Compensating time-stepping error in fractional Laplacians viscoacoustic wavefield modeling

The decoupled fractional Laplacian (DFL) viscous wave equations are commonly solved using the pseudospectral (PS) method, which usually introduces a high spatial accuracy but only second-order temporal accuracy. To eliminate the time-stepping errors, here we adopt the kspace concept to the solver of DFL viscoacoustic wave equation. Different from the existing k-space methods, the proposed k-space method for DFL viscoacoustic wave equation contains two correctors, which are designed to compensate for the time-stepping errors in the dispersion-dominated operator and the loss-dominated operator, respectively. Both theoretical analyses and numerical experiments show that the proposed k-space approach is superior to the traditional PS method mainly in three aspects. First, the proposed approach can effectively compensate for the time-stepping errors. Second, the stability condition is more relax, which makes the selection of sampling intervals more flexible. Finally, the k-space approach allows us to conduct high-accuracy wavefield extrapolation with larger time steps. These features make the proposed scheme be appealing for seismic modeling and imaging problems.