三维非均匀介质中弹性波传播的数值模拟

提出了一种三维非均匀介质中弹性波传播数值模拟的方法，文中称为三维格子法。该算法是二维格子法（一种二维非均匀介质中P－SV波传播的数值模拟算法）向三维非均匀介质情况的推广。在空间离散上该文方法与有限元方法类似，容许根据连续体的形状和介质分界面任意剖面网格，且自然满足自由表面边界条件。不同于常规有限差分法在各个节点上满足动力学微分方程，该算法通过满足各节点周围格子的整体平衡（积分平衡方程）来对问题进行求解，三维格子法所需的计算机内存及计算耗时与同阶精度的规则网格有限差分法相当。算例表明，该文提出的三维格子法具有较高的精度且可很好地模拟三维复杂形状地表对弹性波的反射和绕射。

NUMERICAL SIMULATION OF ELASTIC WAVE PROPAGATION IN 3-D HETEROGENEOUS MEDIA

A new numerical simulation method-3 D grid method-for elastic wave propagation in 3 D heterogeneous media is given. 3 D grid method is the extension of the 2 D grid method that models P SV wave propagation in 2 D heterogeneous media. The space mesh discretization of this method is similar to the finite element method, so the method is flexible to deal with arbitrary surface topography and curved interfaces. The method satisfies the free surface boundary conditions of 3 D topography naturally. The algorithm does not use elastodynamic differential equations at each node as in the conventional finite difference method. It uses integral equilibrium equations around each node. The computational cost and memory requirements for the scheme are nearly the same as those used by the same order finite difference method. Examples show that the algorithm possesses high accuracy and good adaptability for the 3 D elastic wave modeling with surface topography.