内部复杂速度界面处理对有限差分地震波模拟准确性影响研究

发布时间：2018-03-09 05:24

本文选题：有限差分　切入点：高阶交错网格　出处：《中国科学技术大学》2017年硕士论文　论文类型：学位论文

【摘要】：有限差分算法是地震波场数值模拟中的重要工具,其具有实现简单、计算效率高、对内存需求小等特点,在天然地震与勘探地球物理领域中得到了广泛的应用。随着地球科学的进一步发展,研究模型变得更加复杂与庞大,因此需要更高效的正演算法。使用高阶交错网格格式可以在使用较粗网格的情况下,有效的压制色散误差,进而降低计算内存需求节省计算资源。但是,较大的网格步长会造成有限差分网格对复杂内部界面的表征误差增大。实际的地震模型中存在着大量的弹性系数间断界面,因为网格离散介质的局限性,很难在算法中准确地满足内部界面边界条件。尤其在高阶格式的情况下,由于使用了同低阶格式相比更大的空间步长,因此这种问题会更加严重。本文使用高阶交错网格有限差分算法分别讨论了处理介质间断面的不同方法,并分析了界面误差的数值特征,为高精度的地震波数值模拟提供了计算参数的选择依据。本文第一部分,大致介绍了有限差分正演算法的基本情况,并对高阶交错网格与有限差分界面误差研究现状做了简短的总结。第二部分,主要描述波动方程有限差分正演的基本实现,包括网格布局、高阶格式、震源与边界条件处理。第三部分引入内部界面边界条件,显式地分析了有限差分的界面数值误差,同时说明了目前常用的四种介质参数取值方法:直接取值法、格点平均法、体积分平均法、正交各向异性介质法。在第四部分,通过数值实验,分别展示了不同介质处理方法的震相对比,与界面误差受不同因素的变化特征。最后,通过总结分析上述的误差特征,给出高阶交错网格有限差分在实际正演计算中的网格参数选择建议。
[Abstract]:The finite difference algorithm is an important tool in the numerical simulation of seismic wave field. It has the advantages of simple implementation, high computational efficiency and low memory requirement. It has been widely used in the field of natural earthquake and exploration geophysics. With the further development of geoscience, the research model becomes more complex and huge. Therefore, a more efficient forward algorithm is needed. Using higher-order interleaved grid schemes can effectively suppress dispersion errors in the case of coarse grids, thereby reducing the computational memory requirements and saving computing resources. The larger step size of the mesh will cause the finite difference mesh to increase the representation error of the complex internal interface. There are a large number of elastic coefficient discontinuous interfaces in the actual seismic model because of the limitation of the grid discrete medium. It is difficult to satisfy the boundary condition of internal interface accurately in the algorithm, especially in the case of high order scheme, because the space step size is larger than that of lower order scheme. Therefore, this problem will be more serious. In this paper, the different methods of dealing with dielectric discontinuity are discussed by using the high order staggered grid finite difference algorithm, and the numerical characteristics of the interface errors are analyzed. This paper provides a basis for the selection of calculation parameters for high precision seismic wave numerical simulation. In the first part of this paper, the basic situation of the finite difference forward algorithm is introduced. In the second part, the basic realization of finite difference forward modeling of wave equation is described, including grid layout, high order scheme, and so on. In the third part, the interface numerical error of finite difference is analyzed explicitly by introducing the boundary condition of internal interface. At the same time, four commonly used methods for determining the parameters of medium are described: direct method, lattice average method, and so on. The volume average method and the orthotropic medium method. In part 4th, the seismic characteristics of different medium processing methods are shown by numerical experiments, and the interface errors are changed by different factors. By summing up and analyzing the above error characteristics, the paper gives some suggestions on the selection of grid parameters in the actual forward calculation of high order staggered grid finite difference.
【学位授予单位】：中国科学技术大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P631.4;P315.8

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