Domain Decomposition for Large-Scale Viscoacoustic Wave Simulation Using Localized Pseudo-Spectral Method

Abstract

Wave simulation in absorptive media using decoupled fractional Laplacian wave equation has received widespread attention in recent years, largely due to its precise description of frequency independent $Q$ and easy attenuation compensation in seismic processing. With many algorithms to solve the fractional Laplacian, $k$ -space pseudo-spectral method is predominantly used in academia, where the computing facilities support fast Fourier transforms. However, its global nature prevents the parallelization and computational efficiency of the forward solver, especially for large-scale applications. We propose to solve viscoacoustic wave equation using domain decomposition. A local Fourier basis is constructed around the truncated area to improve the periodicity and smoothness of the decomposed wave information. After independently simulating in the subdomains, a pointwise patching procedure is applied to maintain the continuity of the wavefield between subdomains. Numerical experiments show that this new algorithm obtains high computational efficiency without compromising the numerical stability condition of the traditional pseudo-spectral method. This work becomes more attractive for seismic inversion and imaging problems by improving its parallelization.