounding data [J]. Geophysics,1990, 55:1613-1624
[114]Smith T, Hoversten M, Gasperikova E, et al. Sharp boundary inversion of 2D magnetotelluric data [J]. Geophysical Prospecting,1999,47:469-486.
[115]Loke M H, Barker R D. Rapid least-squares inversion of apparent resistivity pseudo sections by a quasi-Newton method [J]. Geophysical Prospecting,1996a, 44:131-152
[116]Loke M H, Barker R D. Practical techniques for 3D resistivity surveys and data inversion [J]. Geophysical Prospecting,1996b,44:499-524
[117]Michael M D, Guust N. Nullspace shuttles [J]. Geophys. J. Int.,1996, 124:372-380
[118]Spichak V, Menville M, Roussignol M. Three dimensional inversion of the magnetotelluric fields using Bayesian statistics [C]. In Proc. Schlumberger Doll Research Symp. on 3D Elect romagnetics, eds Spies B and Oristaglio M, USA,1995, 347-358.
[119]Spichak V and Popova. Artificial neural network inversion of magnetotelluric data in terms of three deimensional earth macroparameters [J]. Geophys J Int,2000, 142:15-26
[120]孙必俊,陈乐寿,王光锷等.关于大地电磁测深资料反演问题[J].地球物理学报,1985,28(2)：218-229.
[121]赵国泽,刘国栋.一种二维大地电磁反演方法[J].地震地质,1985,7：56-58.
[122]吴广耀,胡建德.大地电磁资料的二维连续模型自动反演[J].地球科学-中国地质大学学报.1990,5(增刊)：23-36.
[123]陈乐寿,王光锷等人.一种大地电磁成像技术[J].地球物理学报,1993,36(3)：337-346.
[124]吴小平,吴广耀,胡建德.二维最平型的大地电磁快速反演[J].地球科学-中国地质大学学报,1994,19(6)：821-829.
[125]杨长福,林长佑.大地电磁二维层状模型参数化反演[J].西北地震学报,1994,16(4)：10-19.
[126]戴世坤,徐世浙.MT二维和三维连续介质快速反演[J].石油地球物理勘探,1997,32(3)：305-317.
[127]翁爱华,刘国兴.大地电磁测深资料的超球逼近反演[J].长春科技大学学报,1998,28(3)：330-334.
[128]张翔,胡文宝.带地形的大地电磁测深联合二维反演[J].石油地球物理勘探,1999,34(2)：190-196.
[129]师学明,王家映等.多尺度逐次逼近遗传算法反演大地电磁资料[J].地球物理学报,2000,43(1)：122-130.
[130]苏朱刘,胡文宝.大地电磁测深“降维逼近法”二维反演[J].石油地球物理勘探.2002,37(5)：516-523.
[131]杨辉,王永寿,王家林等人.大地电磁测深拟二维模拟退火约束反演[J].海象油气地质,2001,6(1)：47-52.
[132]谭捍东,余钦范,John Booker等.大地电磁法三维快速松弛反演[J].地球物理学报,2003,46(6)：850-855.
[133]毛立峰,王绪本,高永才.大地电磁概率成像的效果评价[J].地球物理学报,2005,48(2)：429-433.
[134]毛立峰.大地电磁概率成像方法研究[D].成都,成都理工大学.2004.
[135]魏超,朱培民,王家映.量子退火反演的原理和实现[J].地球物理学报,2006,49(2)：577-583.
[136]胡祖志,胡祥云,何展翔.三维大地电磁数据的二维反演解释[J].石油地球物理勘探,2005,40(3)：353-359
[137]刘小军,王家林,吴健生.二维大地电磁正则化共轭梯度法反演算法[J].上海地质,2007a,101(1)：71-74.
[138]刘小军,王家林,陈冰等.二维大地电磁数据的聚焦反演算法探讨[J].石油地球物理勘探,2007b,42(3)：338-342.
[139]张罗磊,于鹏,王家林,吴建生.光滑模型与尖锐边界结合的MT二维反演方法[J].地球物理学报,2009,52(6)：1625-1632.
[140]刘苗,吴建生,于鹏,张罗磊.基于二维小波分解的MT二维反演方法[J].物探与化探,2009,33(3)：337-341.
[141]陈小斌,赵国泽.自动构建大地电磁二维反演的测点中心网格[J].地球物理学报,2009,52(6)：1564-1572.
[142]汤井田,任政勇,化希瑞.地球物理学中的电磁场正演与反演[J].地球物理学进展,2007,22(4)：1181-1194
[143]周军.大地电磁测深视电阻率与阻抗相位联合反演研究[D].成都,成都理工大学,2008.
[144]晋光文.大地电磁资料联合反演评述[J].地球科学-中国地质大学学报,1990,15(曾)：59-67.
[145]Zhdanov M S, Varentov I M. Methods for modeling electromagnetic fields: Results from COMMEMI-the international project on the comparison of modeling methods for electromagnetic induction [J]. Journal of Applied Geophysics,1997, 44:337-351.
[146]J. Torquil Smith, John R. Booker. Magnetotelluric Inversion for minimum structure [J]. GEOPHYSICS.1988,53(12):1565-1576.
[147]李帝铨,王光杰,底青云.基于遗传算法的CSAMT最小构造反演[J].地球物 理学报.2008,51(4)：1234-1245.
[148]Colin G. Farquharson. Constructing piecewise-constant models in multi-dimensional minimum-structure inversions [J]. Geophysics,2008,73(l):kl-k9.
[149]陈小斌.大地电磁正反演新算法研究及资料处理与解释可视化集成系统开发[D].北京,中国地震地质研究所.2003
[150]Colin G. Farquharson, Douglas W. Oldenburg. Non-linear inversion using general measures of data misfit and model structure [J]. Geophys. J. Int.,1998,134:213-227.
[151]Oleg Portniaguine, Michael S. Zhdanov. Focusing geophysical inversion images [J]. GEOPHYSICS,1999,64(3):874-887,
[152]刘海飞,阮百尧,柳建新等.混合范数下的最优化反演方法[J].地球物理学报,2007,50(6)：1877-1883
[153]李墩柱,黄清华,陈小斌.误差对大地电磁测深反演的影响[J].地球物理学报,2009,52(1)：268-274
[154]Huber, P. J. Robust estimation of a location parameter [J]. Annals of Mathematical Statistics,1964,35:73-101.
[155]Ekblom, H., The Ll-estimate as limiting case of an Lp-or Huber-estimate, in Y. Dodge, ed., Statistical data analysis based on the L1-norm and related methods [J]. Elsevier Science Publ.Co., Inc.,1987,109-116.
[156]Last, B. J., K. Kubik. Compact gravity inversion [J]. Geophysics,1983, 48:713-721.
[157]P. R. McGillivray, D. W. Oldenburg. Methods for calculating Frechet and sensitivities for the nonlinear inverse problem:a comparative study [J]. Geophys. Prosp.,1990,38:499-524.
[158]P. R. McGillivray, D. W. Oldenburg, et al. Calculation of sensitivities for the frequency-domain electromagnetic problem [J]. Geophys. J. Int.,1994,116:1-4.
[159]C. G. Farquharson. Approximate Sensitivities for the Multi-Dimensional Electromagnetic Inverse Problem [D]. University of Edinburgh,1995.
[160]C. G. Farquharson, D. W. Oldenburg. Approximate sensitivities for the electromagnetic inverse problem [J]. Geophys. J. Int.,1996,126:235-252.
[161]P. P. de Lugao, P. E. Wannamaker. Calculating the two-dimensional magnetotelluric Jacobian in finite elements using reciprocity [J]. Geophys. J. Int.,1996,127:806-810.
[162]晋光文.大地电磁资料的灵敏度研究[J].地球物理学报,1991,34(4)：465-473.
[163]李世雄,刘家淇.小波变换和反演数学基础[M].北京:地质出版社,1994.
[164]刘贵忠,邸双亮.小波分析及其应用[M].西安：西安电子科技大学出版 社,1992.
[165]宋守根,汤井田,何继善.小波分析与频率电磁测深中静态效应的识别、分离和压制[J].地球物理学报,1995,38(1)：120-127.
[166]汤井田,宋守根,何继善.多分辨分析和重磁异常的识别与分层次提取[J].中国有色金属学报,1994,4(3)：6-15.
[2]Cagniard L. Basic theory of the magnetotelluric methods of geophysical prospecting [J]. Geophysics,1953,18:605-635.
[3]A.A考夫曼,GV凯勒.频率域和时间域电磁测深[M].地质出版社,1987.08
[4]石应骏,刘国栋等.大地电磁测深法教程[M].地震出版社,1985.09
[5]A.A考夫曼,GV凯勒.大地电磁测深法[M].地震出版社,1987.08
[6]陈乐寿,刘任,王天生等.大地电磁测深资料处理与解释[M]石油工业出版社,1989.01
[7]傅良魁.应用地球物理学教程.[M]北京：地质出版社,1990.8
[8]汤井田,何继善.可控源音频大地电磁法及其应用.[M]长沙：中南大学出版社,2005
[9]Coggon J H. Electromagnetic and electrical modeling by the finite element method [J]. Geophysics,1971,36(2):132-151.
[10]Silvester P, Haslam C R S. Magnetotelluric modeling by the finite element method [J]. Geophysical Prospect,1972,20:872-891.
[11]Reddy I K, Rankin D. Magnetotelluric response of a two-dimensional sloping contact by the finite element method [J]. Geophysics,1973,38:847-857.
[12]William L, Rodi. A technique for improving the accuracy of finite element solution for magnetotelluric data [J]. Geophysics,1976,44:483-506.
[13]Rijo L. Modeling of electric and electromagnetic data [D]. Ph.D dissertation, University of Utah,1977.
[14]陈乐寿.有限元法在大地电磁测深正演计算中的应用与改进[J].石油物探,1981,20(3)：84-103.
[15]陈乐寿,孙必俊.有限元法在大地电磁测深中正演计算的改进[J].石油地球物理勘探,1982,17(3)：69-72.
[16]胡建德,王光锷,陈乐寿等.大地电磁二维正演计算中若干问题的讨论[J].石油地球物理勘探,1982,17(6)：47-55.
[17]胡建德,蔡刚.用三角形二次插值法计算二维大地电磁测深曲线[J].石油地球物理勘探,1984,19(4)：358-367.
[18]Wannamaker P E, Stodt J A, Rijo L. Two-dimensional topographic responses in magnetotelluric model using finite elements [J]. Geophysics,1986,51:2131-2144.
[19]Wannamaker P E, Stodt J A, Rijo L. A stable finite element solution for two-dimensional magnetotelluric modeling [J]. Geophysics,1987,88:277-296.
[20]徐世浙,刘斌.电导率分层连续变化的水平层的大地电磁正演[J].地球物理学报,1995,38(2)：262-268.
[21]徐世浙,于涛,李予国等.电导率连续变化的MT有限元正演(Ⅰ)[J].高校地质学报,1995,1(2)：65-73.
[22]李予国,徐世浙,刘斌等.电导率连续变化的MT有限元正演(Ⅱ)[J].高校地质学报,1996,2(4)：448-452.
[23]胡建德,闫述等.线电流源声频大地电磁测深的二维正演计算及响应特点[J].现代地质,1997,11(2)：203-210.
[24]史明娟,徐世浙,刘斌.大地电磁测深二次函数插值的有限元法的正演模拟[J].地球物理学报,1997,40(3)：421-430.
[25]陈小斌.有限元直接迭代算法[J].物探化探计算技术,1999,21(2)：165-171.
[26]陈小斌,张翔,胡文宝.有限元直接迭代算法在MT二维正演中的应用[J].石油地球物理勘探,2000,35(4)：487-496.
[27]陈小斌,胡文宝.有限元直接迭代法及其在线源频率域电磁响应中应用[J].地球物理学报,2002,45(1)：119-130.
[28]底青云,Martyn Unsworth,王妙月.复杂介质有限元法2.5维可控源音频大地电磁法数值模拟[J].地球物理学报,2004,47(4)：723-730.
[29]Kerry Key, Chester Weiss, Adaptive finite-element modeling using unstructured grids:The 2D magnetotelluric example[J]. GEOPHYSICS,2006.71(6).291-299.
[30]刘小军,王家林,于鹏.基于二次场的二维大地电磁有限元数值模拟[J].同济大学学报,2007,35(8)：1113-1117.
[31]Reddy I K. Three-dimensional modeling in magnetotelluric and magnetic variational sounding [J]. Geophysics,1977,51:313-325.
[32]Mogi T. Three-dimensional modeling of magnetotelluric data using finite-element method [J]. Journal of Applied Geophysics,1996,35:185-189.
[33]Zyserman F I, Santos J E. Parallel finite element algorithm with domain decomposition for three-dimensional magnetotelluric modeling [J]. Journal of Applied Geophysics,2000,44:337-351.
[34]Son J S, Song y, Suh J H. High-Frequency Three-Dimensional Electromagnetic Modeling Using Vector Finite Elements [J]. Three-Dimensional Electromagnetics Ⅲ, Adelaide, Australia, February,2003:20-21.
[35]Mitsuhata Y, Uchida T.3D magnetotelluric modeling using the T-Ω finite-element method [J]. Geophysics,2004,69,108-119.
[36]闫述,陈明生.电偶源频率电磁测深三维地电模型有限元正演[J].煤田地质与勘探,2000,28(3)：50-56.
[37]黄临平,戴世坤.复杂条件下3D电磁场有限元计算方法[J].中国地质大学学报,2002,27(6)：775-779.
[38]王若,王妙月,卢元林.三维三分量CASMT法有限元正演模拟研究初探[J].地球物理学进展,2007,22(2)：579-585.
[39]王烨.基于矢量有限元的高频大地电磁法三维数值模拟[D].长沙,中南大学.2008.
[40]张继峰.基于电场双旋度方程的三维可控源电磁法有限单元法数值模拟[D].长沙,中南大学.2008.
[41]Dey A, Morrison H F. Electromagnetic response of two-dimensional inhomogeneities in a dissipative half-space for Turam interpretation [J]. Geophysical Prospecting,1973,21(2):441-450.
[42]Hohmann G W. Three-dimensional induced polarization and electromagnetic modeling [J]. Geophysics,1975,40:309-324.
[43]Ting S C, Hohmann G W. Integral equation modeling of three-dimensional magnetotelluric response [J]. Geophysics,1981,46:182-197.
[44]Wannamaker P E. Hohmann G W, SanFilipo W A. Electromagnetic modeling of three-dimensional bodies in layered earths using integral equation [J]. Geophysics, 1984,49:60-74.
[45]Wannamaker P E. Advances in three-dimensional magnetotelluric modeling using integral equations [J]. Geophysics,1991,56,1716-1728.
[46]Zhdanov M S, Fand S. Quasi-linear approximation in 3-D EM modeling [J]. Geophysics,1996a,61:623-665.
[47]Avdeev D B, Kuvshinov A V, Pankratov O V. High performance three dimensional electromagnetic modeling using modified Neumann series, wide-band numerical solution and examples[J]. Journal of Geomagnetism and Geoelectricity, 1997,49,338-347.
[48]Xiong Z. EM modeling of three-dimensional structures by the method of system iteration using integral equations [J]. Geophysics,1992,57:1556-1561.
[49]Xiong Z. Domain decomposition for 3D electromagnetic modeling [J]. Earth Planets Space,1999,51:1013-1018.
[50]毛先进,鲍光淑,宋守根.半空间中多个三维电阻率响应的边界积分方程模 拟[J].地球物理学报,1996,39(6)：823-834.
[51]曹建章,唐天同,宋建平.三维电磁模拟的积分方程法[J].西安石油学院学报,1998,13(3)：65-68.
[52]鲍光淑,张碧星,敬荣中等.三维电磁响应积分方程法数值模拟[J].中南工业大学学报,1999,30(5)：472-474.
[53]徐凯军,李桐林,张辉等.利用积分方程法的大地电磁三维正演[J].西北地震学报,2006,28(2)：104-107.
[54]徐世浙.地球物理中的有限单元法[M].北京：科学出版社,1994.
[55]Yee.K.S. Numerical solution of initial boundary value problems involving maxwells equations in isotropic media [J]. IEEETrans.Ant.Prop.1966,14:302-307. Lamontagne, Y.and West, G.F. EM response of a rectangular thin plate. [J] Geophysics, 1971,36:26-30
[56]Jepsen,A.F. Numerical modeling in resistivity prospecting. [D] University of California. Berkeley.1975.
[57]Gldman, M.M., Stoyert, C.H. Finite-difference calculations of the transient field of an axiallvsvmmetric earth for vertical magnetic dipole excitation. [J] Geophysics, 1983,48:953-957.
[58]Leppin. M., Electromagnetic modeling of 3-D sources over 2-D inhomo-geneties in the time domain. [J] Geophysics,1992,57:994-1003.
[59]Smith.J.T, Booker.J.R. Rapid inversion of two and three dimensional magnetotelluric data [J].J Geophys Res,1991,96 (B3):3905-3922.
[60]Mackie.R.L, Madden.T.R, Wannamaker.P.E. Three dimensional magnetotelluric modeling using difference equations Theory and comparisons to integral equation solutions. [J]Geophysics,1993,58:215-226.
[61]Wang.T, Hohmann.G.W.A. Finite difference time domain solution for three dimensional electromagnetic modeling [J]. Geophysics,1993,58:797-809.
[62]Mackie.R.L, Smith.T.J, Madden.T.R.3-D electromagnetic modeling using difference equations [J]. The Magnetotelluric Example, RadioSci.1994,29:923-935.
[63]吴小平,徐果明.利用不完全Cholesky共轭梯度法求解点源三维电场.[J]地球物理学报,1998,41(6)：848-858.
[64]段红伟.基于模拟退火算法的实现及应用.计算机与网络[J].1999,40(5)：543-545.
[65]Spitzer. Magnetotelluric static shift and direct current sensitivity [J]. Geophys. J. Int.,2001, 144:289-299
[66]Fomenko.E.Y, Mogi.T.A new computation method for a staggeredgrid of 3D EM field conservative modeling [J]. Earth Planets Space,2002,54:499-509.
[67]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[J].地球物理学报,2003,46(5)：705-711
[68]徐凯军,李桐林.垂直有限线源三维地电场有限差分正演研究[J].吉林大学学报(地球科学版),2006,36(1)：137-147
[69]王彦飞.反演问题的计算方法及其应用[M].高等教育出版社：北京,2007
[70]王家映.地球物理反演理论[M].高等教育出版社：北京,2002.
[71]姚姚.地球物理反演基本理论与应用方法[M].中国地质大学出版社：武汉,2002.
[72]Bostick F X. A simple almost exact method of MT analysis [J]. Workshop on Electrical Methods in Geothermal Exploration,1977,175-177.
[73]Coen, S., Quercia, F., Mackiewicz, M. Direct inversion of one-dimensional MT data. JGR.1983, V.88, No. B3
[74]王家映,周一强.一维大地电磁资料的直接反演法[J].地质科技情报,1987,6(4)：104-114
[75]Gupta, P. K., Sri Niwas, V. K. Gaur. Straightforward inversion scheme (SIS) for one-dimensional magnetotelluric data [J]. Proceedings of the Indian Academy of Sciences (Earth and Planetary Sciences),1996,105:413-429
[76]Sri Niwas, P. K. Gupta, V. K. Gaur. Straightforward inversion of MT data using a normalized impedance function [J]. Geophysics,2007,72(1):F19-F24.
[77]Weidelt P. The inverse problem of geomagnetic induction [J]. Geophysics,1972, 38:257-289.
[78]Oldenburg D W. One-dimensional inversion of natural source magnetotelluric observations [J]. Geophysics,1979,44(7):1218-1244.
[79]Constable S C, Parker R L, Constable C G. Occam's inversion:a practical algorithm for generating smooth models from electromagnetic sounding data [J]. Geophysics,1987,52(3):289-300.
[80]Weaver J T, Agarwal A K. Automatic 1-D inversion of magnetotelluric data by the method of modeling [J]. Geopysics,1993,112:115-123.
[81]Parker R L, Booker J R. One-dimensional inversion and bounding of magnetotelluric apparent resistivity and phase measurements [J]. Phy.Earth Planet.Int, 1996,98:269-282.
[82]Pedersen L B, Gharibi M. Automatic 1-D inversion of magnetotelluric data: Finding the simplest possible model that fits the data[J]. Geophysics,2000, 65(3):773-782.
[83]Santos A B, Sampaio E S, Porsani M J. A robust two-step inversion of complex magnetotelluric apparent resistivity data [J]. Geophyseics,2005,49:109-125.
[84]Haber E. Quasi-Newton methods for large-scale electromagnetic inverse problems [J]. Inverse Problem,2005,21:305-323.
[85]晋光文.大地电磁相位资料的一维反演[J].地震地质,1986,10(4)：159-168.
[86]晋光文.大地电磁视电阻率和阻抗相位资料的联合反演方法研究[J].地震地质,1987,9(4)：81-86.
[87]徐世浙,刘斌.大地电磁一维连续介质反演的曲线对比法[J].地球物理学报,1995,38(5)：676-682.
[88]徐义贤,王家映.大地电磁的多尺度反演[J].地球物理学报,1998,41(5)：704-711.
[89]吴小平,徐果明.大地电磁数据的Occam反演改进[J].地球物理学报,1998,41(4)：547-554.
[90]杨振武,王家映,张胜业,高仕谦.一维大地电磁和地震数据联合反演方法研究[J].石油地球物理勘探,1998,33(1)：78-88.
[91]张大海,徐世浙.带相位信息的一维大地电磁曲线对比反演法.地震地质,2001,23(2)：227-231.
[92]苏朱刘,罗延钟,胡文宝.大地电磁测深“正演修正法”一维反演.石油地球物理勘探,2002,37(2)：138-145.
[93]严良俊、胡文宝
[94]陈小斌,赵国泽,汤吉等.大地电磁自适应正则化反演算法.地球物理学报,2005,48(4)：937-946.
[95]师学明,肖敏,范建柯等.大地电磁阻尼粒子群优化反演法研究[J].地球物理学报,2009,52(4)：1114-1120.
[96]Zhdanov M S, Fang S.3-D quasi-linear electromagnetic inversion [J]. Radio Science,1996,31:741-754.
[97]Zhdanov M S, Fang S, Hursan G. Electromagnetic inversion using quasi-linear approximation [J]. Geophysics,2000,65:1501-1513.
[98]Zhdanov M S, Hursan G 3-D electromagnetic inversion based on quasi-analytical approximation [J]. Inverse Problems,2000,16:1297-1322.
[99]Zhdanov M S, Golubev N, Hursan G. Rapid 3-D inversion of the array magnetotelluric data [J]. PEPI,2003.
[100]Mackie R L, Rieven R, Rodi W. Users manual and software documentation for two-dimensional inversion of magnetotelluric data [M]. Department of Geological Sciences, Indiana University,1997.
[101]de Lugao P, Wannamaker P E. Calculating the two-dimensional magnetotelluric Jacobian in finite elements using reciprocity[J]. Geophysics,1996,127:806-810.
[102]Newman G A, Alumbaugh D L. Three-dimensional massively parallel inversion [J]. Geophysics,1997,128:355-363.
[103]Newman G A, Alumbaugh D L. Three-dimensional magnetotelluric inversion using non-linear conjugate gradients [J]. Geopysics,2000,140:410-424.
[104]Haber E, Oldenburg D. A GCV based method for nonlinear ill-posed problems [J]. Computational Geosciences,2000,4:41-63.
[105]Oldenburg D W. One-dimensional inversion of natural source magnetotelluric observations [J]. Geophysics,1979,44(7):1218-1244.
[106]Oldenburg, D.W. Inversion of electromagnetic data:An overview of new techniques [J]. Surveys in Geophysics,1990,11:231-270.
[107]Oldenburg, D.W.& Ellis, R.G. Efficient inversion of magnetotelluric data in two dimensions, Phys. Earth planet [J]. Inter.,1993,81:177-200
[108]Oldenburg, D.W., McGillivray, P.R.& Ellis, R.G. Generalised subspace methods for large scale inverse problems, Geophys.[J]. J. Int.,1993,114:12-20
[109]Ellis R.G, Oldenburg D.W. Applied geophysical inversion [J]. Geophys.J.Int., 1994,116:5-11
[110]Aruliah D, AscherU, Haber E, et al. A method for the forward modelling of 3D electromagnetic quasi-static problems [J]. Math Modelling Applied Sciences,2001, 11(1):1-21.
[111]Sasaki Y.. Two-dimensional joint inversion of magnetotelluric and dipole-dipole resistivity data [J]. Geophysics,1989,54(2):254-262
[112]Sasaki Y. Full 3-D inversion of electromagnetic data on PC [J]. Journal of Applied Geophysics,2001,45-54.
[113]DeGroot-Hedlin C., Constable S C. Occam's inversion to generate smooth, two-dimensional models from electromagnetic sounding data [J]. Geophysics,1990, 55:1613-1624
[114]Smith T, Hoversten M, Gasperikova E, et al. Sharp boundary inversion of 2D magnetotelluric data [J]. Geophysical Prospecting,1999,47:469-486.
[115]Loke M H, Barker R D. Rapid least-squares inversion of apparent resistivity pseudo sections by a quasi-Newton method [J]. Geophysical Prospecting,1996a, 44:131-152
[116]Loke M H, Barker R D. Practical techniques for 3D resistivity surveys and data inversion [J]. Geophysical Prospecting,1996b,44:499-524
[117]Michael M D, Guust N. Nullspace shuttles [J]. Geophys. J. Int.,1996, 124:372-380
[118]Spichak V, Menville M, Roussignol M. Three dimensional inversion of the magnetotelluric fields using Bayesian statistics [C]. In Proc. Schlumberger Doll Research Symp. on 3D Elect romagnetics, eds Spies B and Oristaglio M, USA,1995, 347-358.
[119]Spichak V and Popova. Artificial neural network inversion of magnetotelluric data in terms of three deimensional earth macroparameters [J]. Geophys J Int,2000, 142:15-26
[120]孙必俊,陈乐寿,王光锷等.关于大地电磁测深资料反演问题[J].地球物理学报,1985,28(2)：218-229.
[121]赵国泽,刘国栋.一种二维大地电磁反演方法[J].地震地质,1985,7：56-58.
[122]吴广耀,胡建德.大地电磁资料的二维连续模型自动反演[J].地球科学-中国地质大学学报.1990,5(增刊)：23-36.
[123]陈乐寿,王光锷等人.一种大地电磁成像技术[J].地球物理学报,1993,36(3)：337-346.
[124]吴小平,吴广耀,胡建德.二维最平型的大地电磁快速反演[J].地球科学-中国地质大学学报,1994,19(6)：821-829.
[125]杨长福,林长佑.大地电磁二维层状模型参数化反演[J].西北地震学报,1994,16(4)：10-19.
[126]戴世坤,徐世浙.MT二维和三维连续介质快速反演[J].石油地球物理勘探,1997,32(3)：305-317.
[127]翁爱华,刘国兴.大地电磁测深资料的超球逼近反演[J].长春科技大学学报,1998,28(3)：330-334.
[128]张翔,胡文宝.带地形的大地电磁测深联合二维反演[J].石油地球物理勘探,1999,34(2)：190-196.
[129]师学明,王家映等.多尺度逐次逼近遗传算法反演大地电磁资料[J].地球物理学报,2000,43(1)：122-130.
[130]苏朱刘,胡文宝.大地电磁测深“降维逼近法”二维反演[J].石油地球物理勘探.2002,37(5)：516-523.
[131]杨辉,王永寿,王家林等人.大地电磁测深拟二维模拟退火约束反演[J].海象油气地质,2001,6(1)：47-52.
[132]谭捍东,余钦范,John Booker等.大地电磁法三维快速松弛反演[J].地球物理学报,2003,46(6)：850-855.
[133]毛立峰,王绪本,高永才.大地电磁概率成像的效果评价[J].地球物理学报,2005,48(2)：429-433.
[134]毛立峰.大地电磁概率成像方法研究[D].成都,成都理工大学.2004.
[135]魏超,朱培民,王家映.量子退火反演的原理和实现[J].地球物理学报,2006,49(2)：577-583.
[136]胡祖志,胡祥云,何展翔.三维大地电磁数据的二维反演解释[J].石油地球物理勘探,2005,40(3)：353-359
[137]刘小军,王家林,吴健生.二维大地电磁正则化共轭梯度法反演算法[J].上海地质,2007a,101(1)：71-74.
[138]刘小军,王家林,陈冰等.二维大地电磁数据的聚焦反演算法探讨[J].石油地球物理勘探,2007b,42(3)：338-342.
[139]张罗磊,于鹏,王家林,吴建生.光滑模型与尖锐边界结合的MT二维反演方法[J].地球物理学报,2009,52(6)：1625-1632.
[140]刘苗,吴建生,于鹏,张罗磊.基于二维小波分解的MT二维反演方法[J].物探与化探,2009,33(3)：337-341.
[141]陈小斌,赵国泽.自动构建大地电磁二维反演的测点中心网格[J].地球物理学报,2009,52(6)：1564-1572.
[142]汤井田,任政勇,化希瑞.地球物理学中的电磁场正演与反演[J].地球物理学进展,2007,22(4)：1181-1194
[143]周军.大地电磁测深视电阻率与阻抗相位联合反演研究[D].成都,成都理工大学,2008.
[144]晋光文.大地电磁资料联合反演评述[J].地球科学-中国地质大学学报,1990,15(曾)：59-67.
[145]Zhdanov M S, Varentov I M. Methods for modeling electromagnetic fields: Results from COMMEMI-the international project on the comparison of modeling methods for electromagnetic induction [J]. Journal of Applied Geophysics,1997, 44:337-351.
[146]J. Torquil Smith, John R. Booker. Magnetotelluric Inversion for minimum structure [J]. GEOPHYSICS.1988,53(12):1565-1576.
[147]李帝铨,王光杰,底青云.基于遗传算法的CSAMT最小构造反演[J].地球物 理学报.2008,51(4)：1234-1245.
[148]Colin G. Farquharson. Constructing piecewise-constant models in multi-dimensional minimum-structure inversions [J]. Geophysics,2008,73(l):kl-k9.
[149]陈小斌.大地电磁正反演新算法研究及资料处理与解释可视化集成系统开发[D].北京,中国地震地质研究所.2003
[150]Colin G. Farquharson, Douglas W. Oldenburg. Non-linear inversion using general measures of data misfit and model structure [J]. Geophys. J. Int.,1998,134:213-227.
[151]Oleg Portniaguine, Michael S. Zhdanov. Focusing geophysical inversion images [J]. GEOPHYSICS,1999,64(3):874-887,
[152]刘海飞,阮百尧,柳建新等.混合范数下的最优化反演方法[J].地球物理学报,2007,50(6)：1877-1883
[153]李墩柱,黄清华,陈小斌.误差对大地电磁测深反演的影响[J].地球物理学报,2009,52(1)：268-274
[154]Huber, P. J. Robust estimation of a location parameter [J]. Annals of Mathematical Statistics,1964,35:73-101.
[155]Ekblom, H., The Ll-estimate as limiting case of an Lp-or Huber-estimate, in Y. Dodge, ed., Statistical data analysis based on the L1-norm and related methods [J]. Elsevier Science Publ.Co., Inc.,1987,109-116.
[156]Last, B. J., K. Kubik. Compact gravity inversion [J]. Geophysics,1983, 48:713-721.
[157]P. R. McGillivray, D. W. Oldenburg. Methods for calculating Frechet and sensitivities for the nonlinear inverse problem:a comparative study [J]. Geophys. Prosp.,1990,38:499-524.
[158]P. R. McGillivray, D. W. Oldenburg, et al. Calculation of sensitivities for the frequency-domain electromagnetic problem [J]. Geophys. J. Int.,1994,116:1-4.
[159]C. G. Farquharson. Approximate Sensitivities for the Multi-Dimensional Electromagnetic Inverse Problem [D]. University of Edinburgh,1995.
[160]C. G. Farquharson, D. W. Oldenburg. Approximate sensitivities for the electromagnetic inverse problem [J]. Geophys. J. Int.,1996,126:235-252.
[161]P. P. de Lugao, P. E. Wannamaker. Calculating the two-dimensional magnetotelluric Jacobian in finite elements using reciprocity [J]. Geophys. J. Int.,1996,127:806-810.
[162]晋光文.大地电磁资料的灵敏度研究[J].地球物理学报,1991,34(4)：465-473.
[163]李世雄,刘家淇.小波变换和反演数学基础[M].北京:地质出版社,1994.
[164]刘贵忠,邸双亮.小波分析及其应用[M].西安：西安电子科技大学出版 社,1992.
[165]宋守根,汤井田,何继善.小波分析与频率电磁测深中静态效应的识别、分离和压制[J].地球物理学报,1995,38(1)：120-127.
[166]汤井田,宋守根,何继善.多分辨分析和重磁异常的识别与分层次提取[J].中国有色金属学报,1994,4(3)：6-15.
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