导　　师： 唐湘蓉;贺振华

学科专业： 070801

授予学位： 硕士

作　　者： ;

机构地区： 成都理工大学

摘　　要： 波动方程叠前深度偏移技术是解决复杂构造和速度横向变化剧烈地区的地震资料成像问题的理想技术，可为复杂地区的高精度构造解释和地质解释提供可靠保证。 传统的偏移方法是基于单程波方程理论，按照深度方向进行延拓的。而逆时偏移/(RTM/)则是在时间方向上实现外推的，而且基于双程波波动方程理论。由于使用双程波波动方程，使得地震波可以在介质中沿各个方向传播，从而不受介质倾角、构造复杂、横向和纵向速度变化大的模型限制，可以处理介质的横向和纵向变速、棱柱波、回转波以及多次波等，从而使得垂直断面、盐丘空腔内幕等复杂构造成像效果均有显著提高，这也是基于单程波波动方程偏移方法难以做到的。 本文实现了频率波数域单程波波动方程和基于有限差分法的双程波波动方程正演和偏移，完成了理论模型的数值模拟实验。在单程波的数值模拟中，分别实现了叠后、叠前偏移。在双程波数值模拟方面，实现了互相关、激发时间两种成像条件下的叠前逆时偏移。 在基于有限差分法正演和偏移算法中，为了压制数值频散，本文提出了一种优化后的声波波动方程，该方程不仅具有低复杂性和低计算成本的优点，而且采用有限差分法求数值解时，数值频散现象相对于标准的声波方程有明显的改善。二维理论模型的数值实验表明，优化后的波动方程不仅极大地提高了图像质量，而且只增加了可忽略不计的计算成本。 针对有限差分法的边界条件问题，本文也进行了一定的分析研究。分别实现了Reynolds边界条件、完全匹配层/(PML/)吸收边界条件和随机边界条件的数值模拟，并对PML边界条件和Reynolds边界条件进行了比较。 文章的最后部分，讨论了一维黏滞弥散系数波动方程，对黏滞系数和弥散系数分别进行了数值模拟实验，分析研究它们对地震波在传播过程中的影响。并把黏滞弥散系数波动方程扩展到了二维，并实现了低伴阴影的二维数值模拟。 Wave equation pre-stack depth migration is an ideal seismic data imagingtechnique for the area where there occur very complicated geologies structure and severlateral velocity variation. The traditional migration methods are calculated by the depth extrapolation, andthe wave theory is based on one-way wave equation; Reverse time migration/(RTM/) isextrapolated on the timeline, and the wave theory is based on two-way wave equation.The use of two-way wave equation, which allows wave propagation along eachdirection, so the media angle is not restricted and it can be used in any model of speedchanging. RTM can handle the model such as vertical and horizontal velocity changing,prismatic wave, turning wave multiples, etc. and the imaging result of complexstructural is improved obviously, which the tradition one-way wave methods can notachieve. This article firstly accomplishes the forward and migration algorithms which usedone-way equation based on frequency wavenumber domain and used two-way equationbased on finite difference method, and we have finished the numerical experiments oftheoretical model for every method. We achieve both of the stack migration and thepre-stack migration in one-way numerical simulation and the pre-stack reverse timemigration in two-way simulate experiments with two different methods. In order to attenuate numerical dispersion in forward and migration simulationwhich are based on finite difference methods, we propose an optimized acoustic waveequation, and which are less complicate, require low calculate cost and shows a betterdispersion attenuation. The results of two dimensional numerical simulation oftheoretical model shows that, the optimized equation do enhanced the quality of imageand require only some supportable calculation. We have also done some research on boundary conditions which is based on finitedifference method. And we finished the numerical simulation of Reynolds boundarycondition, Perfectly Matched Layer/(PML/) boundary and random boundary and havecompared the effect of PML boundary with the Reynolds boundary. This article discusses the one dimension viscous and diffusive wave equation, andstudies the viscous factor and diffusion factor affect in the wave propagation bynumeral simulation in the end of. We expand the viscous and diffusive equation fromone dimension to two dimension, and simulate the low frequency showdownsuccessfully.

关 键 词： 有限差分法 单程波 双程波 频散 逆时偏移

分 类 号： [P631.4]

领　　域： [天文地球] [天文地球]