A Coupled Finite Difference – Gaussian Beam Method for High Frequency Wave Propagation

Abstract

Approximations of geometric optics type are commonly used in simulations of high frequency wave propagation. This form of technique fails when there is strong local variation in the wave speed on the scale of the wavelength or smaller. We propose a domain decomposition approach, coupling Gaussian beam methods where the wave speed is smooth with finite difference methods for the wave equations in domains with strong wave speed variation. In contrast to the standard domain decomposition algorithms, our finite difference domains follow the energy of the wave and change in time. A typical application in seismology presents a great simulation challenge involving the presence of irregularly located sharp inclusions on top of a smoothly varying background wave speed. These sharp inclusions are small compared to the domain size. Due to the scattering nature of the problem, these small inclusions will have a significant effect on the wave field. We present examples in two dimensions, but extensions to higher dimensions are straightforward.