A staggered-grid finite-difference approach based on generally orthogonal curvilinear coordinate system was performed to simulate seismic waves including topographic surface in order to solve the problems when dealing with free surface boundary conditions: complex coordinate rotations and interpolations in conventional finite-difference methods and artifacts caused by staircase approximation to irregular free surface. The physical domain under study was discretized by orthogonal boundary-conforming curvilinear grids, which were then mapped onto regularly rectangular grids in computational domain. The first order elastic velocity-stress equations and free surface boundary conditions were solved in computational domain. The algorithm can not only avoid artifacts caused by staircase approximation to irregular free surface, but also make free surface boundary conditions simple and direct to implement. Numerical results show that the method is feasible and can be applied to the study of seismic wave propagation with topographic surface.%为了解决常规有限差分法在处理起伏地表自由边界条件时存在的需进行复杂坐标旋转和插值运算,以及对起伏地表进行阶梯状离散近似所产生的虚假绕射波等问题,把待求解的物理域离散成贴体正交曲线网格,将该网格映射到计算域的矩形规则网格上,在该计算域内求解一阶弹性波速度-应力方程及相应的自由边界条件,实现了广义正交曲线坐标系下的起伏地表地震波数值模拟问题.该算法简化了自由边界条件的实施,避免了因起伏地表阶梯化网格离散近似所产生的虚假波.数值模拟结果表明,该方法是可行的,可以用于起伏地表条件下地震波传播规律的研究.
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