多道集偏移速度建模方法研究
摘要
随着地震勘探难度的增大和油气藏复杂性的增加，对地震资料成像精度的要求越来越高。为使地震资料更好地为油气田的勘探和开发服务，叠前深度偏移成像已成为人们关注的重点和焦点。目前，有些叠前深度偏移方法已成功地应用于地震资料处理中，并获取了高质量的地震成像剖面。但在叠前深度偏移成像过程中，成像质量直接依赖于偏移速度场的精度。当地下速-深模型正确时，会得到好的地震成像效果；否则，在成像深度和振幅保真上都会出现偏差，偏差的极性和大小取决于速-深模型的精度。考虑到叠前深度偏移对目的层成像的重要性和对速-深模型的敏感性，近年来，地震工作者已把注意力转移到偏移速度建模上。偏移速度建模的方法很多。依据所基于的理论，分为射线法偏移速度建模、波动方程法偏移速度建模、和综合法偏移速度建模；按所使用的道集，分为共中心点(CMP)道集、共成像点(CIP)道集、共反射点(CRP)道集、共反射面(CRS)道集和共聚集点(CFP)道集等方法；波动方程法又分为深度聚集分析(DFA)和剩余曲率分析(RCA)。但上述方法不同程度地受到地下地质构造和速度场复杂性的约束。如地层倾角的大小、上覆构造的复杂性、偏移距的大小、和速度场的横向变化等。为更好地适应以上约束条件，实现复杂构造的准确成像，我们首先从理论上探讨了偏移速度建模过程中，速度误差与深度误差、深度、旅行时误差、速度、和炮检距等的定量关系，修正速度的准则；然后通过多种模型(包括Marmousi模型在内)进行试算，合理选取用于偏移速度建模的射线追踪法、层析成像法、或叠前深度偏移法，基于效果和效率选取偏移速度建模方法。最后，我们提出了四种道集的偏移速度建模方法。一是基于射线追踪的共中心点(CMP)道集偏移速度建模；二是基于剩余曲率分析和波动方程法叠前深度偏移的共成像点(CIP)道集偏移速度建模；三是基于等时原理和射线追踪／波动方程正演模拟的共聚焦点(CFP)道集偏移速度建模；四是基于优化三参数的共反射面(CRS)道集偏移速度建模。有时也可采用多级多道集偏移速度建模方法。模型试算表明了方法的有效性和适用性。
论文涉及到的内容较多。1．包括了叠前深度偏移、正演模拟、CFP偏移、和CRS叠加。在叠前深度偏移中，我们探讨了Kirchhoff积分法、分步富里叶(SSF)法、富里叶有限差分(FFD)法、频率-空间域有限差分(FXFD)法、和广义屏(GS)法(涉及到了相屏(PS)法(同SSF)、扩展的局部Born近似法(单参考慢度法和多参考慢度法)、和扩展的局部Rytov近似法)，以上方法均对Marmousi模型进行了试算。我们推导了适于横向变速的高阶有限差分正演模拟方程，并对Marmousi模型和胜利模型做了零炮检距模拟。CFP偏移是基于等时原理，它是一种新的叠前深度偏移成像方法，对理论模型我们做了CFP偏移处理。CRS叠加是一种与速度无关的地震成像方法，我们推导了全部理论公式，试算了包括Marmousi模型在内的多个模型，处理了胜利探区的一实际资料。上述方法是我们进行偏移速度建模的基础。考虑到计算效率、精度和稳定性，我们采用了SSF和FFD法叠前深度偏移、高阶差分正演模拟、CFP偏移、和CRS叠加。2．偏移速度建模是我们讨论的核心问题。在偏移速度建模中用到了CMP、CIP(或称为CDP或CRP)、CFP、和CRS道集。在CMP道集偏移速度建模中，我们是基于射线理论和最大叠加能量或最大相关系数准则来校正偏移速度，推导了常速和变速射线法求CMP等多种道集中各道反射旅行时的解析式，提出了基于速度扫描的CMP道集偏移速度建模方法，对较复杂模型做了试算。在CIP道集偏移速度建模中，推导了成像深度误差与偏移速度误差之间的基本关系，对偏移后的CIP道集上出现的剩余曲率做了定量描述。简单模型下，给出了利用CIP道集各道成像深度误差求取校正速度的线性插值法；复杂模型下，提出了利用CIP道集各道成像深度误差求取导数函数的单参数法和多参数法，和随后在CIP道集利用广义线性迭代反演计算校正速度的单参数扰动法和多参数同时扰动法，对包括Marmousi模型在内的多个模型做了试算，结果显示了方法的良好适应性和有效性。在CFP道集偏移速度建模中，利用等时原理，通过差异时移(DTS)分析，提出了基于最小二乘原理求取校正速度的约束参数反演法，试算了一模型，结果是令人满意的。在CRS道集偏移速度建模中，推导了优化三参数与偏移速度场之间的定量关系，提出了利用CRS叠加中的优化三参数求取偏移速度场的射线追踪法，模型试算表明了方法的有效性和适应性。
由上述四种偏移速度建模方法试算的结果以及它们所依据的道集和所基于的理论可以得出：对CMP道集偏移速度建模，效率高，但精度依赖于构造的复杂性，在某种意义上来讲，精度随复杂性而降低，存在速度累计误差和多解性问题，适于不太复杂地质体的速度建模，变速射线追踪法会提高CMP道集偏移速度建模对复杂介质的适应性；对CIP道集偏移速度建模，效率较低，但精度和稳定性高，适于复杂地质体的速度建模；对CFP道集偏移速度建模，若基于波动方程模拟，效率一般，但精度和稳定性高，适于复杂地质体的速度建模；若基于射线追踪模拟，效率较高，但精度和稳定性稍差一些，最适于一般地质体的速度建模；对CRS道集偏移速度建模，效率一般，速度分析精度取决于优化三参数的精度，适于较复杂地质体的速度建模。
为了提高偏移速度建模的效率、精度、和稳定性，也可以采用多级多道集的偏移速度建模。比如，第一级用CMP道集、第二级用CIP道集等。值得注意的是：CFP道集和CRS道集偏移速度建模为我们提供了两种新的偏移速度分析方法。随着它们的不断发展和完善，一定会在偏移速度建模中发挥作用，应用会越来越广泛。
There is a higher requirement on the precision of seismic data imaging with the increasing difficulty of the seismic exploration and more complication of the reservoir. In order to have a better service for the E&D of oil field, Pre-SDM imaging has become the focus. Nowadays, several Pre-SDM methods have been applied in seismic data processing successfully, and also get high-quality seismic sections. But in Pre-SDM, imaging quality directly depends on the precision of the velocity field used in migration. When the underground velocity-depth model is correct, we can get good seismic imaging result, or there will appear errors in imaging depth and amplitude fidelity, polarity and magnitude of errors depend on the precision of velocity-depth model. Thinking about the importance of Pre-SDM to target layer imaging and the sensitivity of it to velocity-depth model, seismic workers have tumed their attention to migration velocity modeling in recent years. There are many migration velocity modeling methods. According to the theories on which they base, it can divide into ray-tracing migration velocity modeling, migration velocity modeling of wave equation and comprehensive migration velocity modeling. Whet/based on gathers, it can divide into CMP, CIP, CRP, CRS and CFP gather. Wave equation method can divide into two methods: DFA and RCA. But these methods mentioned above were restricted by underground geological structure and the complication of velocity field, such as reflector dip, the complexity of overburden layer, offset and lateral variation of velocity field. In order to fit this constrain condition better to realize properly imaging of complex structure, we firstly discussed the quantitative relationship between velocity error and depth error, depth, traveltime error, velocity and offset in migration velocity modeling theoretically, and velocity-modified criteria. Then applied it to a variety of models (including Marmousi model), and reasonably selected ray-tracing method, tomographic method or Pre-SDM method used for migration velocity modeling. At the same time, we should select a kind of migration velocity modeling method according to the result and efficiency. Finally, we put forward four kinds of migration velocity modeling: One is CMP gather method based on ray-tracing, another is CIP gather method based on residual curvature analysis and Pre-SDM of wave equation, the third one is CFP gather method, the theory on which it depends is equal-traveltime principle and forward-modeling of ray-tracing or wave function, the last one is CRS gather method based on the theory of optimization of three parameters. Sometimes we can also adapt migration velocity modeling with multi-level and multi-gather, the applications to the models have showed the effectiveness and adaptability of the methods.
This paper has a large range in content. It includes Pre-SDM, forward-modeling ,CFP migration and CRS stack. In PSDM, we discussed Kirchhoff integral method, SSF, FFD, FXFD and GS methods which involves PS method---the same as SSF, extended local Born approximation fourier (single reference slowness and multi reference slowness) and extended local Rytov approximation fourier methods. All of these methods were applied to Marmousi model. We derived the high-order FD equation of forward-modeling which fitted for strong lateral variation in velocity and simulated Marmousi model and Shengli model with zero offset. CFP migration is a new Pre-SDM method based on equal-traveltime principle. We did some theoretical model with CFP method. CRS stack is a seismic imaging method which is velocity-free. We derived all the theoretical formulation, and applied it to many models including Marmousi model and also processed a real data of Shengli area. These methods mentioned above are the base of migration velocity modeling. Taking computing efficiency, precision and stability into consideration, we used Pre-SDM of SSF and FFD, forward-modeling of high-order FD, CFP migration and CRS stack method. The key problem we discussed is migration velocity modeling. In migration velocity modeling, we used CMP, CIP(CDP or CRP), CFP and CRS gather. In CMP gather method, we used ray theory and maximum energy or maximum coefficient of correlation as the criteria to modify migration velocity, derived the analyzing formulation of the reflection travel-time of each trace in a variety of gathers including CMP gather using ray method with constant velocity or variable velocity, and put forward a CMP gather migration velocity modeling method based on velocity scanning. Then we applied it to the complex model. In CIP gather method, we derived the fundamental relationship between imaging depth error and migration velocity error, then made a quantitative description on the residual curvature appeared in post-migration CIP gather. To simple model, we gave the linear interpolation method to find updated velocity using the imaging error in depth of each trace in CIP gather. To complex model, we put forward single parameter and multi-parameter method to get derivative function using error in imaging depth of each trace in CIP gather, and following single parameter disturbing and multi parameter disturbing simultaneously to calculate modified velocity using generalized linear iterative inversion. We also applied it to many models including Marmousi model. The result showed good adaptability and effectiveness of this method. In CFP gather method, we put forward the method of constraint parameter inversion to get modified velocity based on least-square principle using equal-traveltime principle and DTS analysis. Then we applied this method to a model and the result is satisfactory. In CRS gather method, we derived the quantitative relationship between optimal three parameter and migration velocity field, and then put forward ray-tracing method to get migration velocity field using optimal three parameter in CRS stack. The applications proved its effectiveness and adaptability.
According to the results we got above through four kinds of migration velocity modeling, the gathers and the theories on which they based, we can come to the conclusions as followings. To CMP gather method, it has a high efficiency but low precision which depends on the complexity of the structure. In a sense, the more complex the structure is, the lower the precision. There also exist the problems of accumulation error in velocity and non-uniqueness in solution. It fits for velocity modeling in geological body which is not very complex in structure. Ray-tracing method with variable velocity can improve greatly the adaptability of migration velocity modeling of CMP gather to complex media. To CIP gather method, its efficiency is low but has a high precision and stability. This method fits for velocity modeling in complex geological body. To CFP gather method, it has a high precision and stability, and fits for velocity modeling in complex geological body when based on wave equation modeling; when based on ray-tracing modeling it has a high efficiency, but the precision and stability is a little lower, and it fits for velocity modeling in general geological body. To CRS gather method, the precision of velocity analysis depends on the precision of optimization of three parameters. It fits for velocity modeling in complex geological body.
In order to improve the efficiency, precision and stability of migration velocity modeling, we can also use the method of multi-level and multi-gather. For instance, we use CMP gather method in first level and CIP gather method in the second level, etc.. What we should pay more attention to is that CFP and CRS gather migration velocity modeling provide us with two kinds of new migration velocity analysis methods. With their continuous development and perfection, these methods will play more important role in migration velocity modeling and come into wide use in the field.
论文涉及到的内容较多。1．包括了叠前深度偏移、正演模拟、CFP偏移、和CRS叠加。在叠前深度偏移中，我们探讨了Kirchhoff积分法、分步富里叶(SSF)法、富里叶有限差分(FFD)法、频率-空间域有限差分(FXFD)法、和广义屏(GS)法(涉及到了相屏(PS)法(同SSF)、扩展的局部Born近似法(单参考慢度法和多参考慢度法)、和扩展的局部Rytov近似法)，以上方法均对Marmousi模型进行了试算。我们推导了适于横向变速的高阶有限差分正演模拟方程，并对Marmousi模型和胜利模型做了零炮检距模拟。CFP偏移是基于等时原理，它是一种新的叠前深度偏移成像方法，对理论模型我们做了CFP偏移处理。CRS叠加是一种与速度无关的地震成像方法，我们推导了全部理论公式，试算了包括Marmousi模型在内的多个模型，处理了胜利探区的一实际资料。上述方法是我们进行偏移速度建模的基础。考虑到计算效率、精度和稳定性，我们采用了SSF和FFD法叠前深度偏移、高阶差分正演模拟、CFP偏移、和CRS叠加。2．偏移速度建模是我们讨论的核心问题。在偏移速度建模中用到了CMP、CIP(或称为CDP或CRP)、CFP、和CRS道集。在CMP道集偏移速度建模中，我们是基于射线理论和最大叠加能量或最大相关系数准则来校正偏移速度，推导了常速和变速射线法求CMP等多种道集中各道反射旅行时的解析式，提出了基于速度扫描的CMP道集偏移速度建模方法，对较复杂模型做了试算。在CIP道集偏移速度建模中，推导了成像深度误差与偏移速度误差之间的基本关系，对偏移后的CIP道集上出现的剩余曲率做了定量描述。简单模型下，给出了利用CIP道集各道成像深度误差求取校正速度的线性插值法；复杂模型下，提出了利用CIP道集各道成像深度误差求取导数函数的单参数法和多参数法，和随后在CIP道集利用广义线性迭代反演计算校正速度的单参数扰动法和多参数同时扰动法，对包括Marmousi模型在内的多个模型做了试算，结果显示了方法的良好适应性和有效性。在CFP道集偏移速度建模中，利用等时原理，通过差异时移(DTS)分析，提出了基于最小二乘原理求取校正速度的约束参数反演法，试算了一模型，结果是令人满意的。在CRS道集偏移速度建模中，推导了优化三参数与偏移速度场之间的定量关系，提出了利用CRS叠加中的优化三参数求取偏移速度场的射线追踪法，模型试算表明了方法的有效性和适应性。
由上述四种偏移速度建模方法试算的结果以及它们所依据的道集和所基于的理论可以得出：对CMP道集偏移速度建模，效率高，但精度依赖于构造的复杂性，在某种意义上来讲，精度随复杂性而降低，存在速度累计误差和多解性问题，适于不太复杂地质体的速度建模，变速射线追踪法会提高CMP道集偏移速度建模对复杂介质的适应性；对CIP道集偏移速度建模，效率较低，但精度和稳定性高，适于复杂地质体的速度建模；对CFP道集偏移速度建模，若基于波动方程模拟，效率一般，但精度和稳定性高，适于复杂地质体的速度建模；若基于射线追踪模拟，效率较高，但精度和稳定性稍差一些，最适于一般地质体的速度建模；对CRS道集偏移速度建模，效率一般，速度分析精度取决于优化三参数的精度，适于较复杂地质体的速度建模。
为了提高偏移速度建模的效率、精度、和稳定性，也可以采用多级多道集的偏移速度建模。比如，第一级用CMP道集、第二级用CIP道集等。值得注意的是：CFP道集和CRS道集偏移速度建模为我们提供了两种新的偏移速度分析方法。随着它们的不断发展和完善，一定会在偏移速度建模中发挥作用，应用会越来越广泛。
There is a higher requirement on the precision of seismic data imaging with the increasing difficulty of the seismic exploration and more complication of the reservoir. In order to have a better service for the E&D of oil field, Pre-SDM imaging has become the focus. Nowadays, several Pre-SDM methods have been applied in seismic data processing successfully, and also get high-quality seismic sections. But in Pre-SDM, imaging quality directly depends on the precision of the velocity field used in migration. When the underground velocity-depth model is correct, we can get good seismic imaging result, or there will appear errors in imaging depth and amplitude fidelity, polarity and magnitude of errors depend on the precision of velocity-depth model. Thinking about the importance of Pre-SDM to target layer imaging and the sensitivity of it to velocity-depth model, seismic workers have tumed their attention to migration velocity modeling in recent years. There are many migration velocity modeling methods. According to the theories on which they base, it can divide into ray-tracing migration velocity modeling, migration velocity modeling of wave equation and comprehensive migration velocity modeling. Whet/based on gathers, it can divide into CMP, CIP, CRP, CRS and CFP gather. Wave equation method can divide into two methods: DFA and RCA. But these methods mentioned above were restricted by underground geological structure and the complication of velocity field, such as reflector dip, the complexity of overburden layer, offset and lateral variation of velocity field. In order to fit this constrain condition better to realize properly imaging of complex structure, we firstly discussed the quantitative relationship between velocity error and depth error, depth, traveltime error, velocity and offset in migration velocity modeling theoretically, and velocity-modified criteria. Then applied it to a variety of models (including Marmousi model), and reasonably selected ray-tracing method, tomographic method or Pre-SDM method used for migration velocity modeling. At the same time, we should select a kind of migration velocity modeling method according to the result and efficiency. Finally, we put forward four kinds of migration velocity modeling: One is CMP gather method based on ray-tracing, another is CIP gather method based on residual curvature analysis and Pre-SDM of wave equation, the third one is CFP gather method, the theory on which it depends is equal-traveltime principle and forward-modeling of ray-tracing or wave function, the last one is CRS gather method based on the theory of optimization of three parameters. Sometimes we can also adapt migration velocity modeling with multi-level and multi-gather, the applications to the models have showed the effectiveness and adaptability of the methods.
This paper has a large range in content. It includes Pre-SDM, forward-modeling ,CFP migration and CRS stack. In PSDM, we discussed Kirchhoff integral method, SSF, FFD, FXFD and GS methods which involves PS method---the same as SSF, extended local Born approximation fourier (single reference slowness and multi reference slowness) and extended local Rytov approximation fourier methods. All of these methods were applied to Marmousi model. We derived the high-order FD equation of forward-modeling which fitted for strong lateral variation in velocity and simulated Marmousi model and Shengli model with zero offset. CFP migration is a new Pre-SDM method based on equal-traveltime principle. We did some theoretical model with CFP method. CRS stack is a seismic imaging method which is velocity-free. We derived all the theoretical formulation, and applied it to many models including Marmousi model and also processed a real data of Shengli area. These methods mentioned above are the base of migration velocity modeling. Taking computing efficiency, precision and stability into consideration, we used Pre-SDM of SSF and FFD, forward-modeling of high-order FD, CFP migration and CRS stack method. The key problem we discussed is migration velocity modeling. In migration velocity modeling, we used CMP, CIP(CDP or CRP), CFP and CRS gather. In CMP gather method, we used ray theory and maximum energy or maximum coefficient of correlation as the criteria to modify migration velocity, derived the analyzing formulation of the reflection travel-time of each trace in a variety of gathers including CMP gather using ray method with constant velocity or variable velocity, and put forward a CMP gather migration velocity modeling method based on velocity scanning. Then we applied it to the complex model. In CIP gather method, we derived the fundamental relationship between imaging depth error and migration velocity error, then made a quantitative description on the residual curvature appeared in post-migration CIP gather. To simple model, we gave the linear interpolation method to find updated velocity using the imaging error in depth of each trace in CIP gather. To complex model, we put forward single parameter and multi-parameter method to get derivative function using error in imaging depth of each trace in CIP gather, and following single parameter disturbing and multi parameter disturbing simultaneously to calculate modified velocity using generalized linear iterative inversion. We also applied it to many models including Marmousi model. The result showed good adaptability and effectiveness of this method. In CFP gather method, we put forward the method of constraint parameter inversion to get modified velocity based on least-square principle using equal-traveltime principle and DTS analysis. Then we applied this method to a model and the result is satisfactory. In CRS gather method, we derived the quantitative relationship between optimal three parameter and migration velocity field, and then put forward ray-tracing method to get migration velocity field using optimal three parameter in CRS stack. The applications proved its effectiveness and adaptability.
According to the results we got above through four kinds of migration velocity modeling, the gathers and the theories on which they based, we can come to the conclusions as followings. To CMP gather method, it has a high efficiency but low precision which depends on the complexity of the structure. In a sense, the more complex the structure is, the lower the precision. There also exist the problems of accumulation error in velocity and non-uniqueness in solution. It fits for velocity modeling in geological body which is not very complex in structure. Ray-tracing method with variable velocity can improve greatly the adaptability of migration velocity modeling of CMP gather to complex media. To CIP gather method, its efficiency is low but has a high precision and stability. This method fits for velocity modeling in complex geological body. To CFP gather method, it has a high precision and stability, and fits for velocity modeling in complex geological body when based on wave equation modeling; when based on ray-tracing modeling it has a high efficiency, but the precision and stability is a little lower, and it fits for velocity modeling in general geological body. To CRS gather method, the precision of velocity analysis depends on the precision of optimization of three parameters. It fits for velocity modeling in complex geological body.
In order to improve the efficiency, precision and stability of migration velocity modeling, we can also use the method of multi-level and multi-gather. For instance, we use CMP gather method in first level and CIP gather method in the second level, etc.. What we should pay more attention to is that CFP and CRS gather migration velocity modeling provide us with two kinds of new migration velocity analysis methods. With their continuous development and perfection, these methods will play more important role in migration velocity modeling and come into wide use in the field.
引文
[1] 马在田著，1989，地震偏移成像，石油工业出版社
[2] 马在田等编著，1997，计算地球物理学概论，同济大学出版社
[3] 杨文采编著，1989，地球物理反演和地震层析成像，地质出版社
[4] 程玖兵，2000，强横向变速介质中的叠前深度偏移方法研究(硕士论文)
[5] 李振春等，2000，共中心点道集偏移速度分析，石油物探，第一期
[6] 王华忠，1997，三维地震波场最优外推算子及其在深度偏移成像中的应用(博士论文)
[7] 张叔伦等，1999，基于平面波合成的付立叶有限差分叠前深度偏移，石油地球物理勘探，第一期，第34卷
[8] 徐升等，1996，射线追踪的微变网格方法．地球物理学报，38(1)：97～102
[9] Berkhou,J., 1980, Seismic Migration—Imaging of accoustic energy by wave field extrapolation, Elsevier Scientific Publishing Company.
[10] Clearbout,J.F., 1985,Imaging of earth's interior, B lackwell Scientific Publications, Inc.
[11] Al-Yahya,K., 1989, Velocity analysis by iterative profile migration: Geophysics,54,718-729.
[12] Berkhout, A. J., 1984, Seismic Resolution: Geophys. Press, CharpterⅥ, 177-192.
--1985, Seismic migration: Imaging of acoustic energy by wavefield extrapolation, third edition: Elsevier Science Publ. Co., Inc., ChapterⅥ, 185-244.
--1992, Areal shot record technology: J. Seis. Expl., 1,251-264.
--1993, Imaging in seismic exploration and medical ultrasound, a comparison: 3rd International Congress of the Brazilian Geophysical Society, Expanded Abstracts.
[13] Berkhout, A. J., 1997a, Pushing the limits of seismic imaging, Part Ⅰ : Prestack migration in terms of double dynamic focusing: Geophysics, 62,937-953.
[14] Berkhout, A. J., 1997b, Pushing the limits of seismic imaging , PartⅡ: Intergration of prestack migration, velocity estimation, and AVO analysis: Geophysics, 62,954-969.
[15] Berkhout, A. J., and Rietveld,W.E.A., 1994, Determination of macromodels for prestack migration: Part Ⅰ :Estimation of macrovelocities: 64th Ann. Internat. Mtg. Soc. Expl. Geophysics., Expanted Abstracts, 1330-1333.
[16] Bortfeld, R., 1989, Geometrical ray theory: Rays and traveltimes in seismic systems (second-order approximations of the traveltimes ): Geophysics, 54, no. 3,342-349.
[17] Clayton,R.W., and Stolt,R.H., 1981, A Born-WKBJ inversion method for acoustic reflection data: Geophysics, 46, 1559-1567.
[18] Dablain.M.A., 1986, The application of high-order differencing to the scalar wave equation: Geophysics, 51, 54-66.
[19] de Bazelaire, E., 1988, Normal moveout revisited - inhomogeneous media and curved interfaces: Geophysics, 53, no. 2, 143-157.
[20] De Bruin, C. G. M., 1992, Linear AVO inversion by prestack depth migration: Ph. D. thesis, Delft University, The Netherlands.
[21] Deregowski,S.M.,1990, Common-offset migration and velocity analysis: First Break,8,no.6, 225-234.
[22] Gazdag,J.,1978, Wave equation with phase-shift method: Geophysics, 43,1342-1351.
[23] Gazdag,J. and Sguazzero, 1984, Migration of seismic data by phase shift plus interpolation: Geophysics, 49, 1984.
[24] Gelchinsky, B. , 1988, The cmmon-reflecting-element(CRE)method: ASEG/SEG Internat. Geophys.Conf.Expl.Geophys., Extended Abstracts, 71-75.
[25] Gelchinsky, B., 1989, Homeomophic imaging in processing and interpretation of seismic data-foudamentals and schemes: 59 th Annual Intemat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 983.
[26] Gelchinsky, B., Landa, E., and Shtivelman, V., 1985, Algorithms of phase and group correlation: Geophysics, 50, no. 4, 596-608.
[27] Gray,S.H., and May,W.P., 1994, Kirchhoff migration using eikonal equation traveltimes: Geophysics, 59, no. 5, 810-817.
[28] Havid D et al. 1988, Increasing interpretation accuracy: A new approach to interval velocity estimation. The Leading Edge, 9(1): 13-16.
[29] Hocht, G., Perroud, H., and Hubral,P., 1997, Migrating around on parabolas:The Leading Edge, May, 473-476.
[30] Huang L.J.,Michael C.F.,1999, Quasi-linear extended local Born Fourier migration method: 69nd Ann. Internat.Mtg.,Soc.Expl.Geophys., Expanded Abstracts.
[31] Huang L.J..Michael C.F.,1999, Extended pseudo-screen migration with multiple reference velocities: 69nd Ann. Internat.Mtg.,Soc.Expl.Geophys., Expanded Abstracts.
[32] Huang L.J..Michael C.F.,and Wu R.S.,1999a, Extended local Bom Fourier migration method: Geophysics.,64,1524-1534.
[33] Huang L.J..Michael C.F.,and Roberts P.M., 1999b, Extended local Rytov Fourier migration method: Geophysics.,64,1535-1545.
[34] Huang L.J.,and Wu R.S., , 1996, Prestack depth migration with accoustic screen propagators: 66nd Ann. Internat.Mtg.,Soc.Expl.Geophys., Expanded Abstracts,415-418.
[35] Hubral, P., 1983, Computing true amplitude reflections in a laterally inhomeogeneous earth: Geophysics, 48, no.8 1052-1062.
[36] Hubral, P., Hocht,G..and Jager, R., 1999, Seismic illumination: The Leading Edge, 18(11): 1168-1171.
[37] Hubral,P., and Krey.T., 1980, Interval velocity from seismic reflection time measurements: 50~(nd) Ann. Internat. Mtg., Soc, Expl. Geophys.
[38] Hubral , P., Schleicher, J., and Tyger, M., 1996a, A unified approach to 3-D seismic reflection imaging. Part I : Basic concepts: Geophysics, 61, no.3, 742-758.
[39] Jager, R., 1999, The common reflection surface stack—Theory and application: Master's thesis. Universitat Karlsruhe.
[40] J.C.R.Cruz, P. Hubral, M. Tygel, J. Schleicher. and G. Hocht, The common reflecting element (CRE) method revisited: Geophysics, 65, no.3 979-993.
[41] Jin,S.W,and Wu, R.S., 1998, Prestack depth migration using a hybrid pseudo-screen propagator: 68nd Ann. Intemat.Mtg.,Soc.Expl.Geophys., Expanded Abstracts.
[42] Jin,S.W, and Wu, R.S., 1998, Depth migration using the windowed generalized screen propagators: 68nd Ann. Internat.Mtg.,Soc.Expl.Geophys., Expanded Abstracts.
[43] Jin,S.W,and Wu, R.S., 1999, Experimenting with the hybrid pseudo-screen propagator: 69nd Ann. Internat.Mtg.,Soc.Expl.Geophys., Expanded Abstracts.
[44] Kabir. M. M. N., and Verschuur D. J., 2000, A constrained parametric inversion for velocity analysis based on CFP technology: Geophysics, 65, 4, 1210-1222.
[45] Keydar, S., Gelchinsky, B., Shtivelman, V., and Berkovitch, A., 1990, The common-evolute-element (CEE) stack imaging: 60 th Annual Internat. Mtg.. Soc. Expl. Geophys., Expanded Abstracts, 1911-2013.
[46] Koren, Z., and Gelchinsky, B., 1989, Common-reflecting-element (CRE) ray tracing for the calculation of the global multi-offset time field: Geophysics. J. Internal, 99,391-400.
[47] Langan R T. 1985, Tracing of rays through heterogeneous media: An accurate and efficient procedure. Geophysics, 50(9): 1456～1465.
[48] Lafond,C.F., and Levander,A.R., 1993, Migration moveout analysis and depth focusing: Geophysics, 58, 91-100.
[49] Lee,W.B., and Zhang,L.,1992, Residual shot profile migration: Geophysics,57,815-822.
[50] Liu,Z.,1997, An analytical approach to migration velocity analysis: Geophysics, 62, 1238-1249.
[51] Liu,Z., and Bleistain,N., 1992, Velocity analysis by residual moveout: 62~(nd) Ann. Internat. Mtg., Soc, Expl. Geophys., Expl. Geophys., Expanded Abstracts, 1034-1036.
[52] Liu,Z., and Bleistain,N., 1995, Migration velocity analysis: Theory and an iterative algorithm: Geophysics,60,142-153.
[53] Mackay,S., and Abma,R.,1992, Imaging and velocity estimation with depth-focusing analysis: Geophysics,57,1608-1622.
[54] Morse,P.M., and Feshbach, H., 1955, Methods of theoretical physics: McGraw-Hill Book Co.
[55] Muller, T., Jager, R., and Hocht, G., 1998, Common reflection surface stacking method—Imaging with an unknown velocity model: 68th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1764-1767.
[56] Bleistein,N., Cohen,J.K., and Hagin,F.G., 1987, Two and one-half dimensional Born inversion with an arbitrary reference: Geophysics, 52, no. 1, 26-36.
[57] Olalde, C. C. B., 1996, The common-reflecting-element (CRE) method applied to the analysis of complex seismic reflectors: Ph. D. dissertation, Kiel Univ.
[58] Rietveld, W.E.A., 1995, Controlled illumination in prestack seismic migration: Ph. D. thesis, Delft University, The Netherlands.
[59] Rietveld, W.E.A., and Berkhout, A. J., 1994, Prestack depth migration by means of controlled illumination: Geophysics, 59, 5, 801-809.
[60] Ristow,D. and Ruhl.T., 1994, Fourier finite-difference migration: Geophysics, 59,1882-1893.
[61] R. Jaeger, J. Mann, G. Hocht, and P. Huber, 2001, Common-reflection-surface stack: Image and attributes: Geophysics, 66, no. 1, 97-109.
[62] Schleicher, J., Tygel, M., and Hubral, P., 1993, Parabolic and hyperbolic paraxial two-point traveltimes in 3D media: Geophys. Prosp., 41, no, 4, 495-514.
[63] Schleicher, J., Tygel, M., and Hubral, P., 1993, Parabolic and hyperbolic paraxial two-point traveltimes in 3D media: Geophys. Prosp., 41, no, 4,459-513.
[64] Schneider, W.A., Jr., 1995, Robust and efficient upwind finite-difference traveltime calculation in three dimensions: Geophysics, 60, no. 4, 1108-1117.
[65] Schneider, W.A., Jr. et al., 1992, A dynamic programming approach to first arrival traveltime computation in media with arbitrary distributed velocities: Geophysics, 57, no. 1, 39-50.
[66] Steentoft, H., 1993, Imaging of reflection seismic data with the common-reflection-element method: Ph.D. thesis, Kiel Univ.
[67] Steentoft, H., Goedde, W., and Thiel, M., 1992, The power of reflection seismics for mapping of shallow layers: 54th Ann. Internat. Mtg., Eur. Assn. Expl. Geophys., Expanded Abstracts, 730-731.
[68] Steentoft, H., and Rabbel, W., 1992a, Processing of complex data with the CRE method: 54th Ann. Internat. Mtg., Eur. Assn. Geosc. Eng., Abstracts, 560-561.
[69] Steentoft, H., and Rabbel, W., 1992b, The CRE method: A technique of homeomorphic imaging in processing of seismic data: :Acous. Imag., 19, 803-809.
[70] Steentoft, H., and Rabbel, W., 1994, Seismic mapping of the Marmousi data set with the common reflection element method (CRE method): Tectonophysics, 232, 355-363.
[71] Stoffa, P.L., 1990, Split-step Fourier migration: Geophysics, 55, 410-421.
[72] Stolt, R.H.,1978, Migration by Fourier transform: Geophysics, 43, 23-48.
[73] Stork,C., and Clayton,R.W., 1991a, An implementation of tomographic velocity analysis: Geophysics, 56, 472-482.
[74] Stork C and Clayton R W. 1991b, Linear aspects of tomographic velocity analysis. Geophysics, 56(4): 483～495.
[75] Tanner, M . T., and Koeler, F., 1969, Velocity spectra-digital computer derivation and appication of velocity functions: Geelphysics, 34, no, 6, 859-881.
[76] Thore, P. D., de Bazelaire, E., and Ray, M. P., 1994, Three-parameter equation: An efficient tool to enhance the stack: Geophysics, 59, no. 2,297-308.
[77] Thorbecke, J. W., 1997, Common focus point technology: Ph.D. thesis, Delft University, The Netherlands.
[78] Tygel, M., Schleicher, J., and Hubral, P., 1996, A unified approach to 3-D seismic reflection imaging, Part Ⅱ: Theory: Geophysics, 61, no. 3,759-775.
[79] Ursin, B., 1982, Quadratic wavefront and traveltime approximation in inhomogeneous layered media with curved interfaces: Geophysics, 47, no. 7, 1012-1021.
[80] Versteeg,R.,1994, The Marmousi experience: Velocity model determination on a synthetic complex data set: The Leading Edge, 927-936.
[81] Wang．B．等人，1998，利用深度聚焦分析进行层析速度估计，CPS／SEG／EAGE北京国际地球物理研讨会论文集．
[82] Wu R.S.,and Huang L.J., 1992, Scattered field calculation in heterogeneous media using the phase-screen propagator: 62nd Ann. Internat.Mtg.,Soc.Expl.Geophys., Expanded Abstracts, 1289-1292.
[83] Wu R.S., Huang L.J.,and Xie X.B., 1995, Backscattered wave aclculation using the de Wolf approximation and a phase-screen propagator : 65nd Ann. Internat.Mtg.,Soc.Expl.Geophys., Expanded Abstracts, 1293-1296.
[84] Xie.X.B.and Wu R.S., 1998, Improve the wide angle accuracy of screen method under contrast:68nd Ann. Internat.Mtg.,Soc.Expl.Geophys., Expanded Abstracts.
[85] Yihnaz,O., and Chambers,R.,1984, Migration velocity analysis by Wavefield extrapolation: Geophysics,49,1664-1674.
[86] Zhu,J., and Lines,L.R., 1998, Comparison of Kirchhoff and reverse-time migration methods with applications to prestack depth imaging of complex structures: Geophysics. 63, no. 4, 1166-1176.
[2] 马在田等编著，1997，计算地球物理学概论，同济大学出版社
[3] 杨文采编著，1989，地球物理反演和地震层析成像，地质出版社
[4] 程玖兵，2000，强横向变速介质中的叠前深度偏移方法研究(硕士论文)
[5] 李振春等，2000，共中心点道集偏移速度分析，石油物探，第一期
[6] 王华忠，1997，三维地震波场最优外推算子及其在深度偏移成像中的应用(博士论文)
[7] 张叔伦等，1999，基于平面波合成的付立叶有限差分叠前深度偏移，石油地球物理勘探，第一期，第34卷
[8] 徐升等，1996，射线追踪的微变网格方法．地球物理学报，38(1)：97～102
[9] Berkhou,J., 1980, Seismic Migration—Imaging of accoustic energy by wave field extrapolation, Elsevier Scientific Publishing Company.
[10] Clearbout,J.F., 1985,Imaging of earth's interior, B lackwell Scientific Publications, Inc.
[11] Al-Yahya,K., 1989, Velocity analysis by iterative profile migration: Geophysics,54,718-729.
[12] Berkhout, A. J., 1984, Seismic Resolution: Geophys. Press, CharpterⅥ, 177-192.
--1985, Seismic migration: Imaging of acoustic energy by wavefield extrapolation, third edition: Elsevier Science Publ. Co., Inc., ChapterⅥ, 185-244.
--1992, Areal shot record technology: J. Seis. Expl., 1,251-264.
--1993, Imaging in seismic exploration and medical ultrasound, a comparison: 3rd International Congress of the Brazilian Geophysical Society, Expanded Abstracts.
[13] Berkhout, A. J., 1997a, Pushing the limits of seismic imaging, Part Ⅰ : Prestack migration in terms of double dynamic focusing: Geophysics, 62,937-953.
[14] Berkhout, A. J., 1997b, Pushing the limits of seismic imaging , PartⅡ: Intergration of prestack migration, velocity estimation, and AVO analysis: Geophysics, 62,954-969.
[15] Berkhout, A. J., and Rietveld,W.E.A., 1994, Determination of macromodels for prestack migration: Part Ⅰ :Estimation of macrovelocities: 64th Ann. Internat. Mtg. Soc. Expl. Geophysics., Expanted Abstracts, 1330-1333.
[16] Bortfeld, R., 1989, Geometrical ray theory: Rays and traveltimes in seismic systems (second-order approximations of the traveltimes ): Geophysics, 54, no. 3,342-349.
[17] Clayton,R.W., and Stolt,R.H., 1981, A Born-WKBJ inversion method for acoustic reflection data: Geophysics, 46, 1559-1567.
[18] Dablain.M.A., 1986, The application of high-order differencing to the scalar wave equation: Geophysics, 51, 54-66.
[19] de Bazelaire, E., 1988, Normal moveout revisited - inhomogeneous media and curved interfaces: Geophysics, 53, no. 2, 143-157.
[20] De Bruin, C. G. M., 1992, Linear AVO inversion by prestack depth migration: Ph. D. thesis, Delft University, The Netherlands.
[21] Deregowski,S.M.,1990, Common-offset migration and velocity analysis: First Break,8,no.6, 225-234.
[22] Gazdag,J.,1978, Wave equation with phase-shift method: Geophysics, 43,1342-1351.
[23] Gazdag,J. and Sguazzero, 1984, Migration of seismic data by phase shift plus interpolation: Geophysics, 49, 1984.
[24] Gelchinsky, B. , 1988, The cmmon-reflecting-element(CRE)method: ASEG/SEG Internat. Geophys.Conf.Expl.Geophys., Extended Abstracts, 71-75.
[25] Gelchinsky, B., 1989, Homeomophic imaging in processing and interpretation of seismic data-foudamentals and schemes: 59 th Annual Intemat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 983.
[26] Gelchinsky, B., Landa, E., and Shtivelman, V., 1985, Algorithms of phase and group correlation: Geophysics, 50, no. 4, 596-608.
[27] Gray,S.H., and May,W.P., 1994, Kirchhoff migration using eikonal equation traveltimes: Geophysics, 59, no. 5, 810-817.
[28] Havid D et al. 1988, Increasing interpretation accuracy: A new approach to interval velocity estimation. The Leading Edge, 9(1): 13-16.
[29] Hocht, G., Perroud, H., and Hubral,P., 1997, Migrating around on parabolas:The Leading Edge, May, 473-476.
[30] Huang L.J.,Michael C.F.,1999, Quasi-linear extended local Born Fourier migration method: 69nd Ann. Internat.Mtg.,Soc.Expl.Geophys., Expanded Abstracts.
[31] Huang L.J..Michael C.F.,1999, Extended pseudo-screen migration with multiple reference velocities: 69nd Ann. Internat.Mtg.,Soc.Expl.Geophys., Expanded Abstracts.
[32] Huang L.J..Michael C.F.,and Wu R.S.,1999a, Extended local Bom Fourier migration method: Geophysics.,64,1524-1534.
[33] Huang L.J..Michael C.F.,and Roberts P.M., 1999b, Extended local Rytov Fourier migration method: Geophysics.,64,1535-1545.
[34] Huang L.J.,and Wu R.S., , 1996, Prestack depth migration with accoustic screen propagators: 66nd Ann. Internat.Mtg.,Soc.Expl.Geophys., Expanded Abstracts,415-418.
[35] Hubral, P., 1983, Computing true amplitude reflections in a laterally inhomeogeneous earth: Geophysics, 48, no.8 1052-1062.
[36] Hubral, P., Hocht,G..and Jager, R., 1999, Seismic illumination: The Leading Edge, 18(11): 1168-1171.
[37] Hubral,P., and Krey.T., 1980, Interval velocity from seismic reflection time measurements: 50~(nd) Ann. Internat. Mtg., Soc, Expl. Geophys.
[38] Hubral , P., Schleicher, J., and Tyger, M., 1996a, A unified approach to 3-D seismic reflection imaging. Part I : Basic concepts: Geophysics, 61, no.3, 742-758.
[39] Jager, R., 1999, The common reflection surface stack—Theory and application: Master's thesis. Universitat Karlsruhe.
[40] J.C.R.Cruz, P. Hubral, M. Tygel, J. Schleicher. and G. Hocht, The common reflecting element (CRE) method revisited: Geophysics, 65, no.3 979-993.
[41] Jin,S.W,and Wu, R.S., 1998, Prestack depth migration using a hybrid pseudo-screen propagator: 68nd Ann. Intemat.Mtg.,Soc.Expl.Geophys., Expanded Abstracts.
[42] Jin,S.W, and Wu, R.S., 1998, Depth migration using the windowed generalized screen propagators: 68nd Ann. Internat.Mtg.,Soc.Expl.Geophys., Expanded Abstracts.
[43] Jin,S.W,and Wu, R.S., 1999, Experimenting with the hybrid pseudo-screen propagator: 69nd Ann. Internat.Mtg.,Soc.Expl.Geophys., Expanded Abstracts.
[44] Kabir. M. M. N., and Verschuur D. J., 2000, A constrained parametric inversion for velocity analysis based on CFP technology: Geophysics, 65, 4, 1210-1222.
[45] Keydar, S., Gelchinsky, B., Shtivelman, V., and Berkovitch, A., 1990, The common-evolute-element (CEE) stack imaging: 60 th Annual Internat. Mtg.. Soc. Expl. Geophys., Expanded Abstracts, 1911-2013.
[46] Koren, Z., and Gelchinsky, B., 1989, Common-reflecting-element (CRE) ray tracing for the calculation of the global multi-offset time field: Geophysics. J. Internal, 99,391-400.
[47] Langan R T. 1985, Tracing of rays through heterogeneous media: An accurate and efficient procedure. Geophysics, 50(9): 1456～1465.
[48] Lafond,C.F., and Levander,A.R., 1993, Migration moveout analysis and depth focusing: Geophysics, 58, 91-100.
[49] Lee,W.B., and Zhang,L.,1992, Residual shot profile migration: Geophysics,57,815-822.
[50] Liu,Z.,1997, An analytical approach to migration velocity analysis: Geophysics, 62, 1238-1249.
[51] Liu,Z., and Bleistain,N., 1992, Velocity analysis by residual moveout: 62~(nd) Ann. Internat. Mtg., Soc, Expl. Geophys., Expl. Geophys., Expanded Abstracts, 1034-1036.
[52] Liu,Z., and Bleistain,N., 1995, Migration velocity analysis: Theory and an iterative algorithm: Geophysics,60,142-153.
[53] Mackay,S., and Abma,R.,1992, Imaging and velocity estimation with depth-focusing analysis: Geophysics,57,1608-1622.
[54] Morse,P.M., and Feshbach, H., 1955, Methods of theoretical physics: McGraw-Hill Book Co.
[55] Muller, T., Jager, R., and Hocht, G., 1998, Common reflection surface stacking method—Imaging with an unknown velocity model: 68th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1764-1767.
[56] Bleistein,N., Cohen,J.K., and Hagin,F.G., 1987, Two and one-half dimensional Born inversion with an arbitrary reference: Geophysics, 52, no. 1, 26-36.
[57] Olalde, C. C. B., 1996, The common-reflecting-element (CRE) method applied to the analysis of complex seismic reflectors: Ph. D. dissertation, Kiel Univ.
[58] Rietveld, W.E.A., 1995, Controlled illumination in prestack seismic migration: Ph. D. thesis, Delft University, The Netherlands.
[59] Rietveld, W.E.A., and Berkhout, A. J., 1994, Prestack depth migration by means of controlled illumination: Geophysics, 59, 5, 801-809.
[60] Ristow,D. and Ruhl.T., 1994, Fourier finite-difference migration: Geophysics, 59,1882-1893.
[61] R. Jaeger, J. Mann, G. Hocht, and P. Huber, 2001, Common-reflection-surface stack: Image and attributes: Geophysics, 66, no. 1, 97-109.
[62] Schleicher, J., Tygel, M., and Hubral, P., 1993, Parabolic and hyperbolic paraxial two-point traveltimes in 3D media: Geophys. Prosp., 41, no, 4, 495-514.
[63] Schleicher, J., Tygel, M., and Hubral, P., 1993, Parabolic and hyperbolic paraxial two-point traveltimes in 3D media: Geophys. Prosp., 41, no, 4,459-513.
[64] Schneider, W.A., Jr., 1995, Robust and efficient upwind finite-difference traveltime calculation in three dimensions: Geophysics, 60, no. 4, 1108-1117.
[65] Schneider, W.A., Jr. et al., 1992, A dynamic programming approach to first arrival traveltime computation in media with arbitrary distributed velocities: Geophysics, 57, no. 1, 39-50.
[66] Steentoft, H., 1993, Imaging of reflection seismic data with the common-reflection-element method: Ph.D. thesis, Kiel Univ.
[67] Steentoft, H., Goedde, W., and Thiel, M., 1992, The power of reflection seismics for mapping of shallow layers: 54th Ann. Internat. Mtg., Eur. Assn. Expl. Geophys., Expanded Abstracts, 730-731.
[68] Steentoft, H., and Rabbel, W., 1992a, Processing of complex data with the CRE method: 54th Ann. Internat. Mtg., Eur. Assn. Geosc. Eng., Abstracts, 560-561.
[69] Steentoft, H., and Rabbel, W., 1992b, The CRE method: A technique of homeomorphic imaging in processing of seismic data: :Acous. Imag., 19, 803-809.
[70] Steentoft, H., and Rabbel, W., 1994, Seismic mapping of the Marmousi data set with the common reflection element method (CRE method): Tectonophysics, 232, 355-363.
[71] Stoffa, P.L., 1990, Split-step Fourier migration: Geophysics, 55, 410-421.
[72] Stolt, R.H.,1978, Migration by Fourier transform: Geophysics, 43, 23-48.
[73] Stork,C., and Clayton,R.W., 1991a, An implementation of tomographic velocity analysis: Geophysics, 56, 472-482.
[74] Stork C and Clayton R W. 1991b, Linear aspects of tomographic velocity analysis. Geophysics, 56(4): 483～495.
[75] Tanner, M . T., and Koeler, F., 1969, Velocity spectra-digital computer derivation and appication of velocity functions: Geelphysics, 34, no, 6, 859-881.
[76] Thore, P. D., de Bazelaire, E., and Ray, M. P., 1994, Three-parameter equation: An efficient tool to enhance the stack: Geophysics, 59, no. 2,297-308.
[77] Thorbecke, J. W., 1997, Common focus point technology: Ph.D. thesis, Delft University, The Netherlands.
[78] Tygel, M., Schleicher, J., and Hubral, P., 1996, A unified approach to 3-D seismic reflection imaging, Part Ⅱ: Theory: Geophysics, 61, no. 3,759-775.
[79] Ursin, B., 1982, Quadratic wavefront and traveltime approximation in inhomogeneous layered media with curved interfaces: Geophysics, 47, no. 7, 1012-1021.
[80] Versteeg,R.,1994, The Marmousi experience: Velocity model determination on a synthetic complex data set: The Leading Edge, 927-936.
[81] Wang．B．等人，1998，利用深度聚焦分析进行层析速度估计，CPS／SEG／EAGE北京国际地球物理研讨会论文集．
[82] Wu R.S.,and Huang L.J., 1992, Scattered field calculation in heterogeneous media using the phase-screen propagator: 62nd Ann. Internat.Mtg.,Soc.Expl.Geophys., Expanded Abstracts, 1289-1292.
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