An Immersed Free Surface Boundary Treatment for Seismic Wave Simulation

Abstract

Despite its popularity among the seismic community, finite difference method encounters difficulty for applications involving complex topography. Incorporating a free surface boundary treatment within the finite difference framework is appealing due to its efficiency and the effort-saving from existing finite difference codes. We present a free surface boundary treatment within the finite difference framework, with origin from the immersed boundary methods. Inherently, the presented boundary treatment is separated from the rest of the wave simulation, making it suitable for modularized code design. Specifically, we construct an extrapolation operator for each missing grid point to estimate its associated wavefield value at each time step. Although complicated in its mathematical expression, these operators only need to be constructed once for all time steps and source locations. Their associated memory consumption can be significant. Fortunately, simulating multiple shots together can dilute this memory cost. Application of these operators may incur numerical noise, leading to long time instability. In this case, additional numerical procedures such as introducing artificial diffusion are necessary to control the instability. The presented boundary treatment is shown to be capable of modeling both the body wave and surface wave accurately and has the potential on full waveform inversion applications.