A highly accurate constant-Q viscoelastic wave equation temporal extrapolation scheme

Abstract

Summary Numerical simulation of viscoelastic wave equation is a basic tool to analyze the attenuation phenomena of both compressional and shear waves. It has been verified that seismic wave attenuation nearly follows the constant-Q (CQ) model. We develop a highly accurate time-marching scheme for a novel fractional Laplacians CQ viscoelastic wave equation. The time-marching scheme is derived from the analytic solution of the viscoelastic wave equation and it is free of time dispersion and numerical instability when applied in homogeneous media. When simulating wave propagation in heterogeneous media, we adopt a low-rank approximation approach to implement the k-space wave propagator in an efficient way. Our time-marching scheme is formulated as a first-order equation system in terms of particle velocity and stress and it is easy to incorporate an absorbing boundary condition. Numerical examples indicate that our time-marching scheme is more accurate and suffers from a less restrictive stability condition than the traditional pseudo-spectral method, which could bring visible efficiency gain when applied in wave equation-based migration and inversion methods.