Generalized transfer matrix method for propagation of surface waves in layered azimuthally anisotropic half-space
Generalized transfer matrix method for propagation of surface waves in layered azimuthally anisotropic half-space
复制标题
层状方位各向异性半空间中表面波传播的广义传递矩阵法
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Yunling Duan
中科院分区：
文献类型：
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作者：
Tianyun Liu;Chong;Yunling Duan
摘要
本文提出了一种系统有效的方法，即广义传递矩阵法，用于评估多层方位各向异性半空间中表面波的色散曲线和本征函数。除了避免与现有 Thomson-Haskell 方法相关的众所周知的数值困难外，广义传递矩阵方法还具有通过使用奇异值分解（SVD）方法稳健地确定独立偏振矢量、无需任何数值反演即可显式求逆 6 × 6 特征列矩阵以及有效计算层状方位各向异性介质特征函数的能力。通过直接变换，广义传递矩阵方法产生双重递归算法：（1）对于相速度的递归计算，它从下半空间开始到顶层；（2）对于特征函数的递归求解，它从顶层到下半空间开始。广义传递矩阵法在保持Thomson-Haskell传递矩阵法的简单性的同时，具有无条件稳定性和计算效率。相关数值算例表明，广义传递矩阵方法是模拟层状方位各向异性半空间中弹性表面波传播的强大而鲁棒的工具。
SUMMARY
This paper presents a systematic and efficient method, namely the generalized transfer matrix method, for evaluating the dispersion curves and eigenfunctions of surface waves in multilayered azimuthally anisotropic half-space. Apart from avoiding the well-known numerical difficulties associated with the existing Thomson–Haskell method, the generalized transfer matrix method possesses the robust determination of independent polarization vectors by using the singular value decomposition (SVD) approach, the explicit inversion of the 6 × 6 eigencolumn matrix without any resort to numerical inversion and the efficient computation of eigenfunctions for layered azimuthally anisotropic media. By means of straightforward transformations, the generalized transfer matrix method leads to a twofold recursive algorithm: (1) for the recursive computation of phase velocities it starts from the bottom half-space to the top layer and (2) for the recursive solution of eigenfunctions it starts from the top layer to the bottom half-space. While keeping the simplicity of the Thomson–Haskell transfer matrix method, the generalized transfer matrix method is of unconditional stability and computational efficiency. The related numerical examples demonstrate that the generalized transfer matrix method is a powerful and robust tool for simulating the propagation of elastic surface waves in the layered azimuthally anisotropic half-space.