曲线风格有限差分模拟地震波在各向异性介质和固—液耦合介质中的传播

发布时间：2018-01-29 00:55

本文关键词： 曲线坐标贴体网格有限差分各向异性介质固体-液体耦合介质　出处：《中国科学技术大学》2017年博士论文　论文类型：学位论文

【摘要】：在地震学和与它的相关领域中,有限差分方法是一种重要的模拟地震波在复杂介质中传播的数值计算方法;它具有简单直接计算效率高等优点,已经被广泛地应用于地震勘探、强地面运动预测、全波形反演、地震各向异性介质的研究、合成理论地震图等方面。传统的有限差分方法采用矩形网格离散计算区域,并且使用台阶近似的方法来描述复杂的地形;这种对地形的近似既降低了差分方法实施边界条件的精度又会让它在计算中产生虚假的散射波,从而不能正确地计算地形对地震波传播的影响;虽然对它改进的方法在不断地被提出,但是这些方法的适用性还有待深入地研究。本文所研究的曲线网格有限差分方法采用贴体网格描述复杂地形;这种离散地形的方法不仅可以让有限差分方法避免因为台阶近似所导致的虚假散射波,而且还可以方便它准确地实施自由表面边界条件,从而正确地计算出复杂地形对地震波传播的影响。地震波传播过程的数值模拟是研究地震波在各向异性介质中传播规律的重要手段,对地震勘探和天然地震的研究有着重要的意义。传统的有限差分方法采用交错网格中心差分格式;这种方法虽然可以高效率地计算出地震波在各向同性介质中的传播过程,但是当任意各向异性介质出现在计算区域时,它需要对各向异性介质中的地震波场分量进行插值从而导致很大的计算误差。本文所研究的曲线网格有限差分方法采用同位网格DRP/opt MacCormack差分格式;这种方法不仅可以避免传统有限差分方法对各向异性中的地震波场分量的插值所导致的近似,而且还可以结合贴体网格技术和牵引力镜像技术处理复杂地形,从而正确地计算出地震波在任意各向异性介质中的传播过程以及地形对各向异性介质中地震波传播的影响。准确地模拟地震波通过固体-液体界面的物理过程对于研究海洋中的T震相和斯通利波、海底地形对地震波的散射作用以及解释海底地震仪记录的振动数据等具有重要的意义。传统的有限差分方法对复杂的几何形状的固体-液体界面的离散和固体-液体边界条件的实施都做了相当程度的近似,不能准确地模拟起伏的固体-液体界面对地震波传播的影响。本文所研究的曲线网格有限差分方法可以准确地描述固体-液体界面的复杂几何形状,更加准确直接地实施边界条件,为研究复杂几何形状的固体-液体界面对地震波传播的影响提供了一种更加可靠的计算工具。本文将集成了贴体网格、同位网格DRP/opt MacCormack差分格式和牵引力镜像等技术的曲线网格有限差分方法分别推广到了二维和三维情况下含有复杂地形的各向异性介质和含有复杂固体-液体界面形状的固体-液体耦合介质的地震波传播计算问题中,并且将曲线网格有限差分方法计算的结果分别同广义反射/透射系数方法和谱元方法计算的结果进行了对比验证。验证结果表明,本文所研究的曲线网格有限差分方法可以正确并且有效地应用于上述地震波传播问题。
[Abstract]:In the field of seismology and with it, the finite difference method is a calculation method for simulation of seismic wave propagation in complex media is important in numerical; it has simple calculation and high efficiency, has been widely used in seismic exploration and prediction of strong ground motion, full waveform inversion, seismic anisotropy the synthetic seismogram. The traditional finite difference method using rectangular grid discrete computational domain, and use the method of step approximation to describe the complex topography of the terrain; the approximate difference method not only reduces the accuracy of the boundary condition and the implementation will allow it to produce a false scattering wave in the calculation, thus could not correctly calculate topographic effects on seismic wave propagation; although the method is put forward to improve it constantly, but the applicability of these methods still need further study in this research. The curvilinear grid finite difference method is used to describe the complex terrain grid; this method of discrete terrain can not only make the finite difference method to approximate the steps to avoid because of the false scattering wave, but also it can easily and accurately implement the free surface boundary conditions, so as to correctly calculate complex topographic effects on seismic wave propagation the process of seismic wave propagation. Numerical simulation is an important method for studying seismic wave propagation in anisotropic media, it is very important to study the seismic exploration and natural earthquake. The traditional finite difference method on a staggered grid center difference scheme; although this method can efficiently calculate the propagation of seismic waves in in isotropic media, but when arbitrary anisotropic media appear in the computational domain, it takes on seismic wave field in anisotropic medium. The amount of interpolation leads to large calculation error. This paper studies the curvilinear grid finite difference method with collocated grid DRP/opt MacCormack difference scheme; this method can not only avoid the traditional finite difference method to approximate the result of anisotropic seismic wave field in component interpolation, but also can be combined with grid technology and traction mirror technology to deal with complex terrain, so as to correctly calculate the process of seismic wave propagation in arbitrary anisotropic medium and the topographic effects on seismic wave propagation in anisotropic medium. Accurately simulating seismic wave through the solid - liquid interface for the study of physical processes in the ocean T phase and Stone wave, has an important the significance of seabed terrain scattering effect on seismic wave and ocean bottom seismometers recorded vibration data. The traditional finite difference method for complex The geometry of the solid - liquid interface and discrete solid liquid boundary conditions are done with a considerable degree of approximation, cannot accurately simulate the effect of solid - liquid interface on the ups and downs of the seismic wave propagation. The curvilinear grid finite difference method can accurately describe the complex geometry of the solid - liquid interface. A more direct implementation of boundary conditions, and provides a more reliable computational tool for studying the complex geometry of the solid - liquid interface effect on seismic wave propagation. This paper will integrate body fitted grid parity grid DRP/opt MacCormack difference scheme and traction image technology of curvilinear grid finite difference method are extended to in the case of two-dimensional and three-dimensional complex terrain and complex anisotropic medium containing solid - liquid interface shape of solid liquid coupling medium. The calculation of the seismic wave propagation, and the curve of grid finite difference calculation results respectively with generalized reflection / transmission coefficient method and spectral element method calculation results have been verified. The verification results show that the curve grid finite difference method can correctly and effectively applied to the problem of seismic wave propagation.

【学位授予单位】：中国科学技术大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：P631.4

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