Frequency-Domain Finite-Difference Acoustic Modeling with Free Surface Topography using Embedded Boundary Method

Abstract

In this paper, we present a method to model acoustic wave propagation in the frequencydomain in the presence of free surface topography using the embedded boundary method. The advantage of this method is to solve for the pressure field at each frequency on regular finite difference grids but with sub-cell resolution (up to 2nd order accuracy) for the irregular free surface. The topographic free surface condition is implemented in 2nd order accuracy, as in the regular domain so that global 2nd order accuracy is guaranteed. We use the level set method to obtain the projection points and normal directions corresponding to the ghost points in the scheme in the irregular domain. The computational cost for solving the modified sparse matrix for the pressure field increases very little compared to that for a flat surface. We have benchmarked our solver with a 2-D Gaussian hill model and simulated wave propagating in a modified Canadian foothills model. This solver can be used as the forward engine in the full waveform inversion, and we are working underway to perform full waveform inversions with real land survey data with considerable presence of surface topography.