复杂介质地震波场正演模拟方法研究
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摘要
地震数值模拟在地震勘探中具有重要作用。按照原理可分为基于射线理论的射线追踪方法和基于波动理论的波动方程正演。
射线追踪在复杂地表、复杂构造中的反射波追踪是一个难点。本文通过对试射法、全局最短路径法、常速度梯度法的研究,取得了一定的效果。首先,本文对试射法推导了透射线和反射线的传播方向,并将其应用到起伏地表和复杂构造模型中。模型试算表明,算法稳定,可适应复杂介质模型。然而,试射法无法适应强速度变化、难于求出多值走时中的全局最小走时,为此,研究了全局最短路径法。根据图形理论和惠更斯原理,求得任意点的全局最短路径,同时实现了反射波追踪,并对误差进行了分析,算例分析表明,全局最短路径法能够适应强速度变化,可以求出全局最小走时,但只适合两点射线追踪,且存在射线分叉问题。通过研究常速度梯度法基本原理,采用网格剖分的方法,求解一组射线路径的解析表达式,得到了射线追踪路径,结合斯奈尔定律,实现了反射波射线追踪。计算反射波路径时需要有层位信息,常规的层位结构模型,无法适应界面起伏较大或存在许多逆断层的复杂模型,本文提出一种线性连接法和分段结构模型,使得层位模型的建立简洁方便,并将其应用到常速度梯度法中取得了良好的效果。当模型为复杂介质时,采用普通射线法制作合成地震记录,会存在焦散区、空白区等奇异性区域。本文采用高斯射线束代替普通射线进行正演模拟,克服了普通射线法的缺陷,通过模型试算,证明了方法的正确性,且有较高的精度。
射线追踪计算速度快,但无法很好的反映波场的动力学特征。因此,本文对波动方程正演中的非均匀介质二维声波、粘声波、弹性波以及粘弹性波交错网格高阶有限差分正演模拟进行了研究,并以复杂介质模型进行了试算。探讨了三维声波、弹性波高阶交错网格有限差分正演模拟,并以简单层状模型进行了试验。对有限差分中涉及的边界条件、稳定性及频散进行了分析。给出了透明边界、旁轴近似边界和PML边界。对前人得到的几种稳定性条件进行了分析和试算,得到了适于本文的稳定性条件。通过理论推导,对声波有限差分引起频散的几个参数进行了定量分析。
从CRP叠加入手,将射线追踪方法应用于观测系统设计,分析每道覆盖次数,优化观测系统参数。同时,采用照明分析对波动方程在观测系统中的应用进行了探讨。最后对正演软件的研发进行了介绍和应用。
Seismic numerical modeling plays an important role in seismic prospecting. Based on modeling principles, the main methods can be divided into two kinds: ray-tracing method and wave equation method.
Ray-tracing is hard to accomplish for the reflection wave in complex structures with complicated surface. This paper draws some conclusions in the study of trial-and-error method, shortest path ray-tracing method and constant gradient velocity ray-tracing method. Firstly, the propagation directions of transmitted rays and reflective rays are determined and presented, and the trial-and-error method is applied into the models with complex structure and surface. Some digital models show that the algorithm suits complex media and is stable. However, trial-and-error method can hardly work when strong velocity contrast exists, and it is hard to reach the global minimum traveltime point in multiple arrival times. The shortest path ray-tracing method is studied in the paper which aims to solve the problem. Based on the graphic structure and Huygens’Principle, the shortest raypaths and the reflective wave raypaths are calculated, and the precision is analyzed. Example shows that the shortest path ray-tracing method can adapt to strong velocity variation and can get the global minimum traveltimes, but it can only be used for two-point ray-tracing and has a problem of ray bifurcation. Following the basic work of Langan’s constant gradient velocity method, the ray-tracing paths can be derived by solving a set of analytical expressions with a mesh grid method. Combined with Snell’s Law, the reflection wave raypaths are determined. Layer coordinates are needed when calculating the reflection wave raypaths, but the general Layer coordinates description method does not suit complex media with rough surface or reverse faults. In this paper, a linear connection method and segmental architecture description method are put forward to make the description of layer coordinates convenient. And we obtain good results when used in constant velocity gradient method. Unlike the common ray methods, the Gaussian Beams method is valid even in caustic region, critical region, etc. In this paper, the Gaussian Beam method is used in complex media and the model testing results show this method is good.
Ray tracing method can be achieved faster than wave equation method, but it cannot reveal the dynamic characteristics of wavefields. Thus, the staggered-grid high-order finite difference method in inhomogeneous media is studied in this paper, and it is applied to 2-D acoustic wave, visco-acoustic wave, elastic wave and visco-elastic wave in complex media model. The 3-D acoustic wave and elastic wave with the staggered-grid high-order finite difference method is researched and the result is tested with simple layered model. Some key problems including boundary condition, stability and dispersion in finite difference method are analyzed. Transparent boundary, paraxial approximations absorbing boundary and PML absorbing boundary are all presented. Some stable conditions by former scholars are analyzed and re-tested. Also, some parameters which lead to dispersion in acoustic wave finite difference are quantitatively analyzed theoretically.
Based on CRP theory, ray tracing method can be applied to survey geometry design. Through fold number analyzing of every trace, the geometry parameters can be optimized. Meanwhile, illumination analysis is used the use of wave equation in survey geometry design. In the end, a forward modeling software is presented.
射线追踪在复杂地表、复杂构造中的反射波追踪是一个难点。本文通过对试射法、全局最短路径法、常速度梯度法的研究,取得了一定的效果。首先,本文对试射法推导了透射线和反射线的传播方向,并将其应用到起伏地表和复杂构造模型中。模型试算表明,算法稳定,可适应复杂介质模型。然而,试射法无法适应强速度变化、难于求出多值走时中的全局最小走时,为此,研究了全局最短路径法。根据图形理论和惠更斯原理,求得任意点的全局最短路径,同时实现了反射波追踪,并对误差进行了分析,算例分析表明,全局最短路径法能够适应强速度变化,可以求出全局最小走时,但只适合两点射线追踪,且存在射线分叉问题。通过研究常速度梯度法基本原理,采用网格剖分的方法,求解一组射线路径的解析表达式,得到了射线追踪路径,结合斯奈尔定律,实现了反射波射线追踪。计算反射波路径时需要有层位信息,常规的层位结构模型,无法适应界面起伏较大或存在许多逆断层的复杂模型,本文提出一种线性连接法和分段结构模型,使得层位模型的建立简洁方便,并将其应用到常速度梯度法中取得了良好的效果。当模型为复杂介质时,采用普通射线法制作合成地震记录,会存在焦散区、空白区等奇异性区域。本文采用高斯射线束代替普通射线进行正演模拟,克服了普通射线法的缺陷,通过模型试算,证明了方法的正确性,且有较高的精度。
射线追踪计算速度快,但无法很好的反映波场的动力学特征。因此,本文对波动方程正演中的非均匀介质二维声波、粘声波、弹性波以及粘弹性波交错网格高阶有限差分正演模拟进行了研究,并以复杂介质模型进行了试算。探讨了三维声波、弹性波高阶交错网格有限差分正演模拟,并以简单层状模型进行了试验。对有限差分中涉及的边界条件、稳定性及频散进行了分析。给出了透明边界、旁轴近似边界和PML边界。对前人得到的几种稳定性条件进行了分析和试算,得到了适于本文的稳定性条件。通过理论推导,对声波有限差分引起频散的几个参数进行了定量分析。
从CRP叠加入手,将射线追踪方法应用于观测系统设计,分析每道覆盖次数,优化观测系统参数。同时,采用照明分析对波动方程在观测系统中的应用进行了探讨。最后对正演软件的研发进行了介绍和应用。
Seismic numerical modeling plays an important role in seismic prospecting. Based on modeling principles, the main methods can be divided into two kinds: ray-tracing method and wave equation method.
Ray-tracing is hard to accomplish for the reflection wave in complex structures with complicated surface. This paper draws some conclusions in the study of trial-and-error method, shortest path ray-tracing method and constant gradient velocity ray-tracing method. Firstly, the propagation directions of transmitted rays and reflective rays are determined and presented, and the trial-and-error method is applied into the models with complex structure and surface. Some digital models show that the algorithm suits complex media and is stable. However, trial-and-error method can hardly work when strong velocity contrast exists, and it is hard to reach the global minimum traveltime point in multiple arrival times. The shortest path ray-tracing method is studied in the paper which aims to solve the problem. Based on the graphic structure and Huygens’Principle, the shortest raypaths and the reflective wave raypaths are calculated, and the precision is analyzed. Example shows that the shortest path ray-tracing method can adapt to strong velocity variation and can get the global minimum traveltimes, but it can only be used for two-point ray-tracing and has a problem of ray bifurcation. Following the basic work of Langan’s constant gradient velocity method, the ray-tracing paths can be derived by solving a set of analytical expressions with a mesh grid method. Combined with Snell’s Law, the reflection wave raypaths are determined. Layer coordinates are needed when calculating the reflection wave raypaths, but the general Layer coordinates description method does not suit complex media with rough surface or reverse faults. In this paper, a linear connection method and segmental architecture description method are put forward to make the description of layer coordinates convenient. And we obtain good results when used in constant velocity gradient method. Unlike the common ray methods, the Gaussian Beams method is valid even in caustic region, critical region, etc. In this paper, the Gaussian Beam method is used in complex media and the model testing results show this method is good.
Ray tracing method can be achieved faster than wave equation method, but it cannot reveal the dynamic characteristics of wavefields. Thus, the staggered-grid high-order finite difference method in inhomogeneous media is studied in this paper, and it is applied to 2-D acoustic wave, visco-acoustic wave, elastic wave and visco-elastic wave in complex media model. The 3-D acoustic wave and elastic wave with the staggered-grid high-order finite difference method is researched and the result is tested with simple layered model. Some key problems including boundary condition, stability and dispersion in finite difference method are analyzed. Transparent boundary, paraxial approximations absorbing boundary and PML absorbing boundary are all presented. Some stable conditions by former scholars are analyzed and re-tested. Also, some parameters which lead to dispersion in acoustic wave finite difference are quantitatively analyzed theoretically.
Based on CRP theory, ray tracing method can be applied to survey geometry design. Through fold number analyzing of every trace, the geometry parameters can be optimized. Meanwhile, illumination analysis is used the use of wave equation in survey geometry design. In the end, a forward modeling software is presented.
引文
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[2] Julian B R and Gubbins D. Three dimensional seismic ray tracing. J Geophys, 1977, 43:95~114
[3] Pereyra V, Lee W H K and Keller H B. Solving two point seismic ray tracing problems in a heterogeneous medium, PartⅠ: A general adaptive finite difference method. Bull Seis Soc Am, 1980,70:79~99
[4] Um J and Thurber C H. A fast algorithm for tow point seismic ray tracing. Bull Seis Soc Am, 1987,77:972~986
[5] Farra V, Virieux J and Madariaga R. Ray perturbation theory for interfaces. Geophys J Int, 1989,99:377~390
[6] Sambridge M S and Kennett B L N. Boundary value ray tracing in heterogeneous medium: a simple and versatile algorithm. Geophys J Int, 1990, 101: 157~168
[7]蒋先艺,刘贤功,宋葵.复杂构造模型正演模拟.石油工业出版社. 2004, 12
[8]刘学才.地震射线法正演与反演.成都理工大学博士论文. 1991: 4~10.
[9] Vidale, J. E. Finite-difference calculation of travel times, Bull.. Seis. Soc. Am. ,1988, 78, 2062~2076
[10] Podvin, P., andd Lecomte, I., Finite difference computation of travel times in very contrasted velocity model: a massively parallel approach and its associated tools, Geophysics., 1991,105, 271~284
[11] Qin, F., Olsen., K., Luo, Y., and Schuster, G. T., Finite-dlifference solution of the eikonal equation along expanding wavefronts, Geophysics, 1992, 57, 478~487
[12]张霖斌,姚振兴,纪晨.地震初至波走时的有限差分计算.地球物理学进展. 1996, 11, 47~52
[13] Van Trier, J., and Symes, W. W.,Upwind finite-difference calculation of traveltimes, Geophysics, 1991, 56, 812~821
[14] Symes, W. W., A slowness matching finite difference method for traveltimes beyond transmission caustics, 68 Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded abstracts. 1998, 1945~1948
[15] Cassell, B. R., A method for calculating synthetic seismograms in laterally varying media, Geophys. J. R. Astron. Soc., 1982, 69, 339~354
[16] Langan R T, Lerche I and Cutler R I. Tracing of rays through heterogeneous media:an accurate and efficient procedure. Geophysics, 1985, 50(9):1456~1465
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