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A rotated staggered grid finite-difference with the absorbing boundary condition of a perfectly matched layer

机译：具有完全匹配层的吸收边界条件的旋转交错网格的有限差分

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摘要

A rotated staggered grid finite-difference (FD) method with a perfectly matched layer (PML) method is proposed for numerically solving elastic wave equations in inhomogeneous elastic and poroelastic media. Compared with a standard staggered-grid FD, the former has the advantage over the latter in that its physical variables need only to be defined at two locations. In the rotated staggered grid, stress and strain components (or particle velocity and displacement components) are defined at elementary cell centers, and the velocity or displacement components (or the stress and strain components) are defined at vertexes. In this way, no elastic moduli need to be interpolated or averaged. Numerical results from the proposed method have been compared with the standard staggered FD method. The results are in good agreement with each other. Our numerical results show that the proposed algorithm can handle much stronger impedance contrast. This is especially true when simulating fractured medium filled with fluids such as water or gas without giving special treatment. On the other hand, the implemented PML absorbing boundary condition works well in efficiently reducing reflected waves from the artificial interfaces. It generates almost no reflection at artificial interfaces with a boundary of PML thickness of half a wavelength. Our theoretical analysis and numerical tests proved that the PML absorbing algorithm in the rotated staggered grid is almost identical to those in the standard staggered grid. In this paper, we also presented all of the formulations of the PML implementation and modeling examples in elastic, poroelastic, and anisotropic media.
机译：提出了一种具有完美匹配层（PML）方法的旋转交错网格有限差分（FD）方法，用于数值求解非均匀弹性和多孔弹性介质中的弹性波动方程。与标准交错网格FD相比，前者具有优于后者的优势，因为其物理变量仅需要在两个位置定义。在旋转的交错网格中，应力和应变分量（或粒子速度和位移分量）定义在基本单元中心，而速度或位移分量（或应力和应变分量）定义在顶点处。这样，不需要内插或求平均弹性模量。所提出的方法的数值结果已经与标准的交错FD方法进行了比较。结果彼此吻合良好。我们的数值结果表明，该算法可以处理更强的阻抗对比。当模拟充有水或气体等流体的压裂介质而未进行特殊处理时，尤其如此。另一方面，已实现的PML吸收边界条件在有效减少来自人工界面的反射波方面效果很好。在具有半个波长的PML厚度边界的人造界面上，它几乎不产生反射。我们的理论分析和数值测试证明，旋转交错网格中的PML吸收算法与标准交错网格中的PML吸收算法几乎相同。在本文中，我们还介绍了在弹性，多孔弹性和各向异性介质中PML实现的所有公式和建模示例。

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