We develop a compact fourth-order scheme for the three-dimensional elastic wave equation in frequency space, using the first-order velocity-stress formulation. The scheme is implemented numerically for homogeneous media on a staggered grid, and both the acoustic and elastic cases are considered. We use a one-directional point source of impact, for which Pilant developed a closed solution. Numerical results for the acoustic and the elastic cases compare favorably with the analytic solutions and show a very significant improvement over the second-order scheme.

中文翻译：

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使用一阶公式的紧凑三维四阶弹性方案

我们使用一阶速度-应力公式为频率空间中的三维弹性波方程开发了一个紧凑的四阶格式。该方案是针对交错网格上的均质介质在数值上实现的，并且考虑了声学和弹性情况。我们使用单向点冲击源，为此 Pilant 开发了一种封闭式解决方案。声学和弹性情况的数值结果与解析解相比具有优势，并且比二阶方案有非常显着的改进。