基于波动理论的复杂地质构造地震数据成像
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摘要
本文围绕复杂地质构造情况下基于波动理论的地震数据成像课题开展研究。在波场延拓方面，从非稳态相移公式出发，推导出广义高阶屏双平方根波场延拓公式，从而得出了一种新的共中心点-炮检距域叠前深度偏移方法。理论模型和海洋资料的试算结果验证了方法的正确性和有效性。
通过对本文提出的平面波傅立叶有限差分叠前深度偏移方法、最大能量面炮记录叠前深度偏移方法和相位编码面炮记录叠前深度偏移方法的研究，试算和对比，提出了合成震源三原则，根据这些原则，提出了合成震源概念和合成震源记录叠前深度偏移方法。
合成震源既包括了已有的平面波震源，也包括了控制照明震源，分段平面波震源和相位编码震源。合成震源记录叠前深度偏移方法是炮记录偏移、平面波偏移、控制照明偏移和相位编码面炮记录偏移方法的推广和统一形式。合成震源记录叠前深度偏移方法在保证成像质量的前提下，可数倍提高常规面炮记录叠前深度偏移效率。Marmousi模型和三维SEG/EAEG盐丘模型及实际海洋和陆地地震资料的试算结果验证了方法的正确性、有效性和实用性。
结合我国西部地震资料的特点，针对起伏地表情况下的地震数据成像问题，提出了与合成震源记录偏移方法相应的成像方法以及基于共聚焦点技术的基准面向上校正方法。
确定速度模型是叠前成像的关键步骤。在宏观速度模型的建立方面，本文提出了一种基于等时原理的偏移速度分析方法。利用等时原理，把建立速度场问题转化为求取判别函数的局部极值问题，可以利用优化方法求解此问题。模型和野外资料的试算结果验证了方法的正确性和有效性。
The project of seismic data imaging under the complex geology structure is studied in this thesis. A generalized high order screen extrapolator of double square root (DSR) equation is derived from the non-stationary phase shift formula of wavefield continuation, thus a new prestack depth migration method in the cmp-offset domain is proposed. The migration results of the synthetic and ocean field datasets show that this method is correct and effective.
Several prestack depth migration methods are proposed and unified to the synthetic source record migration method. These methods include plane wave migration with Fourier Finite Difference(FFD) extrapolator, maximum energy plane wave migration and prestack migration with phase encoding of areal shot records. The synthetic source is the generalization of plane wave source, controlled illumination source, piecewise plane wave source and areal sources with phase encoding etc. By migrating the synthetic source record, the computational cost of the conventional areal shot record migration can be reduced by several times without significantly degrading the image quality. The synthetic source record migration method is tested on Mamousi model, 3D SEG/EAEG salt model and field datasets. This migration method is proved to be correct, effective and practical.
Undulate acquisition surface is one of the main properties of the seismic datasets from Western China. Based on the synthetic source record migration method and wave stack principle, a method of migrating directly from the undulate surface is presented and tested. A wave equation datuming method is also applied to redatuming the wavefield upward. This datuming method is derived from the Common Focus Point (CFP) concept.
Estimating the macro velocity model is considered to be the key step of prestack imaging procedures. A migration velocity analysis method is proposed, in which the problem of velocity analysis is converted to the problem of determining the local maximums of the defined criterion function. The correctness and effectiveness of the method is proved by the numerical experiments on the theoretical model and field datasets.
通过对本文提出的平面波傅立叶有限差分叠前深度偏移方法、最大能量面炮记录叠前深度偏移方法和相位编码面炮记录叠前深度偏移方法的研究，试算和对比，提出了合成震源三原则，根据这些原则，提出了合成震源概念和合成震源记录叠前深度偏移方法。
合成震源既包括了已有的平面波震源，也包括了控制照明震源，分段平面波震源和相位编码震源。合成震源记录叠前深度偏移方法是炮记录偏移、平面波偏移、控制照明偏移和相位编码面炮记录偏移方法的推广和统一形式。合成震源记录叠前深度偏移方法在保证成像质量的前提下，可数倍提高常规面炮记录叠前深度偏移效率。Marmousi模型和三维SEG/EAEG盐丘模型及实际海洋和陆地地震资料的试算结果验证了方法的正确性、有效性和实用性。
结合我国西部地震资料的特点，针对起伏地表情况下的地震数据成像问题，提出了与合成震源记录偏移方法相应的成像方法以及基于共聚焦点技术的基准面向上校正方法。
确定速度模型是叠前成像的关键步骤。在宏观速度模型的建立方面，本文提出了一种基于等时原理的偏移速度分析方法。利用等时原理，把建立速度场问题转化为求取判别函数的局部极值问题，可以利用优化方法求解此问题。模型和野外资料的试算结果验证了方法的正确性和有效性。
The project of seismic data imaging under the complex geology structure is studied in this thesis. A generalized high order screen extrapolator of double square root (DSR) equation is derived from the non-stationary phase shift formula of wavefield continuation, thus a new prestack depth migration method in the cmp-offset domain is proposed. The migration results of the synthetic and ocean field datasets show that this method is correct and effective.
Several prestack depth migration methods are proposed and unified to the synthetic source record migration method. These methods include plane wave migration with Fourier Finite Difference(FFD) extrapolator, maximum energy plane wave migration and prestack migration with phase encoding of areal shot records. The synthetic source is the generalization of plane wave source, controlled illumination source, piecewise plane wave source and areal sources with phase encoding etc. By migrating the synthetic source record, the computational cost of the conventional areal shot record migration can be reduced by several times without significantly degrading the image quality. The synthetic source record migration method is tested on Mamousi model, 3D SEG/EAEG salt model and field datasets. This migration method is proved to be correct, effective and practical.
Undulate acquisition surface is one of the main properties of the seismic datasets from Western China. Based on the synthetic source record migration method and wave stack principle, a method of migrating directly from the undulate surface is presented and tested. A wave equation datuming method is also applied to redatuming the wavefield upward. This datuming method is derived from the Common Focus Point (CFP) concept.
Estimating the macro velocity model is considered to be the key step of prestack imaging procedures. A migration velocity analysis method is proposed, in which the problem of velocity analysis is converted to the problem of determining the local maximums of the defined criterion function. The correctness and effectiveness of the method is proved by the numerical experiments on the theoretical model and field datasets.
引文
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[3] Versteeg R. Sensitivity of prestack depth migration to the velocity model. Geophysics, 1993, 58(6) : 873-882
[4] Aminzadeh F., Burkhard N., Long J., Kunz T, Dulcos P. Three dimensional SEG/EAEG models-An update. The Leading Edge, 1996, 15:131-134
[5] Dobrin M. Introduction to geophysical prospecting. 3rd ED. McGraw Hill Book Co., 1976, P12
[6] Hagedoorn J. G. A process of seismic reflection interpretation. Geophysical prospecting, 1954, 2: 85-127
[7] Musgrave A. W. Wave-front chart and three dimensional migration. Geophysics, 1961,26: 738-753
[8] Lindsey J. P. Digital migration. Oil and Gas Journal, 1970, 38: 112-115
[9] Timoshin Y. V. New possibilities for imagery. Physics-Acoustics, 1970, 15(3) : 360-367
[10] Claerbout J. F. Coarse grid calculation of waves in inhomogeneous media with application to delineation of complicated seismic structure. Geophysics, 1970, 35: 407-418
[11] Claerbout J. F., Johnson A. G. Extrapolation of time-dependent waveforms along their path of propagation. Journal of Royal Astronomical Society, 1970,26: 285-293
[12] Claerbout J. F., Doherty. Downward continuation of moveout-corrected seismograms. Geophysics, 1972,37:741-768
[13] Lowenthal L., Lu R. R., Sherwood J. W. C. The wave equation applied to migration
[14] French S. W. Two-dimensional and three-dimensional migration of model experiment reflection profiles. Geophysics, 1974, 39: 265-277
[15] Gardner G. H. F., French W. S., Matzuk T. Elements of migration and velocity analysis. Geophysics, 39:811-825
[16] Stolt R. H. Migration by Fourier transform. Geophysics, 1978,43(1) : 23-48
[17] Yilmaz O. Prestack partial migration. Ph.D. thesis, Stanford University, 1979
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