井间地震波场数值模拟及波场特征研究
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摘要
井间地震是油气田勘探开发的一项关键技术,能够实现两井之间构造和储层等地质目标的高精度成像。井间地震数值模拟是研究复杂地层中井间地震波传播规律的有效手段,可以帮助认识井间地震的复杂波场。而识别和分析井间地震波场中各种主要波的传播特征是井间地震采集设计、资料处理、解释以及井间地震资料利用的前提。
论文首先研究井间地震波场数值模拟的方法,接着根据模拟生成的波场识别和分析井间各种主要波的传播特征。重点研究了三种地震波场数值模拟方法:一是弹性介质中改进的突变点加插值的射线追踪方法,这种方法的特点是能够快速地追踪井间地震记录的直达P波和S波、上行和下行反射波、PS和SP反射和透射转换波及干扰波(井筒波),并模拟生成多炮多道的水平分量和垂直分量的井间地震记录。本文根据模拟的结果,结合理论分析,系统总结了上述主要类型波在共炮点、共接收点、共偏移距和共中心深度点等4种道集中的传播规律。模拟的记录和野外实际采集的井间地震记录进行对比,可以识别出野外复杂波场中主要类型的波,以及他们的传播规律,分析结果证明数值模拟是正确的。二是VTI介质交错网格高阶有限差分数值模拟方法,选择这种方法是因为井间地震观测的波场常常显示出明显的各向异性,另外,井间地震要求有较高的模拟精度。本文在前人工作的基础上,推导了VTI介质时间-空间域二维三分量一阶速度-应力弹性波方程及其任意偶数阶时间和空间精度交错网格差分格式,特别是推导了Y-分量的方程、差分格式和边界条件,并研发了相应的数值模拟软件,能够模拟声波、各向同性及横向各向同性介质中各种复杂构造的二维三分量波场,能清楚地识别出快纵波、慢纵波、快横波和慢横波。模拟的结果解释了实际野外地震记录上由于各向异性引起的一些难解释的现象。三是粘弹各向异性介质频率空间域有限差分数值模拟方法,选择频率域主要是易于模拟衰减。本文在重复前人关于频率空间域各向异性准P波波场推导的基础上,补充推导了加入粘弹性的公式,研发了弹性和粘弹性VTI介质准P波正演模拟软件,能模拟更接近井间实际介质的各向同性、各向异性准P波的波场。在频率空间域有限差分算法的实现中改进了大型稀疏带状矩阵的解法,解决了存储空间不够和计算时间过长的问题,解决了利用傅里叶变换的周期性和共轭对称性计算频率域波场的问题。
Cross-well seismic is an important technology in exploration and development of oilfield. This technology could help us in high precision imaging of geological targets as structure and reservoir between wells. The numerical simulation of crosswell seismic is an effective method in studying seismic wave propagation regularity of complex strata between wells which could help us in recognizing complex wave fields of crosswell seismic. The recognition and analysis of crosswell seismic wave propagation is a precondition of crosswell seismic acquisition, data processing and explanation.
In this paper, the numerical simulation methods within crosswell seismic wave fields have been studied, and the main waves’propagation characteristics of crosswell seismic wave field has then been recognized and analyzed based on the analysis of the wave fields generated by numerical stimulation. There are three numerical stimulation methods for seismic wave fields: the first method is ray tracing of mutational point with interpolation in elastic medium, the point of this method is that it could simulate the seismic records which include horizontal component and vertical component of multiple shots and channels crosswell seismic records in a short time. With this method, one can get crosswell seismic records include P-wave and S-wave first-break、up-going reflection wave and down-going reflection wave、reflection and transmitting PS or SP converted wave and tube wave. According to the modeling results and combined with the theoretical analysis, this paper summarizes propagation regularity of the main type waves systematically, which are in the four different gathers of CSP, CRP, COP and CMP. With comparison between modeling recordings and field crosswell recordings, the main types of wave can be recognized in the complex wavefield, and the numerical simulation is proved right under the analysis of propagation characteristics. The second method is the numerical simulation methods of staggered grid high-order finite difference in the VTI media, because the wave fields observed from well-to-well can show obvious anisotropy, and what’s more, the cross-well seismic demands higher simulation precision. This paper is based on summary and analysis of predecessor’s experience to deduce wave equation of three-component, first-order stress-velocity elastic wave equation in VTI medium in time-space domain, and any even-order accurate staggered-grid finite-difference scheme in time-space domain. Specially the Y-component equation、absorbing boundary condition, difference scheme have also been deduced and the software of numerical simulation soft has been researched and developed by myself. The software could simulate sonic wave and three-component wave fields in isotropic and anisotropic medium. So one can recognize fast and slow P-wave、fast and slow S-wave, one can also explain some difficult phenomena of actual seismic records that caused by anisotropy with the simulation result. The third method is the numerical simulation method of anisotropic medium in frequency-space domain. The main reason to choose frequency domain is that it is easy to simulate attenuation in frequency domain. This paper is based on the propagation formula deduction of quasi-p wave in anisotropic media, the formula of attenuation wave propagation which is in viscoelastic media is deduced. And the forward modeling software of quasi-p wave in elastic and viscoelastic media is developed which can closely model real crosswell seismic quasi-p wave fields in isotropic and anisotropic media. At the same time, on the aspect of finite-difference method in frequency-space domain, it improves the algorithm of large sparse-band matrix and solves the problem of memory space inadequate and long computing time, finds the way to calculate wave fileds in frequency domain on the periodicity and conjugate symmetry of fouier transform. .
论文首先研究井间地震波场数值模拟的方法,接着根据模拟生成的波场识别和分析井间各种主要波的传播特征。重点研究了三种地震波场数值模拟方法:一是弹性介质中改进的突变点加插值的射线追踪方法,这种方法的特点是能够快速地追踪井间地震记录的直达P波和S波、上行和下行反射波、PS和SP反射和透射转换波及干扰波(井筒波),并模拟生成多炮多道的水平分量和垂直分量的井间地震记录。本文根据模拟的结果,结合理论分析,系统总结了上述主要类型波在共炮点、共接收点、共偏移距和共中心深度点等4种道集中的传播规律。模拟的记录和野外实际采集的井间地震记录进行对比,可以识别出野外复杂波场中主要类型的波,以及他们的传播规律,分析结果证明数值模拟是正确的。二是VTI介质交错网格高阶有限差分数值模拟方法,选择这种方法是因为井间地震观测的波场常常显示出明显的各向异性,另外,井间地震要求有较高的模拟精度。本文在前人工作的基础上,推导了VTI介质时间-空间域二维三分量一阶速度-应力弹性波方程及其任意偶数阶时间和空间精度交错网格差分格式,特别是推导了Y-分量的方程、差分格式和边界条件,并研发了相应的数值模拟软件,能够模拟声波、各向同性及横向各向同性介质中各种复杂构造的二维三分量波场,能清楚地识别出快纵波、慢纵波、快横波和慢横波。模拟的结果解释了实际野外地震记录上由于各向异性引起的一些难解释的现象。三是粘弹各向异性介质频率空间域有限差分数值模拟方法,选择频率域主要是易于模拟衰减。本文在重复前人关于频率空间域各向异性准P波波场推导的基础上,补充推导了加入粘弹性的公式,研发了弹性和粘弹性VTI介质准P波正演模拟软件,能模拟更接近井间实际介质的各向同性、各向异性准P波的波场。在频率空间域有限差分算法的实现中改进了大型稀疏带状矩阵的解法,解决了存储空间不够和计算时间过长的问题,解决了利用傅里叶变换的周期性和共轭对称性计算频率域波场的问题。
Cross-well seismic is an important technology in exploration and development of oilfield. This technology could help us in high precision imaging of geological targets as structure and reservoir between wells. The numerical simulation of crosswell seismic is an effective method in studying seismic wave propagation regularity of complex strata between wells which could help us in recognizing complex wave fields of crosswell seismic. The recognition and analysis of crosswell seismic wave propagation is a precondition of crosswell seismic acquisition, data processing and explanation.
In this paper, the numerical simulation methods within crosswell seismic wave fields have been studied, and the main waves’propagation characteristics of crosswell seismic wave field has then been recognized and analyzed based on the analysis of the wave fields generated by numerical stimulation. There are three numerical stimulation methods for seismic wave fields: the first method is ray tracing of mutational point with interpolation in elastic medium, the point of this method is that it could simulate the seismic records which include horizontal component and vertical component of multiple shots and channels crosswell seismic records in a short time. With this method, one can get crosswell seismic records include P-wave and S-wave first-break、up-going reflection wave and down-going reflection wave、reflection and transmitting PS or SP converted wave and tube wave. According to the modeling results and combined with the theoretical analysis, this paper summarizes propagation regularity of the main type waves systematically, which are in the four different gathers of CSP, CRP, COP and CMP. With comparison between modeling recordings and field crosswell recordings, the main types of wave can be recognized in the complex wavefield, and the numerical simulation is proved right under the analysis of propagation characteristics. The second method is the numerical simulation methods of staggered grid high-order finite difference in the VTI media, because the wave fields observed from well-to-well can show obvious anisotropy, and what’s more, the cross-well seismic demands higher simulation precision. This paper is based on summary and analysis of predecessor’s experience to deduce wave equation of three-component, first-order stress-velocity elastic wave equation in VTI medium in time-space domain, and any even-order accurate staggered-grid finite-difference scheme in time-space domain. Specially the Y-component equation、absorbing boundary condition, difference scheme have also been deduced and the software of numerical simulation soft has been researched and developed by myself. The software could simulate sonic wave and three-component wave fields in isotropic and anisotropic medium. So one can recognize fast and slow P-wave、fast and slow S-wave, one can also explain some difficult phenomena of actual seismic records that caused by anisotropy with the simulation result. The third method is the numerical simulation method of anisotropic medium in frequency-space domain. The main reason to choose frequency domain is that it is easy to simulate attenuation in frequency domain. This paper is based on the propagation formula deduction of quasi-p wave in anisotropic media, the formula of attenuation wave propagation which is in viscoelastic media is deduced. And the forward modeling software of quasi-p wave in elastic and viscoelastic media is developed which can closely model real crosswell seismic quasi-p wave fields in isotropic and anisotropic media. At the same time, on the aspect of finite-difference method in frequency-space domain, it improves the algorithm of large sparse-band matrix and solves the problem of memory space inadequate and long computing time, finds the way to calculate wave fileds in frequency domain on the periodicity and conjugate symmetry of fouier transform. .
引文
[1] Pessenden,R.A.,Method and apparatus for locating ore bodies.U.S.Patent.1917,(1):240, 328
[2] 朱光明.垂直地震剖面.北京:石油工业出版社,1992
[3] 刘合,王玉普等.国外井间地震技术.北京:石油工业出版社,1998
[4] 宋建国.井间地震技术综述.世界石油科学.1997,81(2):7-13,6
[5] P.Bios,M.LA.Porte,M,Lavergne,and G.Thomas,Well-to-well seismic measurements, Geophysics,1972,37(6):471-480
[6] Mathisen M.E.,et.al.,Time lapse crosswell seismic tomogram interpretation:implications for heavy oil reservoir characterization,thermal recovery process monitoring and tomographic imaging technology. Geophysics, Soc. Of Expl. Geophys., 1995,60:631-650
[7] Lee D.S., Stevenson V.M., etal. Time lapse crosswell seismic tomography to characterize flow structure in the reservoir during the thermal stimulation. Geophysics , Soc. Of Expl. Geophys.,1995,60:660-666
[8] 陈世军,刘洪,周建宇,何惺华.井间地震技术的现状与展望.地球物理学进展,2003, 18(3):524~529.
[9] 李庆忠,王建花.井间地震勘探的误区及出路.石油地球物理勘探,2004,39(1):1-11
[10] 周建宇.井间地震研究与应用:[学位论文].北京:中国科学院研究生院,2002
[11] 曹辉. 井间地震技术发展现状.勘探地球物理进展, 2002,25(6):7-10
[12] Williams,M.C,et.al.,井间地震成像:这种技术的全盛时期来到了吗?,邵祝华译.石油物探译丛,1997,6(3):39-46
[13] Y.Tokua,T,Nye and Murat.,K.,Porosity,permeability,shear strength:Crosswell tomography below an iron foundary.Geophysics,1994,59(10):1542-1550
[14] Harris, J.M., Richard C. Robert T.et.al., High-resolution crosswell imaging of a west Texas carbonate reservoir: Part l-Project summary and interpretation.Geophysics,1995, 60(3):667-681
[15] Schaack M.V., Harris, J.M.,and Rector J.W., High-resolution crosswell imaging of a west Texas carbonate reservoir: Part 2-Wavefield modeling,and analysis,Geophysics,1995,60(3): 682-691
[16] Rector J.W., Lazaratos S.K., Harris J.M.,et.al.,High-resolution crosswell imaging of a west Texas carbonate reservoir: Part 3-Wavefield separation of reflections, Geophysics, 1995,60(3):692-701
[17] Lazaratos S.K., Harris J.M., Rector J.W., ,et.al., High-resolution crosswell imaging of a west Texas carbonate reservoir: Part 4 – Reflection Imaging, Geophysics, 1995,60(3): 702-711
[18] Song,Z-M,Williamson,P.R.,Pratt,R.G.,Frequency-domain acoustic-wave modeling and inversion of crosshole data:Part I-2.5D modeling methods.Geophysics,1995,60(3):784-795
[19] Song,Z-M,Williamson,P.R.,Pratt,R.G.,Frequency-domain acoustic-wave modeling and inversion of crosshole data:Part II-Inversion method,synthetic experiments and real-data results.Geophysics,1995,60(3):796-809
[20] Williamson,P.R.,and Pratt,R.G.,A critical review of acoustic wave modeling procedures in 2.5D,Geophysics,1995,60(3)591-595
[21] Cerveny V., Molotkov I.A.. Psencik. Ray method in seismology. Charles Univ. Press, Prague, 1977.
[22] Byun,B.s.,Seismic parameters for isotropic media,Geophysics,1984,49(11)1908-1914
[23] Tanimoto,T.,Surface-wave ray tracing equations and Permat’s principle in an anisotropic earth.Geophys.J.R.astr.Soc.,1987,88:231-240
[24] Shearer,P.M.,Chapman,C.H.,Ray tracing in azimuthally anisotropic media-I:Results for models of aligned cracks in the upper crust. Geophys.J.1989,96:51-64
[25] Gajewski,D.,Psencik,I.,qP wave phase velocities in weakly anisotropic media Perturbati- on approach:66th Ann. Internat.Mtg.,Soc. Expl. Geophys.,Expanded abstracts,1996,1507-1510
[26] Chapman,C.H.,Shearer,P.M.,Ray tracing in azimuthally anisotropic media-II:Quasi-shear wave coupling:Geophys.J.,1989,96,65-83
[27] 牛滨华,孙春岩编著.半空间介质与地震波传播.北京:石油工业出版社,2002.10
[28] Kosloff D., Baysal E.. Forward Modeling by a Fourrier Method. Geophysics, 1982, 47(10):1954-1966
[29] Smith W. D. The application of finite-element analysis to body wave propagation problems. Geophys. J. Roy. Astr. Soc.,1975,42:747-768
[30] Alterman Z. and Karak F.C.. Propagation of elastic wave in layered media by finite- difference methods. Bull., Seism. Soc. Am., 1968, 58:367-398
[31] Boore D.M.. finite-difference methods for seismic wave propagation in heterogeneous materials, in Methods in computational physics, 11: B.A. Bolt, ed., Academic Press,inc.
[32] Alford R.M., Kelly K.R. and Boore D.M.. Accuracy of finite-difference methods modeling of the acoustic wave equation. Geophysics, 1974, 39(6):834-842
[33] Asakawa E. and Kawanaka T. Seismic ray tracing using linear traveltime interpolation. Geophysical prospecting, 1993, 44:99-11
[34] Rector,J.W.,Lazaratos,S.K.,Harris,J.M.et.al.,Multidomain analysis and wavefiled separation of cross-well seismic data.Geophysics,1994,59(1):27-35
[35] Apsel,R.J.,Dynamic Green’s Functions for layered media and application to boundary- value problems:PH.D.thesis,University of California at san Diego,1979
[36] 杜光升,叶夏根,乔文孝.井间声波场有限差分模拟,声学技术,2000(3):156-157
[37] 孔庆丰.井间地震波场数值模拟技术研究与应用,勘探地球物理进展,2006,29(5):333- 336
[38] 何惺华.井间地震资料中的横波信息,石油物探,2003,42(3):374-378
[39] 何惺华.井间地震资料中的反射波分析,油气地球物理,2005,3(4):1-8
[40] 杜世通.井间地震观测数据模拟和偏移的有限单元法,油气地球物理,2004,2(4):78-82
[41] Mora,P.,Modeling anisotropic seismic waves in 3-D :59th ANN. Internat Mtg.,Soc. Expl. Geophys., Expanded Abstracts,1989,1039-104
[42] Tsings,C.,Vafidis,A.,Elastic wave propogation in transversely isotropic media using finite difference.Geophysical Prospecting,1900,38:933-949
[43] Igel,H.,Mora,P.,Riollet,B.,Anisotropic wave propagation through finite-difference grids[J].Geophysics,1995,60(4):1203-1261
[44] Kosloff,D.,Propagation modeling in elastic anisotropic media.Symposium of the SEG,1989,58,SM1.1
[45] Carcione,S.P.,Brown,R.J.and Lawton,D.C.,Orthorhombic anisotropy:A physical modeling study.Geophysics,1991,56(10):1603-1613
[46] 牛滨华,孙春岩.方位界面及其波场数值模拟.石油地球物理勘探,1994,29(6):685-694
[47] 牛滨华,何樵登,孙春岩.裂隙各向异性介质波场 VSP 多分量记录的数值模拟.地球物理学报,1995,38(4):519-527
[48] 牛滨华,王海君,沈操.实用 P 波速度各向异性提取的一种方法研究.地震各向异性学术研讨会论文摘要集,1998:73-74
[49] 侯安宁,何樵登.各向异性介质中弹性波动高阶差分法及其稳定性的研究,地球物理学报,1995,38(2): 243-251
[50] 何樵登,张中杰.横向各向同性介质中地震波及其数值模拟.吉林:吉林大学出版.1996
[51] 阴可,杨慧珠.各向异性介质中的 AVO.地球物理学报,1998,41(3):382-391
[52] 董良国. 弹性波数值模拟中的吸收边界条件. 石油地球物理勘探, 1999, 34(1):45-56
[53] 张美根.各向异性弹性波正反演问题研究:[学位论文].北京:中国科学院地质与地球物理研究所,2000
[54] 董良国, 马在田, 曹景忠. 一阶弹性波方程交错网格高阶差分法稳定性研究. 地球物理学报, 2000, 43(6):856~864
[55] 董良国,马在田,曹景忠.一阶弹性波方程交错网格高阶差分解法稳定性研究,地球物理学报,2000,43(6): 856-864
[56] 张文波.井间地震交错网格高阶差分数值模拟及逆时偏移成像研究: [学位论文].西安:长安大学,2005
[57] Lysmer,J.,and Drake,L.A.,A finite-element method for seismology,in Bolt,B.A.,Ed.,Meth- ods in computational physics,Vol.11:Seismology:Surface waves and earth oscillations:Acade- mic press Inc.
[58] Marfurt K.J.,Accuracy of finite-difference and finite-element modeling of scalar and elastic wave equations.Geophysics,1984,49(5):533-549
[59] Marfurt,K.J.,and Shin,C.,The future of iterative modeling in geophysical exploration, in Eisner,E.,Ed.,Handbook of geophysical exploration:I-seismic exploration,Vol.21:Supercomputers in seismic exploration:Pergamon Press,203-228
[60] Shin,C.,Nonlinear elastic wave inversion by blocky parameterization:Ph.D.hesis,Univ.of Tulsa.
[61] Pratt,R.G.,and Worhington,M.H.,Inverse theory applied to multi-source crosshole tomography,part I:Acoustic wave-equation method:Geophys.Prosp.,1990,38,287-310
[62] Pratt,R.G., Inverse theory applied to multi-source crosshole tomography,part II:Elastic wave-equation method:Geophys.Prosp.,1990,38,287-310
[63] Pratt,R.G. Frequency-domain elastic wave modeling by finite differences: A tool for crosshole seismic imaging.Geophysics,1990,55(5):626-632
[64] Jo,C.H.,Shin,C.,and Suh,J.H.,An optimal 9-point finite-difference frequency space 2-D scalar wave extrapolator.Geophysics,1996,61(2):529-537
[65] Shin,C.,and Sohn,H.,A frequency-space 2-D scalar wave extrapolator using extended 25-point finite-difference operators.Geophysics,1998,63(1):289-296
[66] 吴国忱,梁锴.VTI 介质频率-空间域准 P 波正演模拟.石油地球物理勘探,2005,40(5): 535-545
[67] 吴国忱.各向异性介质地震波传播和成像.山东东营:中国石油大学出版社,2006
[68] 瑞克 N.H.粘弹性介质中的波.许云,译.北京:地质出版社,1981
[69] Carcione,J.M.et.al.Wave propagation simulation in a linear viscoelastic medium: Geophys. J.Roy.Astr.Soc.1988,93:393-407.Erratum,95,642.
[70] Carcione,J.M.et.al.Wave propagation simulation in a linear viscoelastic medium: Geophys. J.Roy.Astr.Soc.1988,95(4):597-611
[71] Carcione,J.M.,Modeling anelastic singular surface waves in the earth.Geophysics,1992, 57(6):781-792
[72] Carcione,J.M.,Constitutive model and wave equations for linear,viscoelastic, anisotropic media,Geophysics,1995,60(2):537-548
[73] Stekl,I.,and Pratt,R.G.,Accurate viscoelastic modeling by frequency-domain finite differ- rence using rotated operators.Geophyscics,1998,63(5):1779-1794
[74] 阎贫,何继善.横向各向同性粘弹性介质中的地震波.石油物探,1992,31(4):23-34
[75] 宋常瑜,裴正林.井间地震粘弹性波场特征的数值模拟研究,石油物探,2006,45(5): 508-513
[76] 郭智奇,刘财,杨宝俊等.粘弹各向异性介质中地震波场模拟与特征.地球物理学进展,2007,22(3):804-810
[77] 杜启振,刘莲莲,孙晶波.各向异性粘弹性空隙介质地震波场伪谱法正演模拟.物理学报,2007,56(10):6143-6148
[78] 蒋先艺,刘贤功,宋葵.复杂构造模型正演模拟.北京:石油工业出版社,2005
[79] 朱光明,曹建章.高斯射线束合成记录.西安:西北工业大学出版社,1993
[80] 朱光明,突变点加插值射线追踪.孙枢主编,理论与应用地球物理进展[C].北京:气象出版社,2002,255~259
[81] 罗大清,宋炜,吴律.一种有效的处理模型角点反射的方法.石油物探,2000,39(4):26-31
[82] Renolds,A.C.,Boundary conditions for the numerical solutions of wave propagation problems.Geophysics,1978,43(6):1099-1110
[83] Clayton,R.,Engquist,B.,Absorbing boundary conditions for acoustic and elastic wave equation.Bull.Seis.Soc.Am.,1977,67:1529-1540
[84] 董良国.地震波数值模拟与反演中几个关键问题研究:[学位论文].上海:同济大学,2003
[85] Cerjan,C.,Kosloff,D.,Kosloff,R.,etc.,A nonreflectiong boundary condition for discrete acoustic and elastic wave equations.Geophysics,1985,50(4):705-808
[86] Engquist B. and Majda A. Absorbing boundary conditions for the numerical simulation of waves.Math.Comput.1977,32:313-357
[87] Marfurt,K.J.,Accuracy of finite-difference and finite-element modeling of the scalar and elastic wave equations.Geophysics,1984,49(5):533-549
[88] Shin,C.Sponge condition for frequency-domain modeling.Geophysics,1995,60(6): 1870- 1874
[89] Berenger,J.P.,Aperfectly matched layer for absorption of electromagnetic waves.J. Com- put Phys.,1994,114,185-200
[90] 马在田.地震成像技术-有限差分法偏移.北京:石油工业出版社,1989
[91] Sena,A.G., Seismic traveltime equations for azimuthaly anisotropic and isotropic media;Estimation of interval elastic properties.Geophysics,1991,56(12),2090-2101
[92] Leon Thomsen. Weak elastic anisotropy.Geophysics,1986,51(10):1954-1966
[93] 杜世通.地震波动力学.东营:石油大学出版社,2003
[94] Alkhalifah T.,Acoustic approximation for processing in transversely isotropic media. Geophysics,1998,63(2):623-631
[95] Alkhalifah T.,An acoustic wave equation for anisotropic media. Geiophysics,2000,65(4): 1239~1250
[96] Alkhalifah T. An acousitic wave equation for orthorhombic media. Geophysics,2003, 68(4):1169~1172
[97] Min,D-J,Shin,C.et.al., Improved frequency domain elastic wave modeling using averageing difference operators.Geophysics,2000,65(3):884-895
[98] Peter Deuflhard,Newton methods for nonlinear problems:Affine invariance and adaptive algorithms(影印版).北京:科学出版社,2006
[99] 徐成贤,陈志平,李乃成.近代优化方法.北京:科学出版社,2002
[100] 何振亚.自适应信号处理.北京:科学出版社,2002
[101] 吴国忱,梁锴.VTI 介质 qP 波方程高精度有限差分算子.地球物理学进展,2007
[102] 殷文,印兴耀,吴国忱等.高精度频率域弹性波方程有限差分方法及波场模拟.地球物理学报,2006,49(2):561-568 Yin W, Yin X Y, Wu G C, et al. The method of finite difference of high precision elastic wave equations in the frequency domain and wave-field simulation.Chinese J.Geophys. (in Chinese),2006,49(2):561-56
[103] 吴国忱,梁锴. VTI 介质准 P 波频率空间域组合边界条件研究.石油物探,2005,44(4): 301-307
[104] 夏凡,董良国,马在田.三维弹性波数值模拟中的吸收边界条件.地球物理学报,2004, 47(1):132-136 Xia F, Dong L G,Ma Z T. Absorbing boundary conditions in 3D elastic_wave numerical modeling.Chinese J.Geophys. ( in Chinese), 2004,47(1):132-136
[105] Chew, W. C., Liu, Q. H.,Perfectly matched layers for elastodynamics:A new absorbing boundary condition.J. Comp. Acoust.,1996,4:341-359
[106] Rappaport C.M.,Perfectly matched absorbing boundary conditions based on anisotropic lossy mapping of space:IEEE Micorwave Guided Wave Lett,1995,5:90-92
[107] 王守东,声波方程完全匹配层吸收边界.石油地球物理勘探,2003,38 (1):31-34
[108] 吴建平,王正华,李晓梅.稀疏线性方程组高效求解与并行计算.长沙:湖南科学技术出版社,2004
[109] 刘长学.超大规模稀疏矩阵计算方法.上海:上海科学技术出版社,1990
[110] 刘万勋,刘长学.大型稀疏线性方程组的解法.国防工业出版社,1981
[2] 朱光明.垂直地震剖面.北京:石油工业出版社,1992
[3] 刘合,王玉普等.国外井间地震技术.北京:石油工业出版社,1998
[4] 宋建国.井间地震技术综述.世界石油科学.1997,81(2):7-13,6
[5] P.Bios,M.LA.Porte,M,Lavergne,and G.Thomas,Well-to-well seismic measurements, Geophysics,1972,37(6):471-480
[6] Mathisen M.E.,et.al.,Time lapse crosswell seismic tomogram interpretation:implications for heavy oil reservoir characterization,thermal recovery process monitoring and tomographic imaging technology. Geophysics, Soc. Of Expl. Geophys., 1995,60:631-650
[7] Lee D.S., Stevenson V.M., etal. Time lapse crosswell seismic tomography to characterize flow structure in the reservoir during the thermal stimulation. Geophysics , Soc. Of Expl. Geophys.,1995,60:660-666
[8] 陈世军,刘洪,周建宇,何惺华.井间地震技术的现状与展望.地球物理学进展,2003, 18(3):524~529.
[9] 李庆忠,王建花.井间地震勘探的误区及出路.石油地球物理勘探,2004,39(1):1-11
[10] 周建宇.井间地震研究与应用:[学位论文].北京:中国科学院研究生院,2002
[11] 曹辉. 井间地震技术发展现状.勘探地球物理进展, 2002,25(6):7-10
[12] Williams,M.C,et.al.,井间地震成像:这种技术的全盛时期来到了吗?,邵祝华译.石油物探译丛,1997,6(3):39-46
[13] Y.Tokua,T,Nye and Murat.,K.,Porosity,permeability,shear strength:Crosswell tomography below an iron foundary.Geophysics,1994,59(10):1542-1550
[14] Harris, J.M., Richard C. Robert T.et.al., High-resolution crosswell imaging of a west Texas carbonate reservoir: Part l-Project summary and interpretation.Geophysics,1995, 60(3):667-681
[15] Schaack M.V., Harris, J.M.,and Rector J.W., High-resolution crosswell imaging of a west Texas carbonate reservoir: Part 2-Wavefield modeling,and analysis,Geophysics,1995,60(3): 682-691
[16] Rector J.W., Lazaratos S.K., Harris J.M.,et.al.,High-resolution crosswell imaging of a west Texas carbonate reservoir: Part 3-Wavefield separation of reflections, Geophysics, 1995,60(3):692-701
[17] Lazaratos S.K., Harris J.M., Rector J.W., ,et.al., High-resolution crosswell imaging of a west Texas carbonate reservoir: Part 4 – Reflection Imaging, Geophysics, 1995,60(3): 702-711
[18] Song,Z-M,Williamson,P.R.,Pratt,R.G.,Frequency-domain acoustic-wave modeling and inversion of crosshole data:Part I-2.5D modeling methods.Geophysics,1995,60(3):784-795
[19] Song,Z-M,Williamson,P.R.,Pratt,R.G.,Frequency-domain acoustic-wave modeling and inversion of crosshole data:Part II-Inversion method,synthetic experiments and real-data results.Geophysics,1995,60(3):796-809
[20] Williamson,P.R.,and Pratt,R.G.,A critical review of acoustic wave modeling procedures in 2.5D,Geophysics,1995,60(3)591-595
[21] Cerveny V., Molotkov I.A.. Psencik. Ray method in seismology. Charles Univ. Press, Prague, 1977.
[22] Byun,B.s.,Seismic parameters for isotropic media,Geophysics,1984,49(11)1908-1914
[23] Tanimoto,T.,Surface-wave ray tracing equations and Permat’s principle in an anisotropic earth.Geophys.J.R.astr.Soc.,1987,88:231-240
[24] Shearer,P.M.,Chapman,C.H.,Ray tracing in azimuthally anisotropic media-I:Results for models of aligned cracks in the upper crust. Geophys.J.1989,96:51-64
[25] Gajewski,D.,Psencik,I.,qP wave phase velocities in weakly anisotropic media Perturbati- on approach:66th Ann. Internat.Mtg.,Soc. Expl. Geophys.,Expanded abstracts,1996,1507-1510
[26] Chapman,C.H.,Shearer,P.M.,Ray tracing in azimuthally anisotropic media-II:Quasi-shear wave coupling:Geophys.J.,1989,96,65-83
[27] 牛滨华,孙春岩编著.半空间介质与地震波传播.北京:石油工业出版社,2002.10
[28] Kosloff D., Baysal E.. Forward Modeling by a Fourrier Method. Geophysics, 1982, 47(10):1954-1966
[29] Smith W. D. The application of finite-element analysis to body wave propagation problems. Geophys. J. Roy. Astr. Soc.,1975,42:747-768
[30] Alterman Z. and Karak F.C.. Propagation of elastic wave in layered media by finite- difference methods. Bull., Seism. Soc. Am., 1968, 58:367-398
[31] Boore D.M.. finite-difference methods for seismic wave propagation in heterogeneous materials, in Methods in computational physics, 11: B.A. Bolt, ed., Academic Press,inc.
[32] Alford R.M., Kelly K.R. and Boore D.M.. Accuracy of finite-difference methods modeling of the acoustic wave equation. Geophysics, 1974, 39(6):834-842
[33] Asakawa E. and Kawanaka T. Seismic ray tracing using linear traveltime interpolation. Geophysical prospecting, 1993, 44:99-11
[34] Rector,J.W.,Lazaratos,S.K.,Harris,J.M.et.al.,Multidomain analysis and wavefiled separation of cross-well seismic data.Geophysics,1994,59(1):27-35
[35] Apsel,R.J.,Dynamic Green’s Functions for layered media and application to boundary- value problems:PH.D.thesis,University of California at san Diego,1979
[36] 杜光升,叶夏根,乔文孝.井间声波场有限差分模拟,声学技术,2000(3):156-157
[37] 孔庆丰.井间地震波场数值模拟技术研究与应用,勘探地球物理进展,2006,29(5):333- 336
[38] 何惺华.井间地震资料中的横波信息,石油物探,2003,42(3):374-378
[39] 何惺华.井间地震资料中的反射波分析,油气地球物理,2005,3(4):1-8
[40] 杜世通.井间地震观测数据模拟和偏移的有限单元法,油气地球物理,2004,2(4):78-82
[41] Mora,P.,Modeling anisotropic seismic waves in 3-D :59th ANN. Internat Mtg.,Soc. Expl. Geophys., Expanded Abstracts,1989,1039-104
[42] Tsings,C.,Vafidis,A.,Elastic wave propogation in transversely isotropic media using finite difference.Geophysical Prospecting,1900,38:933-949
[43] Igel,H.,Mora,P.,Riollet,B.,Anisotropic wave propagation through finite-difference grids[J].Geophysics,1995,60(4):1203-1261
[44] Kosloff,D.,Propagation modeling in elastic anisotropic media.Symposium of the SEG,1989,58,SM1.1
[45] Carcione,S.P.,Brown,R.J.and Lawton,D.C.,Orthorhombic anisotropy:A physical modeling study.Geophysics,1991,56(10):1603-1613
[46] 牛滨华,孙春岩.方位界面及其波场数值模拟.石油地球物理勘探,1994,29(6):685-694
[47] 牛滨华,何樵登,孙春岩.裂隙各向异性介质波场 VSP 多分量记录的数值模拟.地球物理学报,1995,38(4):519-527
[48] 牛滨华,王海君,沈操.实用 P 波速度各向异性提取的一种方法研究.地震各向异性学术研讨会论文摘要集,1998:73-74
[49] 侯安宁,何樵登.各向异性介质中弹性波动高阶差分法及其稳定性的研究,地球物理学报,1995,38(2): 243-251
[50] 何樵登,张中杰.横向各向同性介质中地震波及其数值模拟.吉林:吉林大学出版.1996
[51] 阴可,杨慧珠.各向异性介质中的 AVO.地球物理学报,1998,41(3):382-391
[52] 董良国. 弹性波数值模拟中的吸收边界条件. 石油地球物理勘探, 1999, 34(1):45-56
[53] 张美根.各向异性弹性波正反演问题研究:[学位论文].北京:中国科学院地质与地球物理研究所,2000
[54] 董良国, 马在田, 曹景忠. 一阶弹性波方程交错网格高阶差分法稳定性研究. 地球物理学报, 2000, 43(6):856~864
[55] 董良国,马在田,曹景忠.一阶弹性波方程交错网格高阶差分解法稳定性研究,地球物理学报,2000,43(6): 856-864
[56] 张文波.井间地震交错网格高阶差分数值模拟及逆时偏移成像研究: [学位论文].西安:长安大学,2005
[57] Lysmer,J.,and Drake,L.A.,A finite-element method for seismology,in Bolt,B.A.,Ed.,Meth- ods in computational physics,Vol.11:Seismology:Surface waves and earth oscillations:Acade- mic press Inc.
[58] Marfurt K.J.,Accuracy of finite-difference and finite-element modeling of scalar and elastic wave equations.Geophysics,1984,49(5):533-549
[59] Marfurt,K.J.,and Shin,C.,The future of iterative modeling in geophysical exploration, in Eisner,E.,Ed.,Handbook of geophysical exploration:I-seismic exploration,Vol.21:Supercomputers in seismic exploration:Pergamon Press,203-228
[60] Shin,C.,Nonlinear elastic wave inversion by blocky parameterization:Ph.D.hesis,Univ.of Tulsa.
[61] Pratt,R.G.,and Worhington,M.H.,Inverse theory applied to multi-source crosshole tomography,part I:Acoustic wave-equation method:Geophys.Prosp.,1990,38,287-310
[62] Pratt,R.G., Inverse theory applied to multi-source crosshole tomography,part II:Elastic wave-equation method:Geophys.Prosp.,1990,38,287-310
[63] Pratt,R.G. Frequency-domain elastic wave modeling by finite differences: A tool for crosshole seismic imaging.Geophysics,1990,55(5):626-632
[64] Jo,C.H.,Shin,C.,and Suh,J.H.,An optimal 9-point finite-difference frequency space 2-D scalar wave extrapolator.Geophysics,1996,61(2):529-537
[65] Shin,C.,and Sohn,H.,A frequency-space 2-D scalar wave extrapolator using extended 25-point finite-difference operators.Geophysics,1998,63(1):289-296
[66] 吴国忱,梁锴.VTI 介质频率-空间域准 P 波正演模拟.石油地球物理勘探,2005,40(5): 535-545
[67] 吴国忱.各向异性介质地震波传播和成像.山东东营:中国石油大学出版社,2006
[68] 瑞克 N.H.粘弹性介质中的波.许云,译.北京:地质出版社,1981
[69] Carcione,J.M.et.al.Wave propagation simulation in a linear viscoelastic medium: Geophys. J.Roy.Astr.Soc.1988,93:393-407.Erratum,95,642.
[70] Carcione,J.M.et.al.Wave propagation simulation in a linear viscoelastic medium: Geophys. J.Roy.Astr.Soc.1988,95(4):597-611
[71] Carcione,J.M.,Modeling anelastic singular surface waves in the earth.Geophysics,1992, 57(6):781-792
[72] Carcione,J.M.,Constitutive model and wave equations for linear,viscoelastic, anisotropic media,Geophysics,1995,60(2):537-548
[73] Stekl,I.,and Pratt,R.G.,Accurate viscoelastic modeling by frequency-domain finite differ- rence using rotated operators.Geophyscics,1998,63(5):1779-1794
[74] 阎贫,何继善.横向各向同性粘弹性介质中的地震波.石油物探,1992,31(4):23-34
[75] 宋常瑜,裴正林.井间地震粘弹性波场特征的数值模拟研究,石油物探,2006,45(5): 508-513
[76] 郭智奇,刘财,杨宝俊等.粘弹各向异性介质中地震波场模拟与特征.地球物理学进展,2007,22(3):804-810
[77] 杜启振,刘莲莲,孙晶波.各向异性粘弹性空隙介质地震波场伪谱法正演模拟.物理学报,2007,56(10):6143-6148
[78] 蒋先艺,刘贤功,宋葵.复杂构造模型正演模拟.北京:石油工业出版社,2005
[79] 朱光明,曹建章.高斯射线束合成记录.西安:西北工业大学出版社,1993
[80] 朱光明,突变点加插值射线追踪.孙枢主编,理论与应用地球物理进展[C].北京:气象出版社,2002,255~259
[81] 罗大清,宋炜,吴律.一种有效的处理模型角点反射的方法.石油物探,2000,39(4):26-31
[82] Renolds,A.C.,Boundary conditions for the numerical solutions of wave propagation problems.Geophysics,1978,43(6):1099-1110
[83] Clayton,R.,Engquist,B.,Absorbing boundary conditions for acoustic and elastic wave equation.Bull.Seis.Soc.Am.,1977,67:1529-1540
[84] 董良国.地震波数值模拟与反演中几个关键问题研究:[学位论文].上海:同济大学,2003
[85] Cerjan,C.,Kosloff,D.,Kosloff,R.,etc.,A nonreflectiong boundary condition for discrete acoustic and elastic wave equations.Geophysics,1985,50(4):705-808
[86] Engquist B. and Majda A. Absorbing boundary conditions for the numerical simulation of waves.Math.Comput.1977,32:313-357
[87] Marfurt,K.J.,Accuracy of finite-difference and finite-element modeling of the scalar and elastic wave equations.Geophysics,1984,49(5):533-549
[88] Shin,C.Sponge condition for frequency-domain modeling.Geophysics,1995,60(6): 1870- 1874
[89] Berenger,J.P.,Aperfectly matched layer for absorption of electromagnetic waves.J. Com- put Phys.,1994,114,185-200
[90] 马在田.地震成像技术-有限差分法偏移.北京:石油工业出版社,1989
[91] Sena,A.G., Seismic traveltime equations for azimuthaly anisotropic and isotropic media;Estimation of interval elastic properties.Geophysics,1991,56(12),2090-2101
[92] Leon Thomsen. Weak elastic anisotropy.Geophysics,1986,51(10):1954-1966
[93] 杜世通.地震波动力学.东营:石油大学出版社,2003
[94] Alkhalifah T.,Acoustic approximation for processing in transversely isotropic media. Geophysics,1998,63(2):623-631
[95] Alkhalifah T.,An acoustic wave equation for anisotropic media. Geiophysics,2000,65(4): 1239~1250
[96] Alkhalifah T. An acousitic wave equation for orthorhombic media. Geophysics,2003, 68(4):1169~1172
[97] Min,D-J,Shin,C.et.al., Improved frequency domain elastic wave modeling using averageing difference operators.Geophysics,2000,65(3):884-895
[98] Peter Deuflhard,Newton methods for nonlinear problems:Affine invariance and adaptive algorithms(影印版).北京:科学出版社,2006
[99] 徐成贤,陈志平,李乃成.近代优化方法.北京:科学出版社,2002
[100] 何振亚.自适应信号处理.北京:科学出版社,2002
[101] 吴国忱,梁锴.VTI 介质 qP 波方程高精度有限差分算子.地球物理学进展,2007
[102] 殷文,印兴耀,吴国忱等.高精度频率域弹性波方程有限差分方法及波场模拟.地球物理学报,2006,49(2):561-568 Yin W, Yin X Y, Wu G C, et al. The method of finite difference of high precision elastic wave equations in the frequency domain and wave-field simulation.Chinese J.Geophys. (in Chinese),2006,49(2):561-56
[103] 吴国忱,梁锴. VTI 介质准 P 波频率空间域组合边界条件研究.石油物探,2005,44(4): 301-307
[104] 夏凡,董良国,马在田.三维弹性波数值模拟中的吸收边界条件.地球物理学报,2004, 47(1):132-136 Xia F, Dong L G,Ma Z T. Absorbing boundary conditions in 3D elastic_wave numerical modeling.Chinese J.Geophys. ( in Chinese), 2004,47(1):132-136
[105] Chew, W. C., Liu, Q. H.,Perfectly matched layers for elastodynamics:A new absorbing boundary condition.J. Comp. Acoust.,1996,4:341-359
[106] Rappaport C.M.,Perfectly matched absorbing boundary conditions based on anisotropic lossy mapping of space:IEEE Micorwave Guided Wave Lett,1995,5:90-92
[107] 王守东,声波方程完全匹配层吸收边界.石油地球物理勘探,2003,38 (1):31-34
[108] 吴建平,王正华,李晓梅.稀疏线性方程组高效求解与并行计算.长沙:湖南科学技术出版社,2004
[109] 刘长学.超大规模稀疏矩阵计算方法.上海:上海科学技术出版社,1990
[110] 刘万勋,刘长学.大型稀疏线性方程组的解法.国防工业出版社,1981