非均匀介质弹性波动方程的不规则网格有限差分方法

从弹性波动方程出发，提出了一种新的空间不规则网格有限差分方法，并用于求解非均匀各向异性介质中的弹性波正演问题。这种方法简单易行，对于复杂几何结构，例如低速层、套管井和非平面界面等，在较细的不规则网格上进行离散，计算时间和占用内存更少。与多重网格差分方法相比，该方法不需要粗、细网格之间的插值，所有网格差分计算在同一次空间迭代中完成。具有复杂几何交界面的模型计算，包括地下透镜体、套管井眼等，在确定弹性常数和密度后，用不规则网格的差分方法更易实现。该方法使用了Higdon吸收边界条件解决人工边界反射问题，引入了新的稳定性条件和网格频散条件，很好地消除了非物理散射波。理论模型的效值计算表明，该方法具有良好的稳定性和计算精度，在模拟非均匀介质弹性波传播时，比相同精度的规则网格有限差分方法计算速度更快。该方法易于推广到非结构网格和三维问题中。

Finite difference method of irregular grid for elastic wave equation in heterogeneous media

This paper presents a new finite-difference (FD) method for spatiall irregular grids to simulate elastic wave propagation in heterogeneous anisotropic media. It is very simple and costs less computing time. Complicated geometrical structures such as low-velocity thin layers, cased borehole and nonplanar interfaces are treated on a fine irregular grid. Unlike multi-grid scheme, this method has no interpolation between the fine and coarse grid and all grids are computed at the same spatial iteration. Models with complex geometrical interfaces, including underground lens structure and cased borehole, are treated in a way similar to regular grid points but with different elastic parameters and density. The Higdon's absorbing boundary condition is adopted to eliminate boundary reflections. Numerical simulations show that this method has satisfactory stability and accuracy. It is more efficient in simulating wave propagation in heterogeneous anisotropic media than conventional method using regular rectangular grid of equal accuracy. The method can be easily extended to unstructural grid and three dimensional problems.