Department of Mechanical Engineering, University College London, London, WC1E 7JE, United Kingdom.
J Acoust Soc Am. 2012 Sep;132(3):1271-83. doi: 10.1121/1.4730897.
A pseudospectral model of linear elastic wave propagation is described based on the first order stress-velocity equations of elastodynamics. k-space adjustments to the spectral gradient calculations are derived from the dyadic Green's function solution to the second-order elastic wave equation and used to (a) ensure the solution is exact for homogeneous wave propagation for timesteps of arbitrarily large size, and (b) also allows larger time steps without loss of accuracy in heterogeneous media. The formulation in k-space allows the wavefield to be split easily into compressional and shear parts. A perfectly matched layer (PML) absorbing boundary condition was developed to effectively impose a radiation condition on the wavefield. The staggered grid, which is essential for accurate simulations, is described, along with other practical details of the implementation. The model is verified through comparison with exact solutions for canonical examples and further examples are given to show the efficiency of the method for practical problems. The efficiency of the model is by virtue of the reduced point-per-wavelength requirement, the use of the fast Fourier transform (FFT) to calculate the gradients in k space, and larger time steps made possible by the k-space adjustments.
基于弹性动力学的一阶应力-速度方程，描述了一种线性弹性波传播的伪谱模型。从二阶弹性波方程的并矢格林函数解导出了 k 空间对谱梯度计算的调整，并用于（a）确保在任意大的时间步长下，对于均匀波传播，解是精确的；（b）在非均匀介质中，也允许更大的时间步长而不会损失精度。k 空间中的公式允许将波场轻松地分为压缩和剪切部分。开发了完全匹配层（PML）吸收边界条件，以有效地对波场施加辐射条件。描述了交错网格，这对于准确模拟是必不可少的，以及实现的其他实际细节。通过与典型示例的精确解进行比较来验证模型，并进一步给出示例以显示该方法在实际问题中的效率。该模型的效率得益于减少的点-波长要求、使用快速傅里叶变换（FFT）在 k 空间中计算梯度以及 k 空间调整所带来的更大的时间步长。
