相位感应测井的反演方法研究
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摘要
本文主要研究了相位感应测井资料的非均匀介质反演方法,分别在一维和二维反演模型中利用两接收线圈的相位差Δφ和幅度比B曲线进行了反演计算。
首先,本文对电磁散射和逆散射的理论和方法进行了概述,着重介绍了高维逆散射问题的反演方法。
快速的测井资料的反演依赖于正演的计算速度,本文使用一维反演模型,提出了采用变分原理建立相位感应测井的反演方程,对相位感应测井的相位差Δφ测井资料进行快速反演,获得一维地层的电阻率分布,从而实现对相位感应测井资料的预处理。
然后,在二维非均匀介质反演模型中,着重阐述了轴对称二维非均匀介质中的数值模式匹配法(NMM),通过相位感应测井的相位差Δφ响应方程建立测井反演方程,并采用共轭梯度法(CG)进行反演计算。研究了反演方法的收敛速度,反演精度和抗噪声能力,分析了地层纵向边界位置的准确程度对地层电阻率反演精度的影响。通过相位差Δφ测井响应曲线确定出地层反演模型的初始值,对地层电阻率和地层纵向边界进行了整体反演计算。利用存在泥浆侵入的相位差Δφ响应曲线,反演计算地层的电阻率分布,对反演地层径向电阻率的能力进行了考察。
针对相位差Δφ和幅度比B测井曲线,采用共轭梯度法(CG)反演计算地层电阻率和介电常数分布。讨论了该反演方法的收敛速度,抗噪声能力,分析了相位感应测井反演过程中,地层纵向边界位置的准确程度影响电参数的反演精度,需要重视地层纵向边界位置的反演。利用相位差Δφ和幅度比B测井响应曲线,对地层电阻率、介电常数和地层纵向边界进行了整体反演计算,并由相位差Δφ和幅度比B测井响应曲线提取地层的纵向边界位置的初始值。为了提高反演计算的稳定性,对反演的步骤进行了研究。利用存在泥浆侵入的相位差Δφ和幅度比B响应曲线,反演计算地层径向的电阻率和介电常数分布,考察了反演地层径向电参数的能力。
最后,基于扩展玻恩近似的两步反演方法,并结合了多重网格技术和遗传算法(GA)对高对比度问题进行了反演。在迭代前期,采用遗传算法进行优化反演计算;在迭代后期保持格林函数不变进行迭代反演,增加了迭代反演过程中的抗噪声能力。并利用相位差Δφ测井响应曲线,采用遗传算法对二维地层模型的电阻率分布进行反演计算。
The inhomogeneous inversion method on the phase induction logging has been studied in this dissertation. The inversion simulation is performed from the phase difference △φ and amplitude ratio B of the two receiver coils in one-dimensional and two-dimensional inverse modeling, respectively.Firstly, the theories and methods of electromagnetic scattering and inverse scattering are reviewed in this paper. The high-dimensional electromagnetic inverse scattering method is introduced mainly.The efficiency of the data inversion highly depends on the speed of the forward modeling. The subsurface structure is modeled as a one-dimension horizontally layered medium, the inversion equation of the phase induction logging is obtained by applying the variation principal. The algorithm is applied to pretreat phase difference △φ logging data, and the formation resistivity distribution of one-dimensional modeling is obtained.Following, in the two-dimensional inverse modeling, the numerical mode-matching (NMM) method as an efficient algorithm is used to model various multiregion vertically and cylindrically stratified inhomogeneous media. The inversion equation is obtained by applying the variation principal in a two-dimensional axisymmetrical inhomogeneous medium, which is solved by using the conjugate gradient (CG) method. The convergence speed, precision and tolerance to noise of the inversion method are discussed, it is found that the accuracy of formation boundary location influents the inversion precision of formation resistivity. The initial value of formation resistivity and boundary location are obtained from phase difference △φ logging response curve, then the formation resistivity and boundary location per bed are simultaneously reconstructed from the phase induction logging data. In order to investigate radial resolution, the formation resistivity is inverted from logging data with mud invasion.The formation resistivity and permittivity are inverted by using the conjugate gradient (CG) method from the phase difference △φ and amplitude ratio B logging data, the convergence speed and tolerance to noise of the inversion method are investigated. The accuracy of formation boundary location influents the inversion precision of formation resistivity and permittivity, the accuracy of boundary location should be paid much attention. The initial value of formation boundary location is obtained from phase difference △φ and amplitude ratio B logging response curves,
首先,本文对电磁散射和逆散射的理论和方法进行了概述,着重介绍了高维逆散射问题的反演方法。
快速的测井资料的反演依赖于正演的计算速度,本文使用一维反演模型,提出了采用变分原理建立相位感应测井的反演方程,对相位感应测井的相位差Δφ测井资料进行快速反演,获得一维地层的电阻率分布,从而实现对相位感应测井资料的预处理。
然后,在二维非均匀介质反演模型中,着重阐述了轴对称二维非均匀介质中的数值模式匹配法(NMM),通过相位感应测井的相位差Δφ响应方程建立测井反演方程,并采用共轭梯度法(CG)进行反演计算。研究了反演方法的收敛速度,反演精度和抗噪声能力,分析了地层纵向边界位置的准确程度对地层电阻率反演精度的影响。通过相位差Δφ测井响应曲线确定出地层反演模型的初始值,对地层电阻率和地层纵向边界进行了整体反演计算。利用存在泥浆侵入的相位差Δφ响应曲线,反演计算地层的电阻率分布,对反演地层径向电阻率的能力进行了考察。
针对相位差Δφ和幅度比B测井曲线,采用共轭梯度法(CG)反演计算地层电阻率和介电常数分布。讨论了该反演方法的收敛速度,抗噪声能力,分析了相位感应测井反演过程中,地层纵向边界位置的准确程度影响电参数的反演精度,需要重视地层纵向边界位置的反演。利用相位差Δφ和幅度比B测井响应曲线,对地层电阻率、介电常数和地层纵向边界进行了整体反演计算,并由相位差Δφ和幅度比B测井响应曲线提取地层的纵向边界位置的初始值。为了提高反演计算的稳定性,对反演的步骤进行了研究。利用存在泥浆侵入的相位差Δφ和幅度比B响应曲线,反演计算地层径向的电阻率和介电常数分布,考察了反演地层径向电参数的能力。
最后,基于扩展玻恩近似的两步反演方法,并结合了多重网格技术和遗传算法(GA)对高对比度问题进行了反演。在迭代前期,采用遗传算法进行优化反演计算;在迭代后期保持格林函数不变进行迭代反演,增加了迭代反演过程中的抗噪声能力。并利用相位差Δφ测井响应曲线,采用遗传算法对二维地层模型的电阻率分布进行反演计算。
The inhomogeneous inversion method on the phase induction logging has been studied in this dissertation. The inversion simulation is performed from the phase difference △φ and amplitude ratio B of the two receiver coils in one-dimensional and two-dimensional inverse modeling, respectively.Firstly, the theories and methods of electromagnetic scattering and inverse scattering are reviewed in this paper. The high-dimensional electromagnetic inverse scattering method is introduced mainly.The efficiency of the data inversion highly depends on the speed of the forward modeling. The subsurface structure is modeled as a one-dimension horizontally layered medium, the inversion equation of the phase induction logging is obtained by applying the variation principal. The algorithm is applied to pretreat phase difference △φ logging data, and the formation resistivity distribution of one-dimensional modeling is obtained.Following, in the two-dimensional inverse modeling, the numerical mode-matching (NMM) method as an efficient algorithm is used to model various multiregion vertically and cylindrically stratified inhomogeneous media. The inversion equation is obtained by applying the variation principal in a two-dimensional axisymmetrical inhomogeneous medium, which is solved by using the conjugate gradient (CG) method. The convergence speed, precision and tolerance to noise of the inversion method are discussed, it is found that the accuracy of formation boundary location influents the inversion precision of formation resistivity. The initial value of formation resistivity and boundary location are obtained from phase difference △φ logging response curve, then the formation resistivity and boundary location per bed are simultaneously reconstructed from the phase induction logging data. In order to investigate radial resolution, the formation resistivity is inverted from logging data with mud invasion.The formation resistivity and permittivity are inverted by using the conjugate gradient (CG) method from the phase difference △φ and amplitude ratio B logging data, the convergence speed and tolerance to noise of the inversion method are investigated. The accuracy of formation boundary location influents the inversion precision of formation resistivity and permittivity, the accuracy of boundary location should be paid much attention. The initial value of formation boundary location is obtained from phase difference △φ and amplitude ratio B logging response curves,
引文
[1] 测井学编写组.测井学.北京:石油工业出版社,1998.
[2] 潭延栋.测井的回顾与展望.地球物理学报,1994,37(增刊):425-428.
[3] 周祥宝,丁进材,薛天才等.BHKH3高频感应测井仪原理及应用效果分析.石油仪器,2003,17(3):37-39.
[4] 卢达.国外高频电磁波测井研究状况.油田地质开发情报,1979,1.
[5] 张丽缓,武清钊,高频等参数感应(BHKH3)测井技术应用.测井技术,2001,25(6):452-455.
[6] 邢光龙,王现银,刘曼芬等.高频等参数感应测井的探测特性分析.测井技术,2003,27(3):212-216.
[7] 刘智涌.相位感应测井仪器设计及其信号处理研究:[硕士学位论文].成都:电子科技大学 2003.
[8] 吴式枢,杨善德,王明达.相位介电测井的物理基础.吉林大学学报,1973,2:58-69.
[9] 张美玲,孙宏智,邢光龙.介电测井资料反演方法及其应用.测井技术,2000,24(1):27-31.
[10] 韩波,刘家琦,李莹等.多层电磁波测井反演.地球物理学报,1998,41(3):416-423.
[11] 邢光龙,张美玲,刘曼芬等.利用高频电磁波测井反演地层介电常数和电阻率.地球物理学报,2002,45(3):435-443.
[12] 金建铭著,王建国译,葛德彪校.电磁场有限元方法.西安电子科技大学出版社,1998.
[13] 李大潜,郑家穆,谭永基等.有限元素法在电法测井中的应用.石油工业出版社,1980.
[14] 曾余庚,徐国华等.电磁场有限单元法.科技出版社,1982.
[15] 王秉中.计算电磁学.电子科技大学,2000.
[16] 哈林登R.F.著,王尔杰,肖良勇,林炽森,宫德明译.计算电磁场的矩量法,国防工业出版社,1981.
[17] Wang J. J. H. Generalized moment methods in electromagnetics-formulation and computer solution of integral equation. John Wiley & Sons, Inc., 1991.
[18] 李世智.电磁散射与辐射问题的矩量法.电子工业出版社,1988.
[19] 周永祖著,聂在平,柳清伙译.非均匀介质中的场与波.电子工业出版社,1992.
[20] Chew W C, Barone S, Anderson B et al. Diffraction of axisymmetric waves in a borehole by bed boundary discontinuities. Geophysics, 1984, 49(10): 1586-1595.
[21] Chew W C, Anderson B. Propagation of electromagnetic waves through geological beds in a geophysical probing environment. Radio Sci., 1985, 20(3): 611-621.
[22] Chew W C, Nie Z, Liu Q H. An efficient solution for the response of electrical well logging tools in a complex environment. IEEE Trans. Geosci. Remote Sens., 1991, 29(2): 308-313.
[23] 聂在平,Chew W C,Liu Q H.电磁波对轴对称二维层状介质的散射.地球物理学报,1992,35(4):479-489.
[24] 聂在平,Chew W C,Liu Q H.多区域柱面分层介质中的电磁散射—电磁波测井分析.电子学报,1992,20(9):12-21.
[25] 聂在平,陈思渊.二维完全非均匀介质中位场格林函数的数值解.地球物理学报,1994,37(5):688-697.
[26] 聂在平,陈思渊.复杂介质环境中双侧向测井响应的高效数值分析.电子学报,1994,22(6):30-38.
[27] 聂在平.非均匀介质中的场与波:理论及其在电测井中的应用.电子学报,1995,23(10):19-24
[28] Hadjidimos A. Iterative methods for the solution of linear systems. North-Holland. 1988.
[29] 戈卢布G H,范洛恩C F.矩阵计算.北京:科学出版社,2001.
[30] Rappaport C, Baharmasel L. An absorbing boundary condition based on anechoic absorber for EM scattering computation. Journal of Electromagnetic Waves and Application, 1992, 6(12): 1621-1634.
[31] Lindman E L. Free-space boundary condition for the time dependent wave equation. Journal of Computational Physics, 1975, 18: 67-78.
[32] Berengeer J P. A perfectly matched layer for the absorption of electromagnetic waves. Joumal of Computational Physics, 1994, 114: 185-200.
[33] Habashy T M, Mtttra R. On some inverse methods in electromagnetics. J. Electromagn. Waves Applicat., 1987, 1(1): 25-58.
[34] 葛德彪.电磁逆散射原理.西北电讯工程学院出版社,1987.
[35] Levy B C. Layer by layer reconstruction methods for the earth resistivity from direct current measurements. IEEE Trans. Geosci. Remote Sens., 1985, 1985, 23(6): 841-850.
[36] Mostafavi M, Mittra R. Remote probing of inhomogeneous media using parameter optimization techniques. Radio Sci., 1972, 7(12): 1105-1111.
[37] Coen S, Mei K K, Anglako D J. Inverse scattering technique applied to remote sensing of layered media. IEEE Trans. Antennas Propagat., 1981, 29(2): 298-306.
[38] Wang Y M, Chew W C. An iterative solution of two-dimensional electromagnetic inverse scattering problem. Int. J. Imaging Syst. Technol., 1989, 1(1): 100-108.
[39] Alumbaugh D L, Morrison H F. Electromagnetic conductivity imaging with an iterative Born inversion. IEEE Trans. Geosci. Remote Sens., 1993, 31(4): 758-763.
[40] Chew W C, Wang Y M. Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method. IEEE Trans. Med. Imag., 1990, 9(2): 218-225.
[41] Liu Q H. Reconstruction of two-dimensional axisymmetric inhomogeneous media. IEEE Trans. Geosci. Remote Sens., 1993, 31(3): 587-594.
[42] 赵延文,聂在平,卢涛,卢达.基于变形玻恩迭代法的多重网格反演方法.电子科技大学学报,2002,3 1(4):340-344.
[43] Nie Zaiping, Zhang Yerong. Hybrid Born iterative method in low-frequency inverse scattering problem. IEEE Trans. Geosci. Remote Sens., 1998, 36(3): 749-753.
[44] Joachimowiez N, Mallorqui J J, Bolomey J C, et al. Convergence and stability assessment of Newton-kantorovich reconstruction algorithms for microwave tomography. IEEE Trans. Med. Imag., 1998, 17(8): 562-570.
[45] Chiu C C, Kiang Y W. Microwave imaging of multiple conducting cylinders. IEEE Trans. Antennas Propagat., 1992, 40(8): 933-941.
[46] Roger A. Newton-Kantorvitch algorithm applied to electromagnetic inverse problem. IEEE Trans. Antennas Propagat., 1981, 29(2): 232-238.
[47] Lin H T, Kiang Y W. Microwave imaging for a dielectric cylinder. IEEE Trans. Microwave Theory Tech., 1994, 42(8): 1572-1579.
[48] Belkebir K, Kleinman R E, Pichot C. Microwave lmaging-location and shape reconstruction from multifrequency scattering data. IEEE Trans. Microwave Theory Tech.., 1997, 45(4): 469-476.
[49] Nie Zaiping, Yang Feng, Zhao Yanwen, Zhang Yerong. Variational Born iteration method and its applications to hybrid inversion. IEEE Trans. Geosci, Remote Sens., 2000, 38(4): 1709-1714.
[50] 杨峰,聂在平.用变分玻恩迭代方法重建二维非均匀介质结构.地球物理学报,2000,43(4):550-556.
[51] Chew W C, Liu Q H. Inversion of induction tool measurements using the distorted Born iterative method and CG-FFHT. IEEE Trans. Geosci. Remote Sens., 1994, 32(4): 878-883.
[52] Van den Berg P M, Van den Horst M. Nonlinear inversion in induction logging using the modified gradient method. Radio Sci., 1995, 30(5): 1355-1369.
[53] Kooij B J, Van den Berg P M. Nonlinear inversion in TE scattering. IEEE Trans. Microwave Theory Tech., 1998, 46(11): 1704-1712.
[54] Wang W, Zhang S. Unrelated illumination method for electromagnetic inverse scattering of inhomogeneous lossy dielectric bodies. IEEE Trans. Antennas Propagat., 1992, 40(11): 1292-1296.
[55] Zhang Z Q, Liu Q H. Two nonlinear inverse method for electromagnetic induction measurements. IEEE Trans. Geosci. Remote Sens., 2001, 39(6): 1331-1339.
[56] Michalski K A. Electromagnetic imaging of elliptical-cylindrical conductors and tunnels using a differential evolution algorithm. Microwave Opt. Tech, Lett., 2001, 28(3): 164-169.
[57] Park C S, Jeong B S. Reconstruction of a high contrast and large object by using the hybrid algorithm combining a Levenberg-Marquardt algorithm and a genetic algorithm. IEEE Trans. Magn,, 1999, 35(3): 1582-1585.
[58] Weile D S, Michielsser E. Genetic algorithm optimization applied to electromagnetic: a review. IEEE Trans. Antennas Propagat., 1997, 45(3): 343-353.
[59] Haupt R L. An introduction to genetic algorithm for electromagnetics. IEEE Antennas Propagat. Mag., 1995, 37(2): 7-15.
[60] Caorsi S, Pastorino M. Two-dimensional microwave imaging approach based on genetic algorithm. IEEE Trans. Antennas Propagat., 2000, 48(3): 370-373.
[61] Garnero L, Franchois A, Hugonin J P et al, Microwave imaging-complex permittivity reconstruction by simulated annealing. IEEE Trans. Microwave Theory Tech., 1991, 39(11): 1801-1807.
[62] Liu Q H et al. Modeling low-frequency electrode-type resistivity tools in invaded thin beds. IEEE Trans. Geosci. Remote Sens., 1994, 32(3): 494-498.
[63] Liu Q H. Nonlinear inversion of electrode-type resistivity measurements. IEEE Trans. Geosci. Remote Sens., 1994, 32(3): 499-507.
[64] 赵延文,聂在平.电极型电阻仪测井成像算法研究.地球物理学报,1997,
[65] 赵延文,聂在平.轴对称二维位场的变形玻恩迭代反演.电子学报,1997,25(12):10-14.
[66] 杨峰,聂在平.用迭代方法和双共轭梯度法重建二维电导率剖面分布.微波学报,2000,16(3):299-304.
[67] 杨峰,聂在平.轴对称二维非均匀介质结构的非线性反演方法.红外与毫米波学报,2000,19(6):419-424.
[68] 杨峰,聂在平.卢涛等.基于双感应测井仪低数据量的反演方法研究.电波科学学报,2001.16(1):118-122.
[69] Moghaddam M, Chew W C. Nonlinear two-dimensional velocity profile inversion using time-domain data. IEEE Trans. Geosci. Remote Sens., 1992, 30(1): 147-156.
[70] Liu Q H, Chew W C. A CG-FFHT method for the scattering solution of axsymmetric inhomogeneous media. Microwave Opt. Tech. Lett., 1993, 6(2): 101-104.
[71] Liu Q H, Chew W C. Application of the conjugate gradient fast Fourier Hankel transfer method with an improved fast Hankel transform algorithm. Radio Sci., 1994, 29(4): 1009-1022.
[72] Zhang G J, Zhang Z Q. Application of successive approximation method to the computation of the Green's function in axisymmetric inhomogeneous media. IEEE Trans. Geosci. Remote Sens., 1998, 36(3): 732-737.
[73] Kleinman R E, van den Berg P M. A modified gradient method for two-dimensional problems in tomography. J. Comput. Appl. Math., 1992, 42:17-35.
[74] Kleinman R E, van den Berg P M. An extended range-modified gradient technique for profile inversion. Radio Sci., 1993, 28(5): 877-884.
[75] Kleinman R E, van den Berg P M. Two-dimensional location and shape reconstruction. Radio Sci., 1994,29(4): 1157-1169.
[76] Liu Q H, Zhang Z Q, Xu X M. The hybrid extended Born approximation and CG-FFT method for electromagnetic induction problems. IEEE Trans. Geosci. Remote Sens., 2001, 39(2): 347-355.
[77] Torres-Verdin C, Habashy T M. Rapid 2.5-dimensional forward modeling and inversion via a new nonlinear scattering approximation. Radio Sci., 1994,29(4): 1051-1079.
[78] Zhang Z Q, Liu Q H. The hybrid extended Born approximation and CG-FFHT method for axisymmetric media. IEEE Trans. Geosci. Remote Sens., 2001, 39(4): 710-717.
[79] Torres-Verdin C, Habashy TM. A two-step linear inversion of two-dimensional electrical conductivity. IEEE Trans. Antennas Propagat., 1995, 43(4): 405-415.
[80] Abubakar A, van den Berg P M. Three-dimensional inverse scattering applied to cross-well induction sensors. IEEE Trans. Geosci. Remote Sens., 2000, 38(4): 1669-1680.
[81] Abubakar A, van den Berg P M. Three-dimensional nonlinear inversion in cross-well electrode logging. Radio Sci., 1998, 33(4): 989-1004.
[82] Abubakar A, van den Berg P M. Nonlinear inversion in electrode logging in highly deviated formation with invasion using an oblique coordinate system. IEEE Trans. Geosci. Remote Sens., 2000, 38(1): 25-38.
[83] Zhdanov M S, Fang S. Three-dimensional quasi-linear electromagnetic inversion. Radio Sci., 1996, 31(4): 741-754.
[84] Zhou C, Liu L. Radar-diffraction tomography using the modified quasi-linear approximation. IEEE Trans. Geosci. Remote Sens., 2000, 38(l):404-415.
[85] Caorsi S, Massa A, Pastorino M. A computational technique based on a real-coded genetic algorithm for microwave imaging purposes. IEEE Trans. Geosci. Remote Sens., 2000, 38(4): 1697-1708.
[86] Qing A, Lee C K, Jen L. Electromagnetic inverse scattering of two-dimensional perfectly conducting objects by real-coded genetic algorithm. IEEE Trans. Geosci. Remote Sens., 2001, 39(3):665-676.
[87] 邹长春,尉中良,柴细元等.利用遗传算法实现最优化测井解释.测井技术,1999,23(5):361-365.
[88] Chen S Y. Low-frequency subsurface electromagnetic modeling. Ph D. thesis, University of Illinois, 2000.
[89] Chert S Y, Chew W C, Kennedy W D. Inversion of 6FF40 induction tool measurement using the distorted Born iterative method. Proc. IEEE, 1997, 3: 1714-1716.
[90] Chert S Y, Chew W C, Kennedy W D. Efficient one dimensional inversion of induction log data. Proc. IEEE, 1998, 2: 990-993.
[91] 邓小波,聂在平,赵延文.一维平面分层介质的快速正反演方法.电波科学学报,2004,19(增刊):83-85.
[92] 潘锦,聂在平.二维平面分层介质中的数值模式匹配—算子矩阵理论及计算方法的应用.电子科学学刊,1994,16(4):388-394.
[93] 赵延文.二维非均匀介质中准静态位场的反演方法及应用研究:[博士学位论文].成都:电子科技大学 1997.
[94] 杨峰.复杂非均匀介质中电磁逆散射方法和应用分析:[博士学位论文].成都:电子科技大学 1997.
[95] 卿安永,李敬,任朗.二维介质柱的微波成像研究.地球物理学报,1998,41(1):117-123.
[96] Cui T J, Chew W C, Alaeddin A, et al. Inverse scattering of two-dimensional dielectric objects buried in a lossy earth using distorted Born iterative method. IEEE Trans. Geosci. Remote Sens., 2001, 39(2): 339-346.
[97] 邓小波,聂在平,赵延文等.利用相位感应测井数据反演电导率.2004全国博士生学术论坛论文集,四川成都,2004,电子科学与技术分论坛,5-8.
[98] Wang H N, Yang S D. A multiparameter iterative inversion of dual-laterolog in horizontally layered media and its error analysis. IEEE Trans. Geoscl. Remote Sens., 2002, 40(2): 482-493.
[99] Habashy T M, Chew W C, Chow E Y. Simultaneous reconstruction of permittivity and conductivity profiles in a radially inhomogeneous slab. Radio Sci., 1986, 21(4): 635-645.
[100] Habashy T M, Oristaglio M L, de Hoop A T. Simultaneous nonlinear reconstruction of two-dimensional permittivity and conductivity. Radio Sci., 1994, 29(4): 1101-1118.
[101] 邓小波,聂在平,赵延文等.利用相位感应测井反演二维轴对称电导率分布.第14届全国电磁兼容学术会议论文集,四川成都,2004,71-74.
[102] 解可新.最优化方法.天沣:天津大学出版社,1997.
[103] Meng Z Q, Takenaka T, Tanaka T. Image reconstruction of two-dimensional impenetrable objects using genetic algorithm. J. Electromagn. Waves Applicat., 1999, 13: 95-118.
[2] 潭延栋.测井的回顾与展望.地球物理学报,1994,37(增刊):425-428.
[3] 周祥宝,丁进材,薛天才等.BHKH3高频感应测井仪原理及应用效果分析.石油仪器,2003,17(3):37-39.
[4] 卢达.国外高频电磁波测井研究状况.油田地质开发情报,1979,1.
[5] 张丽缓,武清钊,高频等参数感应(BHKH3)测井技术应用.测井技术,2001,25(6):452-455.
[6] 邢光龙,王现银,刘曼芬等.高频等参数感应测井的探测特性分析.测井技术,2003,27(3):212-216.
[7] 刘智涌.相位感应测井仪器设计及其信号处理研究:[硕士学位论文].成都:电子科技大学 2003.
[8] 吴式枢,杨善德,王明达.相位介电测井的物理基础.吉林大学学报,1973,2:58-69.
[9] 张美玲,孙宏智,邢光龙.介电测井资料反演方法及其应用.测井技术,2000,24(1):27-31.
[10] 韩波,刘家琦,李莹等.多层电磁波测井反演.地球物理学报,1998,41(3):416-423.
[11] 邢光龙,张美玲,刘曼芬等.利用高频电磁波测井反演地层介电常数和电阻率.地球物理学报,2002,45(3):435-443.
[12] 金建铭著,王建国译,葛德彪校.电磁场有限元方法.西安电子科技大学出版社,1998.
[13] 李大潜,郑家穆,谭永基等.有限元素法在电法测井中的应用.石油工业出版社,1980.
[14] 曾余庚,徐国华等.电磁场有限单元法.科技出版社,1982.
[15] 王秉中.计算电磁学.电子科技大学,2000.
[16] 哈林登R.F.著,王尔杰,肖良勇,林炽森,宫德明译.计算电磁场的矩量法,国防工业出版社,1981.
[17] Wang J. J. H. Generalized moment methods in electromagnetics-formulation and computer solution of integral equation. John Wiley & Sons, Inc., 1991.
[18] 李世智.电磁散射与辐射问题的矩量法.电子工业出版社,1988.
[19] 周永祖著,聂在平,柳清伙译.非均匀介质中的场与波.电子工业出版社,1992.
[20] Chew W C, Barone S, Anderson B et al. Diffraction of axisymmetric waves in a borehole by bed boundary discontinuities. Geophysics, 1984, 49(10): 1586-1595.
[21] Chew W C, Anderson B. Propagation of electromagnetic waves through geological beds in a geophysical probing environment. Radio Sci., 1985, 20(3): 611-621.
[22] Chew W C, Nie Z, Liu Q H. An efficient solution for the response of electrical well logging tools in a complex environment. IEEE Trans. Geosci. Remote Sens., 1991, 29(2): 308-313.
[23] 聂在平,Chew W C,Liu Q H.电磁波对轴对称二维层状介质的散射.地球物理学报,1992,35(4):479-489.
[24] 聂在平,Chew W C,Liu Q H.多区域柱面分层介质中的电磁散射—电磁波测井分析.电子学报,1992,20(9):12-21.
[25] 聂在平,陈思渊.二维完全非均匀介质中位场格林函数的数值解.地球物理学报,1994,37(5):688-697.
[26] 聂在平,陈思渊.复杂介质环境中双侧向测井响应的高效数值分析.电子学报,1994,22(6):30-38.
[27] 聂在平.非均匀介质中的场与波:理论及其在电测井中的应用.电子学报,1995,23(10):19-24
[28] Hadjidimos A. Iterative methods for the solution of linear systems. North-Holland. 1988.
[29] 戈卢布G H,范洛恩C F.矩阵计算.北京:科学出版社,2001.
[30] Rappaport C, Baharmasel L. An absorbing boundary condition based on anechoic absorber for EM scattering computation. Journal of Electromagnetic Waves and Application, 1992, 6(12): 1621-1634.
[31] Lindman E L. Free-space boundary condition for the time dependent wave equation. Journal of Computational Physics, 1975, 18: 67-78.
[32] Berengeer J P. A perfectly matched layer for the absorption of electromagnetic waves. Joumal of Computational Physics, 1994, 114: 185-200.
[33] Habashy T M, Mtttra R. On some inverse methods in electromagnetics. J. Electromagn. Waves Applicat., 1987, 1(1): 25-58.
[34] 葛德彪.电磁逆散射原理.西北电讯工程学院出版社,1987.
[35] Levy B C. Layer by layer reconstruction methods for the earth resistivity from direct current measurements. IEEE Trans. Geosci. Remote Sens., 1985, 1985, 23(6): 841-850.
[36] Mostafavi M, Mittra R. Remote probing of inhomogeneous media using parameter optimization techniques. Radio Sci., 1972, 7(12): 1105-1111.
[37] Coen S, Mei K K, Anglako D J. Inverse scattering technique applied to remote sensing of layered media. IEEE Trans. Antennas Propagat., 1981, 29(2): 298-306.
[38] Wang Y M, Chew W C. An iterative solution of two-dimensional electromagnetic inverse scattering problem. Int. J. Imaging Syst. Technol., 1989, 1(1): 100-108.
[39] Alumbaugh D L, Morrison H F. Electromagnetic conductivity imaging with an iterative Born inversion. IEEE Trans. Geosci. Remote Sens., 1993, 31(4): 758-763.
[40] Chew W C, Wang Y M. Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method. IEEE Trans. Med. Imag., 1990, 9(2): 218-225.
[41] Liu Q H. Reconstruction of two-dimensional axisymmetric inhomogeneous media. IEEE Trans. Geosci. Remote Sens., 1993, 31(3): 587-594.
[42] 赵延文,聂在平,卢涛,卢达.基于变形玻恩迭代法的多重网格反演方法.电子科技大学学报,2002,3 1(4):340-344.
[43] Nie Zaiping, Zhang Yerong. Hybrid Born iterative method in low-frequency inverse scattering problem. IEEE Trans. Geosci. Remote Sens., 1998, 36(3): 749-753.
[44] Joachimowiez N, Mallorqui J J, Bolomey J C, et al. Convergence and stability assessment of Newton-kantorovich reconstruction algorithms for microwave tomography. IEEE Trans. Med. Imag., 1998, 17(8): 562-570.
[45] Chiu C C, Kiang Y W. Microwave imaging of multiple conducting cylinders. IEEE Trans. Antennas Propagat., 1992, 40(8): 933-941.
[46] Roger A. Newton-Kantorvitch algorithm applied to electromagnetic inverse problem. IEEE Trans. Antennas Propagat., 1981, 29(2): 232-238.
[47] Lin H T, Kiang Y W. Microwave imaging for a dielectric cylinder. IEEE Trans. Microwave Theory Tech., 1994, 42(8): 1572-1579.
[48] Belkebir K, Kleinman R E, Pichot C. Microwave lmaging-location and shape reconstruction from multifrequency scattering data. IEEE Trans. Microwave Theory Tech.., 1997, 45(4): 469-476.
[49] Nie Zaiping, Yang Feng, Zhao Yanwen, Zhang Yerong. Variational Born iteration method and its applications to hybrid inversion. IEEE Trans. Geosci, Remote Sens., 2000, 38(4): 1709-1714.
[50] 杨峰,聂在平.用变分玻恩迭代方法重建二维非均匀介质结构.地球物理学报,2000,43(4):550-556.
[51] Chew W C, Liu Q H. Inversion of induction tool measurements using the distorted Born iterative method and CG-FFHT. IEEE Trans. Geosci. Remote Sens., 1994, 32(4): 878-883.
[52] Van den Berg P M, Van den Horst M. Nonlinear inversion in induction logging using the modified gradient method. Radio Sci., 1995, 30(5): 1355-1369.
[53] Kooij B J, Van den Berg P M. Nonlinear inversion in TE scattering. IEEE Trans. Microwave Theory Tech., 1998, 46(11): 1704-1712.
[54] Wang W, Zhang S. Unrelated illumination method for electromagnetic inverse scattering of inhomogeneous lossy dielectric bodies. IEEE Trans. Antennas Propagat., 1992, 40(11): 1292-1296.
[55] Zhang Z Q, Liu Q H. Two nonlinear inverse method for electromagnetic induction measurements. IEEE Trans. Geosci. Remote Sens., 2001, 39(6): 1331-1339.
[56] Michalski K A. Electromagnetic imaging of elliptical-cylindrical conductors and tunnels using a differential evolution algorithm. Microwave Opt. Tech, Lett., 2001, 28(3): 164-169.
[57] Park C S, Jeong B S. Reconstruction of a high contrast and large object by using the hybrid algorithm combining a Levenberg-Marquardt algorithm and a genetic algorithm. IEEE Trans. Magn,, 1999, 35(3): 1582-1585.
[58] Weile D S, Michielsser E. Genetic algorithm optimization applied to electromagnetic: a review. IEEE Trans. Antennas Propagat., 1997, 45(3): 343-353.
[59] Haupt R L. An introduction to genetic algorithm for electromagnetics. IEEE Antennas Propagat. Mag., 1995, 37(2): 7-15.
[60] Caorsi S, Pastorino M. Two-dimensional microwave imaging approach based on genetic algorithm. IEEE Trans. Antennas Propagat., 2000, 48(3): 370-373.
[61] Garnero L, Franchois A, Hugonin J P et al, Microwave imaging-complex permittivity reconstruction by simulated annealing. IEEE Trans. Microwave Theory Tech., 1991, 39(11): 1801-1807.
[62] Liu Q H et al. Modeling low-frequency electrode-type resistivity tools in invaded thin beds. IEEE Trans. Geosci. Remote Sens., 1994, 32(3): 494-498.
[63] Liu Q H. Nonlinear inversion of electrode-type resistivity measurements. IEEE Trans. Geosci. Remote Sens., 1994, 32(3): 499-507.
[64] 赵延文,聂在平.电极型电阻仪测井成像算法研究.地球物理学报,1997,
[65] 赵延文,聂在平.轴对称二维位场的变形玻恩迭代反演.电子学报,1997,25(12):10-14.
[66] 杨峰,聂在平.用迭代方法和双共轭梯度法重建二维电导率剖面分布.微波学报,2000,16(3):299-304.
[67] 杨峰,聂在平.轴对称二维非均匀介质结构的非线性反演方法.红外与毫米波学报,2000,19(6):419-424.
[68] 杨峰,聂在平.卢涛等.基于双感应测井仪低数据量的反演方法研究.电波科学学报,2001.16(1):118-122.
[69] Moghaddam M, Chew W C. Nonlinear two-dimensional velocity profile inversion using time-domain data. IEEE Trans. Geosci. Remote Sens., 1992, 30(1): 147-156.
[70] Liu Q H, Chew W C. A CG-FFHT method for the scattering solution of axsymmetric inhomogeneous media. Microwave Opt. Tech. Lett., 1993, 6(2): 101-104.
[71] Liu Q H, Chew W C. Application of the conjugate gradient fast Fourier Hankel transfer method with an improved fast Hankel transform algorithm. Radio Sci., 1994, 29(4): 1009-1022.
[72] Zhang G J, Zhang Z Q. Application of successive approximation method to the computation of the Green's function in axisymmetric inhomogeneous media. IEEE Trans. Geosci. Remote Sens., 1998, 36(3): 732-737.
[73] Kleinman R E, van den Berg P M. A modified gradient method for two-dimensional problems in tomography. J. Comput. Appl. Math., 1992, 42:17-35.
[74] Kleinman R E, van den Berg P M. An extended range-modified gradient technique for profile inversion. Radio Sci., 1993, 28(5): 877-884.
[75] Kleinman R E, van den Berg P M. Two-dimensional location and shape reconstruction. Radio Sci., 1994,29(4): 1157-1169.
[76] Liu Q H, Zhang Z Q, Xu X M. The hybrid extended Born approximation and CG-FFT method for electromagnetic induction problems. IEEE Trans. Geosci. Remote Sens., 2001, 39(2): 347-355.
[77] Torres-Verdin C, Habashy T M. Rapid 2.5-dimensional forward modeling and inversion via a new nonlinear scattering approximation. Radio Sci., 1994,29(4): 1051-1079.
[78] Zhang Z Q, Liu Q H. The hybrid extended Born approximation and CG-FFHT method for axisymmetric media. IEEE Trans. Geosci. Remote Sens., 2001, 39(4): 710-717.
[79] Torres-Verdin C, Habashy TM. A two-step linear inversion of two-dimensional electrical conductivity. IEEE Trans. Antennas Propagat., 1995, 43(4): 405-415.
[80] Abubakar A, van den Berg P M. Three-dimensional inverse scattering applied to cross-well induction sensors. IEEE Trans. Geosci. Remote Sens., 2000, 38(4): 1669-1680.
[81] Abubakar A, van den Berg P M. Three-dimensional nonlinear inversion in cross-well electrode logging. Radio Sci., 1998, 33(4): 989-1004.
[82] Abubakar A, van den Berg P M. Nonlinear inversion in electrode logging in highly deviated formation with invasion using an oblique coordinate system. IEEE Trans. Geosci. Remote Sens., 2000, 38(1): 25-38.
[83] Zhdanov M S, Fang S. Three-dimensional quasi-linear electromagnetic inversion. Radio Sci., 1996, 31(4): 741-754.
[84] Zhou C, Liu L. Radar-diffraction tomography using the modified quasi-linear approximation. IEEE Trans. Geosci. Remote Sens., 2000, 38(l):404-415.
[85] Caorsi S, Massa A, Pastorino M. A computational technique based on a real-coded genetic algorithm for microwave imaging purposes. IEEE Trans. Geosci. Remote Sens., 2000, 38(4): 1697-1708.
[86] Qing A, Lee C K, Jen L. Electromagnetic inverse scattering of two-dimensional perfectly conducting objects by real-coded genetic algorithm. IEEE Trans. Geosci. Remote Sens., 2001, 39(3):665-676.
[87] 邹长春,尉中良,柴细元等.利用遗传算法实现最优化测井解释.测井技术,1999,23(5):361-365.
[88] Chen S Y. Low-frequency subsurface electromagnetic modeling. Ph D. thesis, University of Illinois, 2000.
[89] Chert S Y, Chew W C, Kennedy W D. Inversion of 6FF40 induction tool measurement using the distorted Born iterative method. Proc. IEEE, 1997, 3: 1714-1716.
[90] Chert S Y, Chew W C, Kennedy W D. Efficient one dimensional inversion of induction log data. Proc. IEEE, 1998, 2: 990-993.
[91] 邓小波,聂在平,赵延文.一维平面分层介质的快速正反演方法.电波科学学报,2004,19(增刊):83-85.
[92] 潘锦,聂在平.二维平面分层介质中的数值模式匹配—算子矩阵理论及计算方法的应用.电子科学学刊,1994,16(4):388-394.
[93] 赵延文.二维非均匀介质中准静态位场的反演方法及应用研究:[博士学位论文].成都:电子科技大学 1997.
[94] 杨峰.复杂非均匀介质中电磁逆散射方法和应用分析:[博士学位论文].成都:电子科技大学 1997.
[95] 卿安永,李敬,任朗.二维介质柱的微波成像研究.地球物理学报,1998,41(1):117-123.
[96] Cui T J, Chew W C, Alaeddin A, et al. Inverse scattering of two-dimensional dielectric objects buried in a lossy earth using distorted Born iterative method. IEEE Trans. Geosci. Remote Sens., 2001, 39(2): 339-346.
[97] 邓小波,聂在平,赵延文等.利用相位感应测井数据反演电导率.2004全国博士生学术论坛论文集,四川成都,2004,电子科学与技术分论坛,5-8.
[98] Wang H N, Yang S D. A multiparameter iterative inversion of dual-laterolog in horizontally layered media and its error analysis. IEEE Trans. Geoscl. Remote Sens., 2002, 40(2): 482-493.
[99] Habashy T M, Chew W C, Chow E Y. Simultaneous reconstruction of permittivity and conductivity profiles in a radially inhomogeneous slab. Radio Sci., 1986, 21(4): 635-645.
[100] Habashy T M, Oristaglio M L, de Hoop A T. Simultaneous nonlinear reconstruction of two-dimensional permittivity and conductivity. Radio Sci., 1994, 29(4): 1101-1118.
[101] 邓小波,聂在平,赵延文等.利用相位感应测井反演二维轴对称电导率分布.第14届全国电磁兼容学术会议论文集,四川成都,2004,71-74.
[102] 解可新.最优化方法.天沣:天津大学出版社,1997.
[103] Meng Z Q, Takenaka T, Tanaka T. Image reconstruction of two-dimensional impenetrable objects using genetic algorithm. J. Electromagn. Waves Applicat., 1999, 13: 95-118.