本文關鍵詞： 曲線坐標 貼體網格 有限差分 各向異性介質 固體-液體耦合介質　出處：《中國科學技術大學》2017年博士論文　論文類型：學位論文

【摘要】：在地震學和與它的相關領域中,有限差分方法是一種重要的模擬地震波在復雜介質中傳播的數(shù)值計算方法;它具有簡單直接計算效率高等優(yōu)點,已經被廣泛地應用于地震勘探、強地面運動預測、全波形反演、地震各向異性介質的研究、合成理論地震圖等方面。傳統(tǒng)的有限差分方法采用矩形網格離散計算區(qū)域,并且使用臺階近似的方法來描述復雜的地形;這種對地形的近似既降低了差分方法實施邊界條件的精度又會讓它在計算中產生虛假的散射波,從而不能正確地計算地形對地震波傳播的影響;雖然對它改進的方法在不斷地被提出,但是這些方法的適用性還有待深入地研究。本文所研究的曲線網格有限差分方法采用貼體網格描述復雜地形;這種離散地形的方法不僅可以讓有限差分方法避免因為臺階近似所導致的虛假散射波,而且還可以方便它準確地實施自由表面邊界條件,從而正確地計算出復雜地形對地震波傳播的影響。地震波傳播過程的數(shù)值模擬是研究地震波在各向異性介質中傳播規(guī)律的重要手段,對地震勘探和天然地震的研究有著重要的意義。傳統(tǒng)的有限差分方法采用交錯網格中心差分格式;這種方法雖然可以高效率地計算出地震波在各向同性介質中的傳播過程,但是當任意各向異性介質出現(xiàn)在計算區(qū)域時,它需要對各向異性介質中的地震波場分量進行插值從而導致很大的計算誤差。本文所研究的曲線網格有限差分方法采用同位網格DRP/opt MacCormack差分格式;這種方法不僅可以避免傳統(tǒng)有限差分方法對各向異性中的地震波場分量的插值所導致的近似,而且還可以結合貼體網格技術和牽引力鏡像技術處理復雜地形,從而正確地計算出地震波在任意各向異性介質中的傳播過程以及地形對各向異性介質中地震波傳播的影響。準確地模擬地震波通過固體-液體界面的物理過程對于研究海洋中的T震相和斯通利波、海底地形對地震波的散射作用以及解釋海底地震儀記錄的振動數(shù)據(jù)等具有重要的意義。傳統(tǒng)的有限差分方法對復雜的幾何形狀的固體-液體界面的離散和固體-液體邊界條件的實施都做了相當程度的近似,不能準確地模擬起伏的固體-液體界面對地震波傳播的影響。本文所研究的曲線網格有限差分方法可以準確地描述固體-液體界面的復雜幾何形狀,更加準確直接地實施邊界條件,為研究復雜幾何形狀的固體-液體界面對地震波傳播的影響提供了一種更加可靠的計算工具。本文將集成了貼體網格、同位網格DRP/opt MacCormack差分格式和牽引力鏡像等技術的曲線網格有限差分方法分別推廣到了二維和三維情況下含有復雜地形的各向異性介質和含有復雜固體-液體界面形狀的固體-液體耦合介質的地震波傳播計算問題中,并且將曲線網格有限差分方法計算的結果分別同廣義反射/透射系數(shù)方法和譜元方法計算的結果進行了對比驗證。驗證結果表明,本文所研究的曲線網格有限差分方法可以正確并且有效地應用于上述地震波傳播問題。
[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.

【學位授予單位】：中國科學技術大學
【學位級別】：博士
【學位授予年份】：2017
【分類號】：P631.4

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本文編號：1472043