In this paper, we propose a smoothing scheme for seismic wave propagation simulation. The proposed scheme is based on a diffusionized wave equation with the fourth-order spatial derivative term. So, the solution requires higher regularity in the usual weak formulation. Reducing the diffusionized wave equation to a coupled system of diffusion equations yields a mixed FEM to ease the regularity. We mathematically explain how our scheme works for smoothing. We construct a semi-implicit time integration scheme and apply it to the wave equation. This numerical experiment reveals that our scheme is effective for filtering short wavelength components in seismic wave propagation simulation.

中文翻译：

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一种用扩散波方程混合有限元模拟地震波传播的平滑方案

在本文中，我们提出了一种用于地震波传播模拟的平滑方案。所提出的方案基于具有四阶空间导数项的扩散波动方程。因此，该解决方案在通常的弱公式中需要更高的规律性。将扩散波动方程简化为扩散方程的耦合系统会产生混合 FEM 以缓解规律性。我们在数学上解释了我们的方案如何用于平滑。我们构建了一个半隐式时间积分方案并将其应用于波动方程。该数值实验表明，我们的方案对于在地震波传播模拟中过滤短波长分量是有效的。