A first-order k-space model for elastic wave propagation in heterogeneous media.

Abstract

A pseudospectral model of linear elastic wave propagation is described based on the first order elastodynamic equations. A k-space adjustment to the spectral gradient calculations is derived from the dyadic Green’s function solution to the second-order elastic wave equation and used to ensure the solution is exact for homogeneous wave propagation for time-steps of arbitrarily large size. This adjustment also allows larger time-steps without loss of accuracy in weakly heterogeneous media. Along with an appropriate smoothing function, the model is applied for media with high-contrast inhomogeneities. An absorbing boundary condition has been developed to effectively impose a radiation condition on the wavefield. The staggered grid, which is essential for accurate simulations, is described in detail, along with other practical details of the implementation. The model compares favorably to exact solutions for canonical examples and to the conventional pseudospectral and finite difference time-domain codes. The numerical results show the accuracy of the method. It is also very efficient compared to alternative numerical techniques due to the use of the FFT to calculate the gradients in k space leading to reduced number of point per-wavelength and larger time-steps are made possible by the k-space adjustment.