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无限域中的波动方程数值模拟往往需要稳定有效的吸收边界来消除人为边界截断所引起的虚假反射。本文首先写出了全匹配层(PML)内SH波的波动方程推导结果,并给出了方程的Crank-Nicolson计算格式与其中空间导数2阶,6阶,10阶精度的有限差分算法以及伪谱法算法。然后设计了均匀各向同性介质模型和分层溶洞模型并引入图像处理中的信噪比(SNR)概念来定量研究边界吸收效果同PML宽度、不同精度算法的关系。数值结果表明当匹配层宽度比较薄时可以用低精度的有限差格式来获得比较好的吸收效果,当匹配层比较宽时,采用高精度的算法可以获得很好的吸收效果。最后对“反射系数”进行了讨论,指出“反射系数”的不足和文中用SNR来定量衡量吸收边界。
Numerical simulation of wave equation in infinite domain often requires a stable and effective absorption boundary to eliminate the false reflections caused by artificial boundary truncation. In this paper, firstly, the derivation of the wave equation of SH wave in the PML is given and the finite difference algorithm of the Crank-Nicolson scheme and the second, sixth and tenth orders of the spatial derivatives are given. Spectrum algorithm. Then we design the homogeneous isotropic medium model and layered karst model and introduce the concept of signal-to-noise ratio (SNR) in image processing to quantitatively study the relationship between the boundary absorption effect and PML width and different accuracy algorithms. The numerical results show that when the matching layer width is thinner, the finite difference scheme with low accuracy can obtain the better absorption effect. When the matching layer is wider, the high-precision algorithm can obtain good absorption effect. Finally, we discuss the “reflection coefficient” and point out the shortcomings of “reflection coefficient” and the quantitative measurement of absorption boundary by SNR.