Time-space domain high-order staggered-grid finite difference method for porous media

Finite difference methods have been used extensively in seismic modeling. However, these methods generally suffer from numerical dispersion problems. In a porous medium, the numerical dispersion becomes even worse for the presence of three different waves. Traditionally, the finite difference coefficients of spatial derivatives are designed in the space domain. In this paper, we develop a high-order staggered-grid finite difference (SFD) method, in which the finite difference coefficients are calculated in both time and space domains. Based on the dispersion relation for the minimum velocity in a porous medium, the SFD coefficients can be derived using a Taylor expansion. During this procedure, we propose an efficient algorithm to compute SFD coefficients by efficiently solving the Vandermonde matrix when the order of accuracy is large. Dispersion analysis indicates that the time-space domain SFD method has better accuracy compared to the conventional SFD method; this proposed method also works better on the minimum velocity than the other two velocities in porous media. The numerical results show that the time-space domain SFD method can significantly reduce the numerical dispersion of the slow P wave and the proposed method with large time step retains nearly the same accuracy as the conventional SFD method with small time step.