转换波叠前时间偏移方法研究
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摘要
偏移是地震数据处理三大技术(反褶积、叠加和偏移)之一。随着地震勘探技术的发展和勘探目标复杂程度的增大,对地震偏移成像的精度提出了更高的要求。在共中心点叠加基础上的叠后偏移已经不能很好的适应地质解释的要求,因此,叠前偏移成为地震资料处理必不可少的环节。叠前时间偏移方法以双平方根方程非零炮检距成像理论为基础,沿着非零炮检距的旅行时轨迹(Cheops金字塔)对振幅求和。相对于叠前深度偏移来说,叠前时间偏移在构造复杂、速度横向变化不剧烈的情况下也可以得到比较理想的成像效果,并且它对速度模型不是很敏感,也比较节省计算时间。另外,相对于基于有限差分法的叠前时间偏移来说,本文讨论的基于克希霍夫法的叠前时间偏移运算效率比较高,而且适应能力也比较强。
随着转换波地震勘探技术的发展,转换波偏移成像技术成为研究的重点。转换波勘探提供了与纵波不同的信息,从而能获得地下含流体性、裂隙及弹性参数等信息。对转换波资料的分析与处理,在一定程度上能够弥补纵波勘探的不足,而转换波资料的偏移是其处理的重要环节。
本论文在前人工作的基础上,研究并实现了三种实用的二维纵波叠前时间偏移方法,即等效偏移距偏移、非成像炮集偏移以及倾角时差校正加叠前成像方法,并对其各自不同的求和路径及形成的中间道集进行了分析,通过对这三种方法进行对比研究,说明了叠前时间偏移是对双平方根方程定义的旅行时曲面的绕射求和,这三种方法的区别就在于其定义的求和路径不同；实现了快速、有效的基于等效偏移距偏移方法的转换波叠前时间偏移,该方法在将转换波数据映射到共转换散射点道集时,去除了转换波射线路径的不对称性,简化了转换波的处理过程；作者编程实现了P-P、P-SV波叠前时间偏移程序,并用几组典型模型和实际资料进行了试算,验证了方法的有效性,结果表明,该几种方法可以对陡倾角地质体进行正确成像,对复杂构造以及小尺度地质体也可以成像,成像效果比常规成像方法的偏移结果更加接近真实地质体。
Migration is one of the three most important seismic data processing techniques which are deconvolution, stack and migration. With the development of seismic prospecting technique and the increase of complexity in seismic prospecting, higher demand for the precision of seismic migration is put forward. Post-stack migration based on the CMP stack can not adapt to the requirements of geological interpretation, so pre-stack migration become indispensable step in seismic data processing. Pre-stack time migration, whose basis is non-zero offset imaging theory of double square root equation, sum the amplitude along non-zero offset travel-time path. The pre-stack time migration can also get ideal imaging result when the structure is not very complex and the transverse variation of velocity is not severe. It is notable that the pre-stack time migration is insensitive to the velocity model and can save the computation time comparing with pre-stack depth migration. In addition, relative to the pre-stack time migration based on finite difference method, the pre-stack time migration based on the Kirchhoff method discussed in this paper has higher operation efficiency and better adaptability.
With the development of P-SV wave seismic prospecting technique, the P-SV wave migration becomes the key problem on the research. The P-SV wave prospecting can provide information different from P wave, such as fluid and fissure in the media, elastic parameters and so on. So the analysis and processing for P-SV wave data can remedy the deficiency of P wave prospecting, in which P-SV wave migration is an important step for data processing.
This paper studies and achieves three practical 2-D P wave pre-stack time migration methods on the basis of the previous researches. The three methods are Equivalent Offset Migration, Non-Imaging Shot-Record Migration, Dip Moveout and Prestack Imaging. Then this paper analyzes their different summation paths and middle step gathers respectively. The pre-stack time migration can be considered as diffraction summation over the travel-time surface defined by double square root equation and the differences of these three methods are that they define different summation paths by comparing and studying these three methods. This paper achieves the rapid and effective P-SV wave pre-stack time migration which is based on the Equivalent Offset Migration method. This method gets rid of the asymmetry of P-SV wave ray path and simplifies the P-SV wave processing step during P-SV wave data is mapped into the common converted scatter point gathers. The paper achieves P-P and P-SV pre-stack time migration programs, and the validity of these methods is verified by using several typical models and practical data. The results show that steep slope geological body, complex structure and small size geological body can be imaged correctly using these pre-stack time migration methods, and the imaging effect is more close to real geological body than conventional migration method.
随着转换波地震勘探技术的发展,转换波偏移成像技术成为研究的重点。转换波勘探提供了与纵波不同的信息,从而能获得地下含流体性、裂隙及弹性参数等信息。对转换波资料的分析与处理,在一定程度上能够弥补纵波勘探的不足,而转换波资料的偏移是其处理的重要环节。
本论文在前人工作的基础上,研究并实现了三种实用的二维纵波叠前时间偏移方法,即等效偏移距偏移、非成像炮集偏移以及倾角时差校正加叠前成像方法,并对其各自不同的求和路径及形成的中间道集进行了分析,通过对这三种方法进行对比研究,说明了叠前时间偏移是对双平方根方程定义的旅行时曲面的绕射求和,这三种方法的区别就在于其定义的求和路径不同；实现了快速、有效的基于等效偏移距偏移方法的转换波叠前时间偏移,该方法在将转换波数据映射到共转换散射点道集时,去除了转换波射线路径的不对称性,简化了转换波的处理过程；作者编程实现了P-P、P-SV波叠前时间偏移程序,并用几组典型模型和实际资料进行了试算,验证了方法的有效性,结果表明,该几种方法可以对陡倾角地质体进行正确成像,对复杂构造以及小尺度地质体也可以成像,成像效果比常规成像方法的偏移结果更加接近真实地质体。
Migration is one of the three most important seismic data processing techniques which are deconvolution, stack and migration. With the development of seismic prospecting technique and the increase of complexity in seismic prospecting, higher demand for the precision of seismic migration is put forward. Post-stack migration based on the CMP stack can not adapt to the requirements of geological interpretation, so pre-stack migration become indispensable step in seismic data processing. Pre-stack time migration, whose basis is non-zero offset imaging theory of double square root equation, sum the amplitude along non-zero offset travel-time path. The pre-stack time migration can also get ideal imaging result when the structure is not very complex and the transverse variation of velocity is not severe. It is notable that the pre-stack time migration is insensitive to the velocity model and can save the computation time comparing with pre-stack depth migration. In addition, relative to the pre-stack time migration based on finite difference method, the pre-stack time migration based on the Kirchhoff method discussed in this paper has higher operation efficiency and better adaptability.
With the development of P-SV wave seismic prospecting technique, the P-SV wave migration becomes the key problem on the research. The P-SV wave prospecting can provide information different from P wave, such as fluid and fissure in the media, elastic parameters and so on. So the analysis and processing for P-SV wave data can remedy the deficiency of P wave prospecting, in which P-SV wave migration is an important step for data processing.
This paper studies and achieves three practical 2-D P wave pre-stack time migration methods on the basis of the previous researches. The three methods are Equivalent Offset Migration, Non-Imaging Shot-Record Migration, Dip Moveout and Prestack Imaging. Then this paper analyzes their different summation paths and middle step gathers respectively. The pre-stack time migration can be considered as diffraction summation over the travel-time surface defined by double square root equation and the differences of these three methods are that they define different summation paths by comparing and studying these three methods. This paper achieves the rapid and effective P-SV wave pre-stack time migration which is based on the Equivalent Offset Migration method. This method gets rid of the asymmetry of P-SV wave ray path and simplifies the P-SV wave processing step during P-SV wave data is mapped into the common converted scatter point gathers. The paper achieves P-P and P-SV pre-stack time migration programs, and the validity of these methods is verified by using several typical models and practical data. The results show that steep slope geological body, complex structure and small size geological body can be imaged correctly using these pre-stack time migration methods, and the imaging effect is more close to real geological body than conventional migration method.
引文
[1]李振春,张军华.地震数据处理方法[M].东营：石油大学出版社,2004
[2]马在田.论反射地震偏移成像[J].勘探地球物理进展,2002,25(3)：1-5
[3]崔汝国,覃天,凌勋等.叠前时间偏移成像技术及其应用[J].物探与化探,2006,30(6)：541-544
[4]Gray, S.H., Etgen, J., Dellinger, J., et al. Seismic migration problems and solutions[J]. Geophysics,2001,66(5):1622-1640
[5]Wu, W.J.. The advantage and significance of prestack migration[J].2001, SEG Int'l Exposition and Annual Meeting, San Antonio, Texas,1-4
[6]王棣,王华忠,马在田等.叠前时间偏移方法综述[J].勘探地球物理进展,2004,27(5)：313-320
[7]曹孟起,刘占族.叠前时间偏移处理技术及应用[J].石油地球物理勘探,2006,41(3)：286-289
[8]蒋芳芬,李玉.地震资料叠前时间偏移处理技术[J].中国地球物理2008：92
[9]张丽艳,刘洋.转换波叠前时间偏移方法综述[J].地球物理学进展,2005,20(4)：1134-1139
[10]张明,韩大匡,姚逢昌等.转换波成像方法综述[J].石油物探,2006,45(5)：553-556
[11]王洁,马永生,张铁强.偏移技术概述[J].中国西部油气地质,2007,3(1)：079-084
[12]Claerbout, J.F. and Doherty, S.M.. Downward continuation of moveout-corrected seismograms[J]. Geophysics,1972,37(5):741-768
[13]Schneider, W.A.. Integral formulation for migration in two and three dimensions[J]. Geophysics,1978,43(1):49-76
[14]Stolt, R.H.. Migration by Fourier transform[J]. Geophysics,1978,43(1):23-48
[15]Gazdag, J.. Wave equation migration with the phase-shift method[J]. Geophysics,1978, 43(7):1342-1351
[16]Gazdag, J. and Sguazzero, P.. Migration of seismic data by phase shift plus interpolation[J]. Geophysics,1984,49(2):124-131
[17]Yilmaz, O. and Claerbout, J.F.. Prestack partial migration[J]. Geophysics,1980,45(12): 1753-1779
[18]Baysal, E., Kosloff, D.D., Sherwood, J.W.C.. Reverse time migration[J]. Geophysics, 1983,48(11):1514-1524
[19]Hale, D.. Dip-moveout by Fourier transform[J]. Geophysics,1984,49(6):741-757
[20]Stoffa, P.L., Fokkema, J.T. et al. Split-step Fourier migration[J]. Geophysics,1990,55(4): 410-421
[21]Ristow, D. and Ruhl, T.. Fourier finite-difference migration[J]. Geophysics,1994,59(12): 1882-1893
[22]Hill, N.R.. Gaussian beam migration[J]. Geophysics,1990,55(11):1416-1428
[23]Li, Z.. Compensating finite-difference errors in 3-D migration and modeling[J]. Geophysics,1991,56(10):1650-1660
[24]Berryhill, J.R.. Kinematics of crossline prestack migration[J]. Geophysics,1991,56(10): 1674-1676
[25]Biondi, B. and Palacharla, G.3-D prestack migration of common-azimuth data[J]. Geophysics,1996,61(6):1822-1832
[26]Hill, N.R.. Prestack Gaussian-beam depth migration[J]. Geophysics,2001,66(4): 1240-1250
[27]吴如山,金胜汶,谢小碧.广义屏传播算子及其在地震波偏移成像方面的应用[J].石油地球物理勘探,2001,36(6)：655-664
[28]Fowler, P.J.. A comparative overview of prestack time migration methods[J].1997,67th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts,1571-1574
[29]Bancroft, J.C. and Geiger, H.D.. Equivalent offset CRP gathers[J].64th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts,672-675
[30]Berryhill, J.R.. System and method of seismic shot-record migration.1996, United States Patent 5,544,126
[31]Wang, S., Bancroft, J.C., Lawton, D.C. et al. Converted-wave (P-S) prestack migration and migration velocity analysis[J].1995, CREWES 1995 Research Report
[32]Wang, W. and Pham, L.D.. Converted-wave prestack imaging and velocity analysis by pseudo-offset migration[J].2001,63rd EAGE Conference, Expanded Abstracts
[33]Wang, W., Pham, L.D. and Lou, M.. Converted-wave prestack time migration for isotropic and anisotropic media[J].2002, SEG Int'l Exposition and 72nd Annual Meeting, Salt Lake City, Utah
[34]Winbow, G.A. and Schneider, W.A.. Weights for 3-D controlled amplitude prestack time migration[J].1999, SEG 1999 Expanded Abstracts
[35]Geiger, H.D.. Amplitude-preserving weights for Kirchhoff prestack time migration[J]. 2002, SEG Int'l Exposition and 72nd Annual Meeting, Salt Lake City, Utah
[36]Cheng Jiubing and Ma Zaitian.3-D Angle-Domain Imaging in Kirchhoff Prestack Time Migration[J].2009, SEG Houston 2009 International Exposition and Annual Meeting, 2939-2943
[37]Dubrulle, A.A.. Numerical methods for the migration of constant-offset sections in homogeneous and horizontally layered media[J]. Geophysics,1983,48(9):1195-1203
[38]王棣,王华忠,马在田等.频率波数域共偏移距叠前时间偏移方法[J].石油物探,2004,43(1)：8-10
[39]Ekren, B.O. and Ursin, B.. True-amplitude frequency-wavenumber constant-offset migration[J]. Geophysics,1999,64(3):915-924
[40]Mosher, C.C., Keho, T.H., Weglein, A.B. et al. The impact of migration on AVO[J]. Geophysics,1996,61(6):1603-1615
[41]Pan, J. and Negut, D.. A phase shift plus interpolation algorithm for prestack time migration[J]. SEG Las Vegas 2008 Annual Meeting,2407-2411
[42]渥·伊尔马滋著,刘怀山等译.地震资料分析——地震资料处理、反演和解释[M].北京：石油工业出版社,2006
[43]Bancroft, J.C., Geiger, H.D. and Margrave, G..R. The equivalent offset method of prestack time migration[J]. Geophysics,1998,63(6):2042-2053
[44]Bancroft, J.C., Geiger, H.D., Foltinek, D.S. et al. Prestack migration by equivalent offsets and CSP gathers[J].1994, CREWES 1994 Research Report
[45]Bancroft, J.C., Geiger, H.D., Wang, S. et al. Prestack migration by equivalent offsets and CSP gathers:an update[J].1995, CREWES 1995 Research Report
[46]Li, X., Xu, Y. and Bancroft, J.C.. Equivalent offset migration:the implementation and application update[J].1997, CREWES 1997 Research Report
[47]Li, X. and Bancroft, J.C.. An efficient and accurate algorithm for constructing common scatter point gathers[J].1996, CREWES 1996 Research Report
[48]Margrave, G.F., Bancroft, J.C. and Geiger, H.D.. The theoretical basis for prestack migration by equivalent offset[J].1996, CREWES 1996 Research Report
[49]Margrave, G.F., Bancroft, J.C. and Geiger, H.D.. Fourier prestack migration by equivalent wavenumber[J]. Geophysics,1999,64(1):197-207
[50]王伟.基于等效偏移距方法叠前时间偏移的研究[D].北京：中国地质大学硕士学位论文,2005
[51]王伟,尹军杰,刘学伟等.等效偏移距方法及应用[J].地球物理学报,2007,50(6)：1823-1830
[52]许卓,韩立国,廉玉广.基于等效偏移距的偏移成像方法[J].吉林大学学报(地球科学版),2007,37(Sup)：57-60
[53]Popovici, A.M.. Berryhill's "pure migration"=Gardner's PSI[J].2001, Stanford Exploration Project, Report 82,1-11
[54]Bancroft, J.C.,Margrave, G. and Geiger, H.D.. A kinematic comparison of DMO-PSI, and equivalent offset migration (EOM)[J].1997, SEG Technical Program Expanded Abstracts 16: 1575-1578
[55]Bancroft, J.C..A kinematic comparison of EOM with DMO-PSI in the prestack volume[J]. CREWES Project, University of Calgary
[56]Bednar, J.B.. A theoretical comparison of equivalent offset migration and dip moveout prestack imaging[J].1997, Stanford Exploration Project, Report 95,250-263
[57]Bednar, J.B.. A theoretical comparison of equivalent-offset migration and dip moveout-prestack imaging[J]. Geophysics,1999,64(1):191-196
[58]Forel, D. and Gardner, G.H.F.. A three-dimensional perspective on two-dimensional dip moveout[J]. Geophysics,1988,53(5):604-610
[59]Bancroft, J.C. and Geiger, H.D.. Anatomy of common scatterpoint (CSP) gathers formed during equivalent offset prestack migration (EOM)[J].1997, CREWES 1997 Research Report
[60]Galdona, L.A. and Bancroft, J.C..Energy distribution on CSP gathers as they approach a scatterpoint[J].1998, CREWES 1998 Research Report
[61]Bancroft, J.C. and Geiger, H.D.. Energy concentration as a function of dip on Cheop's pyramid and CSP gathers[J].1996, CREWES 1996 Research Report
[62]Wang, S., Bancroft, J.C. and Lawton, D.C.. Converted-wave (P-SV) prestack migration and migration velocity analysis[J].67th SEG Annual Meeting 1997, Expanded Abstracts: 1575-1578
[63]Beckett, J.K. and Bancroft, J.C.. Matched filters in P-Sv pre-stack migration[J].72nd SEG Annual Meeting 2002, Expanded Abstracts:1-4
[64]Li, X. and Bancroft, J.C.. A new algorithm for converted wave pre-stack migration[J]. CREWES project research report, v.9,26.1-26.13
[65]Li, X. and Bancroft, J.C.. Converted wave migration and common conversion point binning by equivalent offset[J].67th SEG Annual Meeting 1997, Expanded Abstracts: 1587-1590
[66]许卓.基于等效偏移距的多波叠前偏移研究[D].吉林：吉林大学,2009
[67]Bancroft, J.C. and Li, X.. Efficient computation of the equivalent offset traveltimes for EOM[J].1998 SEG Expanded Abstracts
[68]Bancroft, J.C. Natural anti-aliasing in equivalent offset prestack migration[J].66th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts,1465-1466b
[69]Bancroft, J.C. Seismic Imaging:amplitudes and inversion-Part 1[J].2002, CSEG Recorder,11-12,14,16-22,24,26-28
[70]周学明.交错网格高阶差分数值模拟及叠前逆时偏移[D].西安：长安大学,2010
[71]Bancroft, J.C. Review of seismic imaging:Poststack[J].2001, CREWES 2001 Research Report,535-549
[72]Bancroft, J.C. Review of seismic imaging:Prestack[J].2001, CREWES 2001 Research Report,551-571
[73]Bednar, J.B.. A brief history of seismic migration[J]. Geophysics,2005,70(3):3MJ-20MJ
[74]Claerbout, J.F.. Imaging the Earth's Interior[M]. Blackwell Scientific Publications,1985
[75]Claerbout, J.F.. Basic Earth Imaging[M]. Stanford Exploration Project,2005
[76]贺振华.反射地震资料偏移处理与反演方法[M].重庆大学出版社,1989
[77]克莱鲍特著,徐云译.地震成像理论及方法[M].石油工业出版社,1991
[78]陆基孟.地震勘探原理[M].东营：石油大学出版社,1993
[79]王华忠,徐蔚亚,徐兆涛等.DMO和叠前时间偏移的共同起点[J].石油地球物理勘探,2002,37(3)：224-229
[80]王勇等.地震成像新方法[M].北京：石油工业出版社,2005
[2]马在田.论反射地震偏移成像[J].勘探地球物理进展,2002,25(3)：1-5
[3]崔汝国,覃天,凌勋等.叠前时间偏移成像技术及其应用[J].物探与化探,2006,30(6)：541-544
[4]Gray, S.H., Etgen, J., Dellinger, J., et al. Seismic migration problems and solutions[J]. Geophysics,2001,66(5):1622-1640
[5]Wu, W.J.. The advantage and significance of prestack migration[J].2001, SEG Int'l Exposition and Annual Meeting, San Antonio, Texas,1-4
[6]王棣,王华忠,马在田等.叠前时间偏移方法综述[J].勘探地球物理进展,2004,27(5)：313-320
[7]曹孟起,刘占族.叠前时间偏移处理技术及应用[J].石油地球物理勘探,2006,41(3)：286-289
[8]蒋芳芬,李玉.地震资料叠前时间偏移处理技术[J].中国地球物理2008：92
[9]张丽艳,刘洋.转换波叠前时间偏移方法综述[J].地球物理学进展,2005,20(4)：1134-1139
[10]张明,韩大匡,姚逢昌等.转换波成像方法综述[J].石油物探,2006,45(5)：553-556
[11]王洁,马永生,张铁强.偏移技术概述[J].中国西部油气地质,2007,3(1)：079-084
[12]Claerbout, J.F. and Doherty, S.M.. Downward continuation of moveout-corrected seismograms[J]. Geophysics,1972,37(5):741-768
[13]Schneider, W.A.. Integral formulation for migration in two and three dimensions[J]. Geophysics,1978,43(1):49-76
[14]Stolt, R.H.. Migration by Fourier transform[J]. Geophysics,1978,43(1):23-48
[15]Gazdag, J.. Wave equation migration with the phase-shift method[J]. Geophysics,1978, 43(7):1342-1351
[16]Gazdag, J. and Sguazzero, P.. Migration of seismic data by phase shift plus interpolation[J]. Geophysics,1984,49(2):124-131
[17]Yilmaz, O. and Claerbout, J.F.. Prestack partial migration[J]. Geophysics,1980,45(12): 1753-1779
[18]Baysal, E., Kosloff, D.D., Sherwood, J.W.C.. Reverse time migration[J]. Geophysics, 1983,48(11):1514-1524
[19]Hale, D.. Dip-moveout by Fourier transform[J]. Geophysics,1984,49(6):741-757
[20]Stoffa, P.L., Fokkema, J.T. et al. Split-step Fourier migration[J]. Geophysics,1990,55(4): 410-421
[21]Ristow, D. and Ruhl, T.. Fourier finite-difference migration[J]. Geophysics,1994,59(12): 1882-1893
[22]Hill, N.R.. Gaussian beam migration[J]. Geophysics,1990,55(11):1416-1428
[23]Li, Z.. Compensating finite-difference errors in 3-D migration and modeling[J]. Geophysics,1991,56(10):1650-1660
[24]Berryhill, J.R.. Kinematics of crossline prestack migration[J]. Geophysics,1991,56(10): 1674-1676
[25]Biondi, B. and Palacharla, G.3-D prestack migration of common-azimuth data[J]. Geophysics,1996,61(6):1822-1832
[26]Hill, N.R.. Prestack Gaussian-beam depth migration[J]. Geophysics,2001,66(4): 1240-1250
[27]吴如山,金胜汶,谢小碧.广义屏传播算子及其在地震波偏移成像方面的应用[J].石油地球物理勘探,2001,36(6)：655-664
[28]Fowler, P.J.. A comparative overview of prestack time migration methods[J].1997,67th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts,1571-1574
[29]Bancroft, J.C. and Geiger, H.D.. Equivalent offset CRP gathers[J].64th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts,672-675
[30]Berryhill, J.R.. System and method of seismic shot-record migration.1996, United States Patent 5,544,126
[31]Wang, S., Bancroft, J.C., Lawton, D.C. et al. Converted-wave (P-S) prestack migration and migration velocity analysis[J].1995, CREWES 1995 Research Report
[32]Wang, W. and Pham, L.D.. Converted-wave prestack imaging and velocity analysis by pseudo-offset migration[J].2001,63rd EAGE Conference, Expanded Abstracts
[33]Wang, W., Pham, L.D. and Lou, M.. Converted-wave prestack time migration for isotropic and anisotropic media[J].2002, SEG Int'l Exposition and 72nd Annual Meeting, Salt Lake City, Utah
[34]Winbow, G.A. and Schneider, W.A.. Weights for 3-D controlled amplitude prestack time migration[J].1999, SEG 1999 Expanded Abstracts
[35]Geiger, H.D.. Amplitude-preserving weights for Kirchhoff prestack time migration[J]. 2002, SEG Int'l Exposition and 72nd Annual Meeting, Salt Lake City, Utah
[36]Cheng Jiubing and Ma Zaitian.3-D Angle-Domain Imaging in Kirchhoff Prestack Time Migration[J].2009, SEG Houston 2009 International Exposition and Annual Meeting, 2939-2943
[37]Dubrulle, A.A.. Numerical methods for the migration of constant-offset sections in homogeneous and horizontally layered media[J]. Geophysics,1983,48(9):1195-1203
[38]王棣,王华忠,马在田等.频率波数域共偏移距叠前时间偏移方法[J].石油物探,2004,43(1)：8-10
[39]Ekren, B.O. and Ursin, B.. True-amplitude frequency-wavenumber constant-offset migration[J]. Geophysics,1999,64(3):915-924
[40]Mosher, C.C., Keho, T.H., Weglein, A.B. et al. The impact of migration on AVO[J]. Geophysics,1996,61(6):1603-1615
[41]Pan, J. and Negut, D.. A phase shift plus interpolation algorithm for prestack time migration[J]. SEG Las Vegas 2008 Annual Meeting,2407-2411
[42]渥·伊尔马滋著,刘怀山等译.地震资料分析——地震资料处理、反演和解释[M].北京：石油工业出版社,2006
[43]Bancroft, J.C., Geiger, H.D. and Margrave, G..R. The equivalent offset method of prestack time migration[J]. Geophysics,1998,63(6):2042-2053
[44]Bancroft, J.C., Geiger, H.D., Foltinek, D.S. et al. Prestack migration by equivalent offsets and CSP gathers[J].1994, CREWES 1994 Research Report
[45]Bancroft, J.C., Geiger, H.D., Wang, S. et al. Prestack migration by equivalent offsets and CSP gathers:an update[J].1995, CREWES 1995 Research Report
[46]Li, X., Xu, Y. and Bancroft, J.C.. Equivalent offset migration:the implementation and application update[J].1997, CREWES 1997 Research Report
[47]Li, X. and Bancroft, J.C.. An efficient and accurate algorithm for constructing common scatter point gathers[J].1996, CREWES 1996 Research Report
[48]Margrave, G.F., Bancroft, J.C. and Geiger, H.D.. The theoretical basis for prestack migration by equivalent offset[J].1996, CREWES 1996 Research Report
[49]Margrave, G.F., Bancroft, J.C. and Geiger, H.D.. Fourier prestack migration by equivalent wavenumber[J]. Geophysics,1999,64(1):197-207
[50]王伟.基于等效偏移距方法叠前时间偏移的研究[D].北京：中国地质大学硕士学位论文,2005
[51]王伟,尹军杰,刘学伟等.等效偏移距方法及应用[J].地球物理学报,2007,50(6)：1823-1830
[52]许卓,韩立国,廉玉广.基于等效偏移距的偏移成像方法[J].吉林大学学报(地球科学版),2007,37(Sup)：57-60
[53]Popovici, A.M.. Berryhill's "pure migration"=Gardner's PSI[J].2001, Stanford Exploration Project, Report 82,1-11
[54]Bancroft, J.C.,Margrave, G. and Geiger, H.D.. A kinematic comparison of DMO-PSI, and equivalent offset migration (EOM)[J].1997, SEG Technical Program Expanded Abstracts 16: 1575-1578
[55]Bancroft, J.C..A kinematic comparison of EOM with DMO-PSI in the prestack volume[J]. CREWES Project, University of Calgary
[56]Bednar, J.B.. A theoretical comparison of equivalent offset migration and dip moveout prestack imaging[J].1997, Stanford Exploration Project, Report 95,250-263
[57]Bednar, J.B.. A theoretical comparison of equivalent-offset migration and dip moveout-prestack imaging[J]. Geophysics,1999,64(1):191-196
[58]Forel, D. and Gardner, G.H.F.. A three-dimensional perspective on two-dimensional dip moveout[J]. Geophysics,1988,53(5):604-610
[59]Bancroft, J.C. and Geiger, H.D.. Anatomy of common scatterpoint (CSP) gathers formed during equivalent offset prestack migration (EOM)[J].1997, CREWES 1997 Research Report
[60]Galdona, L.A. and Bancroft, J.C..Energy distribution on CSP gathers as they approach a scatterpoint[J].1998, CREWES 1998 Research Report
[61]Bancroft, J.C. and Geiger, H.D.. Energy concentration as a function of dip on Cheop's pyramid and CSP gathers[J].1996, CREWES 1996 Research Report
[62]Wang, S., Bancroft, J.C. and Lawton, D.C.. Converted-wave (P-SV) prestack migration and migration velocity analysis[J].67th SEG Annual Meeting 1997, Expanded Abstracts: 1575-1578
[63]Beckett, J.K. and Bancroft, J.C.. Matched filters in P-Sv pre-stack migration[J].72nd SEG Annual Meeting 2002, Expanded Abstracts:1-4
[64]Li, X. and Bancroft, J.C.. A new algorithm for converted wave pre-stack migration[J]. CREWES project research report, v.9,26.1-26.13
[65]Li, X. and Bancroft, J.C.. Converted wave migration and common conversion point binning by equivalent offset[J].67th SEG Annual Meeting 1997, Expanded Abstracts: 1587-1590
[66]许卓.基于等效偏移距的多波叠前偏移研究[D].吉林：吉林大学,2009
[67]Bancroft, J.C. and Li, X.. Efficient computation of the equivalent offset traveltimes for EOM[J].1998 SEG Expanded Abstracts
[68]Bancroft, J.C. Natural anti-aliasing in equivalent offset prestack migration[J].66th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts,1465-1466b
[69]Bancroft, J.C. Seismic Imaging:amplitudes and inversion-Part 1[J].2002, CSEG Recorder,11-12,14,16-22,24,26-28
[70]周学明.交错网格高阶差分数值模拟及叠前逆时偏移[D].西安：长安大学,2010
[71]Bancroft, J.C. Review of seismic imaging:Poststack[J].2001, CREWES 2001 Research Report,535-549
[72]Bancroft, J.C. Review of seismic imaging:Prestack[J].2001, CREWES 2001 Research Report,551-571
[73]Bednar, J.B.. A brief history of seismic migration[J]. Geophysics,2005,70(3):3MJ-20MJ
[74]Claerbout, J.F.. Imaging the Earth's Interior[M]. Blackwell Scientific Publications,1985
[75]Claerbout, J.F.. Basic Earth Imaging[M]. Stanford Exploration Project,2005
[76]贺振华.反射地震资料偏移处理与反演方法[M].重庆大学出版社,1989
[77]克莱鲍特著,徐云译.地震成像理论及方法[M].石油工业出版社,1991
[78]陆基孟.地震勘探原理[M].东营：石油大学出版社,1993
[79]王华忠,徐蔚亚,徐兆涛等.DMO和叠前时间偏移的共同起点[J].石油地球物理勘探,2002,37(3)：224-229
[80]王勇等.地震成像新方法[M].北京：石油工业出版社,2005