Applications of a Precise Integration Method In Forward Seismic Modeling
Applications of a Precise Integration Method In Forward Seismic Modeling
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DOI：
10.1190/1.2792909
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
G. Tang;T. Hu;Jinhua Yang
中科院分区：
文献类型：
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作者：
G. Tang;T. Hu;Jinhua Yang
地震正演模拟是模拟西北地区近地表低速带和深部精细构造响应的有效工具。地震正演模拟的主要目标是精确求解波动方程。有限差分法是求解该方程的一种常用的数值方法。如果网格配置适当，高阶差分格式可以获得很高的精度。然而，它的数值色散和稳定性的标准也是非常严格的。为了解决这些问题，本文提出了一种新的精细积分方法，它采用时间域积分格式而不是传统的低阶差分格式。精细积分法在空间域中采用差分近似，将声波或弹性波方程转换成一组关于时间的微分方程，然后使用积分法求解该方程系统。最终的解决方案是由于一个指数函数矩阵的集成。理论上，该解决方案在时间域中是准确的，因此提高了总准确度。考虑到计算机的容量和速度，将整个空间域划分为若干个子域，然后将解组合在一起。文中的试验表明，这种改进的子域精细积分法比有限差分法更稳定、更精确。此外，它可以大大减少数值色散与FDM相同的网格配置，但它可能会花费更多的CPU时间。最后通过数值试验验证了该方法的有效性，并给出了应用实例，表明该方法在地球物理勘探领域具有潜在的应用价值。
Forward seismic modeling is a useful tool for simulating the response of the low velocity zones near the ground surface and delicate structures at a deeper depth in northwestern China. The main objective of forward seismic modeling is to solve the wave equation accurately. The finite difference method (FDM) is a commonly used numerical method for solving the equation. It can obtain very high accuracy with high-order difference scheme if the grid configuration is appropriate. However it shows numerical dispersion and its stability criteria is also very strict. In order to deal with these problems, a new precise integration method is advanced in this paper, using an integration scheme in the temporal domain rather than a traditional low-order difference scheme. The precise integration method employs a difference approximation in the spatial domain, converting the acoustic or elastic wave equation into a set of differential equations with respect to time and then solves this equation system using an integration method. The final solution is attributed to an integration of a matrix of exponential functions. Theoretically this solution is accurate in the temporal domain, hence increasing the total accuracy. The whole spatial domain can be divided into several sub-domains, considering computer capacity and speed and then the solutions put together. This revised sub-domain precise integration method (SPIM) is more stable than the FDM and more accurate as is tested in the text. Besides it can greatly reduce the numerical dispersion with the same grid configuration as the FDM, though it may take a little more CPU time. A numerical test is presented to justify this method and then an application is shown to indicate that the SPIM is of potential value in the geophysical exploration field.