复电阻率法三维正反演问题研究
|
摘要
电磁法勘探是一种有效的地球物理手段,随着高分辨率探测技术的发展,对电磁法正反演技术要求也越来越高。复电阻率法可以用多个参数从不同角度评价地质异常体,适合做精细反演解释。目前,复电阻率法正反演方法还不能满足实际工作的要求,三维数值模拟及反演解释仍处于探索阶段。本文研究复电阻率法三维正反演算法,推动复电阻率法正反演进入实用化阶段。
复电阻率法三维正演问题采用交错采样有限差分算法。选取有限长度电偶源,将总场分解成一次场和二次场分别求解。在有限长度电偶源激发下,通过解层状介质的边值问题,采用快速汉克尔变换计算得到一次场的分布。基于Cole-Cole模型建立复电阻率模型,采用交错网格对研究区域剖分,将连续的积分方程离散化,设定边界处二次场值为零,形成线性方程组,解线性方程组可得到二次场。通过与已有算法计算结果对比来检验了三维交错采样有限差分算法的精度。
复电阻率法三维反演的目的是获得Cole-Cole模型参数的分布,本文采用了三维共轭梯度—最小二乘顺序反演方案。为了获得每个网格单元随频率变化的复电阻率值,三维共轭梯度反演应用“拟正演”算法,每进行一次模型参数更新量计算只需要1次正演和2次“拟正演”,避免实际计算雅克比矩阵。计算雅可比矩阵的转置与一个向量的乘积可得到模型的更新方向,雅可比矩阵与另一个向量的乘积可得到模型更新步长。计算中仅需存储上一次反演模型更新方向,有效减小了存储空间的需求。
对三维共轭梯度反演获得的复电阻率模型,利用最小二乘法反演获得每个网格单元Cole-Cole模型参数的分布。使用理论模型合成数据对反演算法的稳定性和有效性进行了检验。
Electromagnetic method exploration is one of effective geophysical methods. High resolution exploring technology was developed in recent year, which asked for more efficient forward modeling and inversion method. Complex Resistivity(CR) method could be used for analyzing abnormally from different way with several parameters, and the method was suitable for small scale inversion. CR modeling and inversion technology could not meet the needs from application; Three Dimension(3D) modeling and inversion were still in the stage of researching. We carry out 3D CR modeling and inversion in the thesis, and made some progress in artificial data inversion.
We choose 3D staggered grid finite difference method to solve modeling problem. Finite length electric dipole source was used to calculate electromagnetic field. Total field was divided into primary field and secondary field. Primary field was calculated by solving layer earth with finite length electric dipole source, Hankel transform was also used in the calculation. We set up CR with Cole-Cole model and mesh grid with staggered grid. After discretizing continual integral equation, linear equation was formed. Direchlet boundary was used as boundary condition. Secondary field could be obtained by solving linear equation. Cross check was made with integral equation code to testify accuracy of 3D staggered simulation method.
The goal of CR 3D inversion is to get distribution of Cole-Cole model parameters, 3D Conjugate Gradient(CG) Least Square sequence inverse method was used as inversing method. In order to get the CR model parameter in each cell that changes with frequency, pseudo-modeling was used in 3D CG inversion to avoid computing Jacobin matrix. One time modeling and two time pseudo-modeling were computed in each time inversion. Updating direction was obtained by computing transformed Jacobin matrix multiply with a vector, updating step could be obtained by Jacobin matrix multiply with another vector. Updating vector was the only vector need be stored in each inversion, demands for storage space was decreased.
CR model could be got by 3D CG inversion. Least square method was used to obtain Cole-Cole model parameter in each cell. Artificial data by theoretical model was used to check the stabilization and validation of the code.
复电阻率法三维正演问题采用交错采样有限差分算法。选取有限长度电偶源,将总场分解成一次场和二次场分别求解。在有限长度电偶源激发下,通过解层状介质的边值问题,采用快速汉克尔变换计算得到一次场的分布。基于Cole-Cole模型建立复电阻率模型,采用交错网格对研究区域剖分,将连续的积分方程离散化,设定边界处二次场值为零,形成线性方程组,解线性方程组可得到二次场。通过与已有算法计算结果对比来检验了三维交错采样有限差分算法的精度。
复电阻率法三维反演的目的是获得Cole-Cole模型参数的分布,本文采用了三维共轭梯度—最小二乘顺序反演方案。为了获得每个网格单元随频率变化的复电阻率值,三维共轭梯度反演应用“拟正演”算法,每进行一次模型参数更新量计算只需要1次正演和2次“拟正演”,避免实际计算雅克比矩阵。计算雅可比矩阵的转置与一个向量的乘积可得到模型的更新方向,雅可比矩阵与另一个向量的乘积可得到模型更新步长。计算中仅需存储上一次反演模型更新方向,有效减小了存储空间的需求。
对三维共轭梯度反演获得的复电阻率模型,利用最小二乘法反演获得每个网格单元Cole-Cole模型参数的分布。使用理论模型合成数据对反演算法的稳定性和有效性进行了检验。
Electromagnetic method exploration is one of effective geophysical methods. High resolution exploring technology was developed in recent year, which asked for more efficient forward modeling and inversion method. Complex Resistivity(CR) method could be used for analyzing abnormally from different way with several parameters, and the method was suitable for small scale inversion. CR modeling and inversion technology could not meet the needs from application; Three Dimension(3D) modeling and inversion were still in the stage of researching. We carry out 3D CR modeling and inversion in the thesis, and made some progress in artificial data inversion.
We choose 3D staggered grid finite difference method to solve modeling problem. Finite length electric dipole source was used to calculate electromagnetic field. Total field was divided into primary field and secondary field. Primary field was calculated by solving layer earth with finite length electric dipole source, Hankel transform was also used in the calculation. We set up CR with Cole-Cole model and mesh grid with staggered grid. After discretizing continual integral equation, linear equation was formed. Direchlet boundary was used as boundary condition. Secondary field could be obtained by solving linear equation. Cross check was made with integral equation code to testify accuracy of 3D staggered simulation method.
The goal of CR 3D inversion is to get distribution of Cole-Cole model parameters, 3D Conjugate Gradient(CG) Least Square sequence inverse method was used as inversing method. In order to get the CR model parameter in each cell that changes with frequency, pseudo-modeling was used in 3D CG inversion to avoid computing Jacobin matrix. One time modeling and two time pseudo-modeling were computed in each time inversion. Updating direction was obtained by computing transformed Jacobin matrix multiply with a vector, updating step could be obtained by Jacobin matrix multiply with another vector. Updating vector was the only vector need be stored in each inversion, demands for storage space was decreased.
CR model could be got by 3D CG inversion. Least square method was used to obtain Cole-Cole model parameter in each cell. Artificial data by theoretical model was used to check the stabilization and validation of the code.
引文
Andrey N.Tikhonov, Vasiliy Y Arsenin. Solution of ill-posed problems. Washington D.C:V.H. Winston & Sons,1977
Avdeev D B, Avdeeva A D. A rigorous three-dimensional magnetotelluric inversion. Progress in Electromagnetics Research,2006,62:41-48
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. Journal of Geomagnetism and Geoelectricity,1997,49:338-347
Bleil D F. Induced polarization:A method of geophysical prospecting. Geophysics,1953, 18:636-661
Brewitt-Taylor C R, Weaver J T. On the finite difference solution of two-dimensional induction problems. Geophysics,1976,47:375-396
Brown RJ. EM coupling in multi-frequency IP and a generalization of the Cole-Cole impedance model, Geophysical prospecting,1985,33:282-302
Coggon J H. Electromagnetic and electrical modeling by the finite element method. Geophysics, 1971,36(2):132-151
Constable S C, Parker R L, Constable C G. Occam's inversion:A practical algorithm for generating smooth models from electromagnetic sounding data. Geophysics,1987,52:289-300
de Groot-Hedlin C, Constable S. Occam's inversion to generate smooth, two-dimensional models from magnetotelluric data. Geophysics,1990,55(12):1613-1624
de Lugao P, Portnigauine O, Zhdanov M S. Fast and stable two-dimensional inversion of magnetotelluric data. Journal of Geomagnetism and Geoelectricity,1997,49:1469-1497
de Lugao P, Wannamaker P E. Calculating the two-dimensional magnetotelluric Jacobian in finite elements using reciprocity. Geophysics,1996,127:806-810
Dey A, Morrison H F. Electromagnetic coupling in frequency and time-domain induced polarization surveys over a multilayered earth. Geophysics,1973,38(2):380-405
Dey A, Morrison H F. Electromagnetic response of two-dimensional inhomogeneities in a dissipative half-space for Turam interpretation. Geophysical Prospecting,1973,21(2):441-450
Dias C A. Developments in a model to describe low-frequency electrical polarization of rocks. Geophysics,2000,65:437-451
Fomenko E Y, Mogi T. A new computation method for a staggered grid of 3D EM field conservative modeling. Earth Planets Space,2002,54:499-509
Franke A, Ralph B, Klaus S.2D finite element modeling of plane-wave diffusive time-harmonic electromagnetic fields using adaptive unstructured grids. Proceeding of the 17th workshop,2004, S.2: 1-6
Gupysdstms D. Effect of surface polarization on resistivity modeling. Geophysics,1983, 48:98-106
Gupysdstms D. True and apparent spectra of buried polarizable targets. Geophysics, 1984,49:98-106
Haber E, Ascher U, and Oldenburg D. Fast simulation of 3D electromagnetic problems using potentials. Journal of Computational Physics,2000,163:150-171
Hallof P G On the interpretation of resistivity and induced polarization results:[Ph.D. thesis]. Massachusetts Institute of Technology
Hohmann G W. Three-dimensional induced polarization and electromagnetic modeling. Geophysics,1975,40:309-324
Jaggar S R, Fell, P A. Fowward and inverse Cole-Cole modeling in analysis of frequency domain electrical impedance data. Expl. Geophys,1988,19:463-470
Jones F W, Pascoe A J. Geomagnetic effects of sloping and shelving discontinuities of earth conductivity. Geophysics,1971,36:58-66
Kaijun Xu. Three-dimensional Complex Resistivity Modelling and Inversion with Topography. EGU2011,2011,13:125-125
Mackie R L, Madden T R, Wannamaker P E. Three-dimensional magnetotelluric modeling using difference euuations-theory and comparisons to integral equation solutions. Geophysics,1994,58: 215-226
Mackie R L, Madden T R. Three-dimensional magnetotelluric inversion using conjugate gradients. Geophys J Int,1993,115:215-229
Mackie R L, Smith J I, Madden T R. Three-dimensional electromagnetic modeling using finite difference equations:The magnetotelluric example. Radio Science,1994,29:923-936
Mackie R L, Rieven R, Rodi W. Users manual and software documentation for two-dimensional inversion of magnetotelluric data. Indiana:Department of Geological Sciences, Indiana University, 1997
Madden T R. Transmission systems and network analogies to geophysical forward and inversion problem. ONR Technical Report,1972:72-83
Major J, Silic J. Restrictions on the use of Cole-Cole dispersion models in complex resistivity interpretation. Geophysics,1981,46(6):916-931
Meng YL, Luo YZ. Calculation of harmonic electromagnetic field and scale modeling laws of surface polarizable bodies. Chinese journal of Geophysics,1989,32:145-158
Mitsuhata Y, Uchida T.3D magnetotelluric modeling using the T-Ω finite-element method.Geophysics,2004,69:108-119
Mogi T. Three-dimensional modeling of magnetotelluric data using finite-element method. Journal of Applied Geophysics,1996,35:185-189
Newman G A, Alumbaugh D L. Three-dimensional magnetotelluric inversion using non-linear conjugate gradients. Geophysics,2000,140:410-424
Newman G A, Alumbaugh D L. Three-dimensional massively parallel electromagnetotelluric inversion-Ⅰ.Theory. Geophys J Int,1997,128:345-354
Newman G A, Alumbaugh D L. Three-dimensional massively parallel electromagnetotelluric inversion-Ⅱ.Analysis of a crosswell electromagnetic experiment. Geophys J Int,1997,128:355-363
Newman G A. Solution accelerators for large-scale 3D electromagnetic inverse problems.74th Ann Internat Mtg Expl Geophys Expanded Abstracts,2004
Pelton W H, Ward S H, Hallof P G. et al. Mineral discrimination and removal of inductive coupling with multrfrequency IP. Geophysics,1978,43(3):588-609
Reddy I K. Three-dimensional modeling in magnetotelluric and magnetic variational sounding. Geophysics,1977,51:313-325
Rijo L. Modeling of electric and electromagnetic data:[Ph.D dissertation], University of Utah, 1977
Rodi W, Mackie R L. Nonlinear conjugate gradient algorithm for 2-D magnetotelluric inversion. Geophysics,2001,66:174-187
Sasaki Y. Three-dimensional frequency-domain electromagnetic modeling using the finite-difference method. Geophysics Exploration,1999,52:421-431
Seigel H O. Mathematical formulation and type curves for induced polarization. Geophysics, 1959,24:547-565
Siripunvaraporn W, Egbert G, Lenbury Y, et al. Three-dimensional magnetotelluric inversion: data-space method. Physics of The Earth and Planetary Interiors,2005,150(1-3):3-14
Siripunvaraporn W, Egbert G. An efficient data-subspace inversion method for 2-D magnetotelluric data. Geophysics,2000,65:791-803
Smith J T, Booker J R. Rapid inversion of two-and three-dimensional magnetotelluric data. J. Geophys Res,1991,96:3905-3922
Smith J T. Conservative modeling of 3-D electromagnetic fields, Part Ⅰ:Properties and error analysis. Geophysics,1996,61:1308-1318
Smith J T. Conservative modeling of 3-D electromagnetic fields, Part Ⅱ:Biconjugate gradient solution and an accelerator. Geophysics,1996b,61:1319-1324
Soininen H. The behavior of the apparent resistivity phase spectrum in the case of a polarizable prism in an unpolarizable half-space. Geophysics,1984,49:1534-1540
Soininen H. The behavior of the apparent resistivity phase spectrum in the case of two polarizable media. Geophysics,1985,50:810-819
Spichak V, Popova. Artificial neural network inversion of magnetotelluric data in terms of three-deimensional earth macroparameters. Geophys J Int,2000,142:15-26
Swift C M. Theoretical magnetotelluric and Turam response from two-dimensional inhomogeneities. Geophysics,1971,36:1-12
Tan Handong, Tongtuo and Lin Changhong. The parallel 3D magnetotelluric forward modeling algorithm. Applied Geophysics,2006,3(4):197-202
Ting S C, Hohmann G W. Integral equation modeling of three-dimensional magnetotelluric response. Geophysics,1981,46:182-197
Wait J R. Overvoltage research and its geophysical applications:Pergamon Press, Inc
Wang T, Hohmann G W. A finite difference time-domain solution for three dimensional electromagnetic modeling. Geophysics,1993,58:797-809
Wang T, Fang S.3-D electromagnetic anisotropy modeling using finite difference. Geophysics, 2001,66:1386-1398
Wang Xiangchun,Liu Xuewei.3-D acoustic wave equation forward modeling with topography. Applied Geophysics,2007,4(1):8-15
Wannamaker P E, Hohmann G W, SanFilipo W A. Electromagnetic modeling of three-dimensional bodies in layered earths using integral equation. Geophysics,1984,49:60-74
Wannamaker P E, Stodt J A, Rijo L. A stable finite element solution for two-dimensional magnetotelluric modeling. Geophysics,1987,88:277-296
Wannamaker P E, Stodt J A, Rijo L. Two-dimensional topographic responses in magnetotelluric model using finite elements, Geophysics,1986,51:2131-2144
Wannamaker P E. Advances in three-dimensional magnetotelluric modeling using integral equations. Geophysics,1991,56:1716-1728
Weerachai S, Egbert G, Lenbury Y. Numerical accuracy of magnetotelluric modeling:A comparison of finite difference approximations. Earth Planets Space,2002,54:721-725
William L, Rodi. A technique for improving the accuracy of finite element solution for magnetotelluric data. Geophysics,1976,44:483-506
Wong J. An electrochemical model of the IP phenomenon in disseminated sulfide ores, Geophysics 1979,44:1245-1265
Xiang J, N B Jones, D Cheng et al. direct inversion of the apparent complex-resistivity spectrum. Geophysics,2001,66(5):1399-1404
Xiong Z, Luo Y, Wang S et al. Induced-polarization and electromagnetic modeling of a three-dimensional body in a two-layer anisotropic earth, Geophysics 1986,51:2235-2246
Xiong Z. Domain decomposition for 3D electromagnetic modeling. Earth Planets Space,1999, 51:1013-1018
Xiong Z. EM modeling of three-dimensional structures by the method of system iteration using integral equations. Geophysics,1992,57:1556-1561
Zhdanov M S, Fand S. Quasi-linear approximation in 3-D EM modeling. Geophysics,1996a,61: 623-665
Zhdanov M S, Fang S, Hursan G. Electromagnetic inversion using quasi-linear approximation. Geophysics,2000,65(5):1501-1513
Zhdanov M S, Keller G V. The geoelectrical methods in geophysical exploration[M]. Methods in Geochemisty and Geophysics,1994
Zonge K L, Hughes L J, Carlson N R. Hydrocarbon exploration using induced polarization,apparent resistivity and electromagnetic scattering, Presented at the fifty-first annual international meeting and exposition SEG,1981
Zyserman F I, Santos J E. Parallel finite element algorithm with domain decomposition for three-dimensional magnetotelluric modeling. Journal of Applied Geophysics,2000,44:337-351
Zyserman F I, Santos J E. Parallel finite element algorithm with domain decomposition of three-dimensional magnetotelluric modeling. Journal of Applied Geophysics,2000,44:337-351
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.中南工业大学学报,1999,30(5)：472-474
曹建章,唐天同,宋建平.三维电磁模拟的积分方程法.西安石油学院学报,1998,13(3)：65-68
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.石油地球物理勘探,1982,17(3)：69-72
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.石油物探,1981,20(3)：84-103
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.石油地球物理勘探,2000,35(4)：487-496
陈小斌.有限元直接迭代算法.物探化探计算技术,1999,21(2)：165-171
傅良魁,张虎豹.频谱激电法中的若干理论研究,物探与化探,1985,9:410-419
傅良魁.复电阻率法异常的频谱及空间分布规律,物探与化探,1981,46-53
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.石油地球物理勘探,1984,19(4)：358-367
胡建德,王光愕,陈乐寿等.大地电磁二维正演计算中若干问题的讨论.石油地球物理勘探,1982,17(6)：47-55
黄临平,戴世坤.复杂条件下3D电磁场有限元计算方法.中国地质大学学报,2002,27(6)：775-779
柯马罗夫B.A著,激发极化电法勘探(阎立光等译),北京：地质出版社,1983
李建平.带地形的三维复电阻率电磁场正反演研究：[博士学位论文].吉林大学,2008
李学民,曹俊兴,贺桃娥.断层构造的大地电磁响应曲线变化特征的研究.天然气工业,2004,24(7)：42-57
李予国,徐世浙,刘斌等.电导率连续变化的MT有限元正演(Ⅱ).高校地质学报,1996,2(4)：448-452
林昌洪.大地电磁张量阻抗三维共轭梯度反演研究：[博士学位论文].中国地质大学(北京),2009
刘春明.伪随机激电多参数谱法研究：[博士学位论文].中南大学,2006
刘树才,周圣武.二维电法数值模拟中的网格剖分方法.物化探计算技术,1995,17(1)：49-53
刘崧,官善友,高鹏飞.求极化椭球体真cole-cole参数的联合谱激电反演.地球物理学报,1994,37(增刊2)：542-551
刘崧,薛继安,徐建华.求地下真柯尔—柯尔参数的研究.物探与化探,2000,24(1)：51-61
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.同济大学学报,2007,35(8)：1113-1117
刘正栋,关洪军,聂永平等.稳定点电流源场三维有限差分正演模拟.解放军理工大学学报,2000,1(3)：45-50
罗延钟,方胜.视复电阻率频谱的一种近似反演方法,地球科学,1986,11：93-102
罗延钟,万乐.二维地形不平条件下外电场的有限差分模拟.物化探计算技术,1984,6(4)：15-26
罗延钟,万乐.用数值模拟方法构组保角变换坐标网.物化探计算技术,1986,8(1)：23-31
罗延钟,吴之训.谱激电法中频率相关系数的应用.地球物理学报,1992,35(4):490-499
罗延钟,张桂青.频率域激电法原理.北京：地质出版社,1988
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.地球物理学报,1996,39(6)：823-834
裴正林.三维各向异性介质中弹性波方程交错网格高阶有限差分模拟.石油大学学报(自然科学版),2004,28(5)：23-29
阮百尧,罗涧林等.一种新的复电阻率频谱参数递推反演方法,物化探计算技术,2003,25(4)：298-301
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,2003,46(2)：281-289
宋维琪,全兆歧.3-D瞬变电磁场的有限差分正演计算.石油地球物理勘探,2000,35(6)：751-756
谭捍东,余钦范,魏文博等.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, 2003,46(5)：705-711
汤井田,任政勇,化希瑞.地球物理学中的电磁场正演与反演.地球物理学进展,2007,22(4)：1181-1194
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.地球物理学进展,2007,22(2)：579-585
王自力,张赛珍.一种真复电阻率谱参数的求解方法,地球物理学报,1990,33:712-727
吴小平,徐果明.利用不完全Cholesky共轭梯度法求解电源三维电场,地球物理学报,1998,41(6)：848-855
邢涛等.大定源瞬变电磁法三维正演程序开发.工程地球物理学报,2008,5(6)：664-669
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.西北地震学报,2006,28(2)：104-107
徐凯军.2.5维复电阻率电磁场正反演研究：[博士学位论文].吉林大学,2007
徐世浙,刘斌.点源二维电场中纵剖面上电位的计算.地球物理学报,1996,39(4):551-560
徐世浙,于涛,李予国等.电导率连续变化的MT有限元正演(Ⅰ).高校地质学报,1995,1(2)：65-73
徐世浙.地球物理中的有限单元法.北京：科学出版社,1994
徐志峰.频率域可控源电磁三维正演：[博士学位论文].中国科学技术大学,2010
张辉.复电阻率三维电磁场正反演研究：[博士学位论文].吉林大学,2006
赵广茂.带地形的复电阻率2.5维电磁场正反演研究：[博士学位论文].吉林大学,2009
赵生凯,徐世浙.有限单元法计算良导嵌入体的大地电磁测深曲线.物探化探计算技术,1983,5(1)：14-21
周熙襄,钟本善,江东玉.点源二维电阻率法有限差分正演计算.物化探电子计算技术,1983,5(3)：34-38
朱伯芳.有限单元法原理与应用.北京：水利出版社,1979
Avdeev D B, Avdeeva A D. A rigorous three-dimensional magnetotelluric inversion. Progress in Electromagnetics Research,2006,62:41-48
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. Journal of Geomagnetism and Geoelectricity,1997,49:338-347
Bleil D F. Induced polarization:A method of geophysical prospecting. Geophysics,1953, 18:636-661
Brewitt-Taylor C R, Weaver J T. On the finite difference solution of two-dimensional induction problems. Geophysics,1976,47:375-396
Brown RJ. EM coupling in multi-frequency IP and a generalization of the Cole-Cole impedance model, Geophysical prospecting,1985,33:282-302
Coggon J H. Electromagnetic and electrical modeling by the finite element method. Geophysics, 1971,36(2):132-151
Constable S C, Parker R L, Constable C G. Occam's inversion:A practical algorithm for generating smooth models from electromagnetic sounding data. Geophysics,1987,52:289-300
de Groot-Hedlin C, Constable S. Occam's inversion to generate smooth, two-dimensional models from magnetotelluric data. Geophysics,1990,55(12):1613-1624
de Lugao P, Portnigauine O, Zhdanov M S. Fast and stable two-dimensional inversion of magnetotelluric data. Journal of Geomagnetism and Geoelectricity,1997,49:1469-1497
de Lugao P, Wannamaker P E. Calculating the two-dimensional magnetotelluric Jacobian in finite elements using reciprocity. Geophysics,1996,127:806-810
Dey A, Morrison H F. Electromagnetic coupling in frequency and time-domain induced polarization surveys over a multilayered earth. Geophysics,1973,38(2):380-405
Dey A, Morrison H F. Electromagnetic response of two-dimensional inhomogeneities in a dissipative half-space for Turam interpretation. Geophysical Prospecting,1973,21(2):441-450
Dias C A. Developments in a model to describe low-frequency electrical polarization of rocks. Geophysics,2000,65:437-451
Fomenko E Y, Mogi T. A new computation method for a staggered grid of 3D EM field conservative modeling. Earth Planets Space,2002,54:499-509
Franke A, Ralph B, Klaus S.2D finite element modeling of plane-wave diffusive time-harmonic electromagnetic fields using adaptive unstructured grids. Proceeding of the 17th workshop,2004, S.2: 1-6
Gupysdstms D. Effect of surface polarization on resistivity modeling. Geophysics,1983, 48:98-106
Gupysdstms D. True and apparent spectra of buried polarizable targets. Geophysics, 1984,49:98-106
Haber E, Ascher U, and Oldenburg D. Fast simulation of 3D electromagnetic problems using potentials. Journal of Computational Physics,2000,163:150-171
Hallof P G On the interpretation of resistivity and induced polarization results:[Ph.D. thesis]. Massachusetts Institute of Technology
Hohmann G W. Three-dimensional induced polarization and electromagnetic modeling. Geophysics,1975,40:309-324
Jaggar S R, Fell, P A. Fowward and inverse Cole-Cole modeling in analysis of frequency domain electrical impedance data. Expl. Geophys,1988,19:463-470
Jones F W, Pascoe A J. Geomagnetic effects of sloping and shelving discontinuities of earth conductivity. Geophysics,1971,36:58-66
Kaijun Xu. Three-dimensional Complex Resistivity Modelling and Inversion with Topography. EGU2011,2011,13:125-125
Mackie R L, Madden T R, Wannamaker P E. Three-dimensional magnetotelluric modeling using difference euuations-theory and comparisons to integral equation solutions. Geophysics,1994,58: 215-226
Mackie R L, Madden T R. Three-dimensional magnetotelluric inversion using conjugate gradients. Geophys J Int,1993,115:215-229
Mackie R L, Smith J I, Madden T R. Three-dimensional electromagnetic modeling using finite difference equations:The magnetotelluric example. Radio Science,1994,29:923-936
Mackie R L, Rieven R, Rodi W. Users manual and software documentation for two-dimensional inversion of magnetotelluric data. Indiana:Department of Geological Sciences, Indiana University, 1997
Madden T R. Transmission systems and network analogies to geophysical forward and inversion problem. ONR Technical Report,1972:72-83
Major J, Silic J. Restrictions on the use of Cole-Cole dispersion models in complex resistivity interpretation. Geophysics,1981,46(6):916-931
Meng YL, Luo YZ. Calculation of harmonic electromagnetic field and scale modeling laws of surface polarizable bodies. Chinese journal of Geophysics,1989,32:145-158
Mitsuhata Y, Uchida T.3D magnetotelluric modeling using the T-Ω finite-element method.Geophysics,2004,69:108-119
Mogi T. Three-dimensional modeling of magnetotelluric data using finite-element method. Journal of Applied Geophysics,1996,35:185-189
Newman G A, Alumbaugh D L. Three-dimensional magnetotelluric inversion using non-linear conjugate gradients. Geophysics,2000,140:410-424
Newman G A, Alumbaugh D L. Three-dimensional massively parallel electromagnetotelluric inversion-Ⅰ.Theory. Geophys J Int,1997,128:345-354
Newman G A, Alumbaugh D L. Three-dimensional massively parallel electromagnetotelluric inversion-Ⅱ.Analysis of a crosswell electromagnetic experiment. Geophys J Int,1997,128:355-363
Newman G A. Solution accelerators for large-scale 3D electromagnetic inverse problems.74th Ann Internat Mtg Expl Geophys Expanded Abstracts,2004
Pelton W H, Ward S H, Hallof P G. et al. Mineral discrimination and removal of inductive coupling with multrfrequency IP. Geophysics,1978,43(3):588-609
Reddy I K. Three-dimensional modeling in magnetotelluric and magnetic variational sounding. Geophysics,1977,51:313-325
Rijo L. Modeling of electric and electromagnetic data:[Ph.D dissertation], University of Utah, 1977
Rodi W, Mackie R L. Nonlinear conjugate gradient algorithm for 2-D magnetotelluric inversion. Geophysics,2001,66:174-187
Sasaki Y. Three-dimensional frequency-domain electromagnetic modeling using the finite-difference method. Geophysics Exploration,1999,52:421-431
Seigel H O. Mathematical formulation and type curves for induced polarization. Geophysics, 1959,24:547-565
Siripunvaraporn W, Egbert G, Lenbury Y, et al. Three-dimensional magnetotelluric inversion: data-space method. Physics of The Earth and Planetary Interiors,2005,150(1-3):3-14
Siripunvaraporn W, Egbert G. An efficient data-subspace inversion method for 2-D magnetotelluric data. Geophysics,2000,65:791-803
Smith J T, Booker J R. Rapid inversion of two-and three-dimensional magnetotelluric data. J. Geophys Res,1991,96:3905-3922
Smith J T. Conservative modeling of 3-D electromagnetic fields, Part Ⅰ:Properties and error analysis. Geophysics,1996,61:1308-1318
Smith J T. Conservative modeling of 3-D electromagnetic fields, Part Ⅱ:Biconjugate gradient solution and an accelerator. Geophysics,1996b,61:1319-1324
Soininen H. The behavior of the apparent resistivity phase spectrum in the case of a polarizable prism in an unpolarizable half-space. Geophysics,1984,49:1534-1540
Soininen H. The behavior of the apparent resistivity phase spectrum in the case of two polarizable media. Geophysics,1985,50:810-819
Spichak V, Popova. Artificial neural network inversion of magnetotelluric data in terms of three-deimensional earth macroparameters. Geophys J Int,2000,142:15-26
Swift C M. Theoretical magnetotelluric and Turam response from two-dimensional inhomogeneities. Geophysics,1971,36:1-12
Tan Handong, Tongtuo and Lin Changhong. The parallel 3D magnetotelluric forward modeling algorithm. Applied Geophysics,2006,3(4):197-202
Ting S C, Hohmann G W. Integral equation modeling of three-dimensional magnetotelluric response. Geophysics,1981,46:182-197
Wait J R. Overvoltage research and its geophysical applications:Pergamon Press, Inc
Wang T, Hohmann G W. A finite difference time-domain solution for three dimensional electromagnetic modeling. Geophysics,1993,58:797-809
Wang T, Fang S.3-D electromagnetic anisotropy modeling using finite difference. Geophysics, 2001,66:1386-1398
Wang Xiangchun,Liu Xuewei.3-D acoustic wave equation forward modeling with topography. Applied Geophysics,2007,4(1):8-15
Wannamaker P E, Hohmann G W, SanFilipo W A. Electromagnetic modeling of three-dimensional bodies in layered earths using integral equation. Geophysics,1984,49:60-74
Wannamaker P E, Stodt J A, Rijo L. A stable finite element solution for two-dimensional magnetotelluric modeling. Geophysics,1987,88:277-296
Wannamaker P E, Stodt J A, Rijo L. Two-dimensional topographic responses in magnetotelluric model using finite elements, Geophysics,1986,51:2131-2144
Wannamaker P E. Advances in three-dimensional magnetotelluric modeling using integral equations. Geophysics,1991,56:1716-1728
Weerachai S, Egbert G, Lenbury Y. Numerical accuracy of magnetotelluric modeling:A comparison of finite difference approximations. Earth Planets Space,2002,54:721-725
William L, Rodi. A technique for improving the accuracy of finite element solution for magnetotelluric data. Geophysics,1976,44:483-506
Wong J. An electrochemical model of the IP phenomenon in disseminated sulfide ores, Geophysics 1979,44:1245-1265
Xiang J, N B Jones, D Cheng et al. direct inversion of the apparent complex-resistivity spectrum. Geophysics,2001,66(5):1399-1404
Xiong Z, Luo Y, Wang S et al. Induced-polarization and electromagnetic modeling of a three-dimensional body in a two-layer anisotropic earth, Geophysics 1986,51:2235-2246
Xiong Z. Domain decomposition for 3D electromagnetic modeling. Earth Planets Space,1999, 51:1013-1018
Xiong Z. EM modeling of three-dimensional structures by the method of system iteration using integral equations. Geophysics,1992,57:1556-1561
Zhdanov M S, Fand S. Quasi-linear approximation in 3-D EM modeling. Geophysics,1996a,61: 623-665
Zhdanov M S, Fang S, Hursan G. Electromagnetic inversion using quasi-linear approximation. Geophysics,2000,65(5):1501-1513
Zhdanov M S, Keller G V. The geoelectrical methods in geophysical exploration[M]. Methods in Geochemisty and Geophysics,1994
Zonge K L, Hughes L J, Carlson N R. Hydrocarbon exploration using induced polarization,apparent resistivity and electromagnetic scattering, Presented at the fifty-first annual international meeting and exposition SEG,1981
Zyserman F I, Santos J E. Parallel finite element algorithm with domain decomposition for three-dimensional magnetotelluric modeling. Journal of Applied Geophysics,2000,44:337-351
Zyserman F I, Santos J E. Parallel finite element algorithm with domain decomposition of three-dimensional magnetotelluric modeling. Journal of Applied Geophysics,2000,44:337-351
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.中南工业大学学报,1999,30(5)：472-474
曹建章,唐天同,宋建平.三维电磁模拟的积分方程法.西安石油学院学报,1998,13(3)：65-68
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.石油地球物理勘探,1982,17(3)：69-72
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.石油物探,1981,20(3)：84-103
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.石油地球物理勘探,2000,35(4)：487-496
陈小斌.有限元直接迭代算法.物探化探计算技术,1999,21(2)：165-171
傅良魁,张虎豹.频谱激电法中的若干理论研究,物探与化探,1985,9:410-419
傅良魁.复电阻率法异常的频谱及空间分布规律,物探与化探,1981,46-53
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.石油地球物理勘探,1984,19(4)：358-367
胡建德,王光愕,陈乐寿等.大地电磁二维正演计算中若干问题的讨论.石油地球物理勘探,1982,17(6)：47-55
黄临平,戴世坤.复杂条件下3D电磁场有限元计算方法.中国地质大学学报,2002,27(6)：775-779
柯马罗夫B.A著,激发极化电法勘探(阎立光等译),北京：地质出版社,1983
李建平.带地形的三维复电阻率电磁场正反演研究：[博士学位论文].吉林大学,2008
李学民,曹俊兴,贺桃娥.断层构造的大地电磁响应曲线变化特征的研究.天然气工业,2004,24(7)：42-57
李予国,徐世浙,刘斌等.电导率连续变化的MT有限元正演(Ⅱ).高校地质学报,1996,2(4)：448-452
林昌洪.大地电磁张量阻抗三维共轭梯度反演研究：[博士学位论文].中国地质大学(北京),2009
刘春明.伪随机激电多参数谱法研究：[博士学位论文].中南大学,2006
刘树才,周圣武.二维电法数值模拟中的网格剖分方法.物化探计算技术,1995,17(1)：49-53
刘崧,官善友,高鹏飞.求极化椭球体真cole-cole参数的联合谱激电反演.地球物理学报,1994,37(增刊2)：542-551
刘崧,薛继安,徐建华.求地下真柯尔—柯尔参数的研究.物探与化探,2000,24(1)：51-61
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.同济大学学报,2007,35(8)：1113-1117
刘正栋,关洪军,聂永平等.稳定点电流源场三维有限差分正演模拟.解放军理工大学学报,2000,1(3)：45-50
罗延钟,方胜.视复电阻率频谱的一种近似反演方法,地球科学,1986,11：93-102
罗延钟,万乐.二维地形不平条件下外电场的有限差分模拟.物化探计算技术,1984,6(4)：15-26
罗延钟,万乐.用数值模拟方法构组保角变换坐标网.物化探计算技术,1986,8(1)：23-31
罗延钟,吴之训.谱激电法中频率相关系数的应用.地球物理学报,1992,35(4):490-499
罗延钟,张桂青.频率域激电法原理.北京：地质出版社,1988
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.地球物理学报,1996,39(6)：823-834
裴正林.三维各向异性介质中弹性波方程交错网格高阶有限差分模拟.石油大学学报(自然科学版),2004,28(5)：23-29
阮百尧,罗涧林等.一种新的复电阻率频谱参数递推反演方法,物化探计算技术,2003,25(4)：298-301
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,2003,46(2)：281-289
宋维琪,全兆歧.3-D瞬变电磁场的有限差分正演计算.石油地球物理勘探,2000,35(6)：751-756
谭捍东,余钦范,魏文博等.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, 2003,46(5)：705-711
汤井田,任政勇,化希瑞.地球物理学中的电磁场正演与反演.地球物理学进展,2007,22(4)：1181-1194
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.地球物理学进展,2007,22(2)：579-585
王自力,张赛珍.一种真复电阻率谱参数的求解方法,地球物理学报,1990,33:712-727
吴小平,徐果明.利用不完全Cholesky共轭梯度法求解电源三维电场,地球物理学报,1998,41(6)：848-855
邢涛等.大定源瞬变电磁法三维正演程序开发.工程地球物理学报,2008,5(6)：664-669
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.西北地震学报,2006,28(2)：104-107
徐凯军.2.5维复电阻率电磁场正反演研究：[博士学位论文].吉林大学,2007
徐世浙,刘斌.点源二维电场中纵剖面上电位的计算.地球物理学报,1996,39(4):551-560
徐世浙,于涛,李予国等.电导率连续变化的MT有限元正演(Ⅰ).高校地质学报,1995,1(2)：65-73
徐世浙.地球物理中的有限单元法.北京：科学出版社,1994
徐志峰.频率域可控源电磁三维正演：[博士学位论文].中国科学技术大学,2010
张辉.复电阻率三维电磁场正反演研究：[博士学位论文].吉林大学,2006
赵广茂.带地形的复电阻率2.5维电磁场正反演研究：[博士学位论文].吉林大学,2009
赵生凯,徐世浙.有限单元法计算良导嵌入体的大地电磁测深曲线.物探化探计算技术,1983,5(1)：14-21
周熙襄,钟本善,江东玉.点源二维电阻率法有限差分正演计算.物化探电子计算技术,1983,5(3)：34-38
朱伯芳.有限单元法原理与应用.北京：水利出版社,1979
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |