Solving fractional Laplacian viscoelastic wave equations using domain decomposition

Fractional Laplacian viscoacoustic/viscoelastic wave equations offer separate controls over amplitude loss and phase dispersion, and have been used in Q-compensated reverse-time migration and full waveform inversion. Previously, the spatially varying-order fractional Laplacians have been solved with the global Fourier pseudo-spectral method by representing the spatially varying order with an average value, which introduces numerical errors into simulations. To reduce the errors, we propose a local pseudo-spectral method, which uses a large number of block-variable values instead of just one to represent the spatially varying order. A numerical implementation scheme for parallel computing, domain decomposition, has been adopted to take advantage of the local pseudo-spectral method, which improves both numerical accuracy and computing efficiency. A tapering internal boundary condition is used to reduce the Fourier artifacts caused by wavefield truncation at subdomain boundaries. An overlap-add communication scheme bewteen subdomains is applied for reducing the additional cost associated with boundary padding and for interpolating the wavefields from different subdomains within the overlapping boundaries. Numerical examples verify the effectiveness of the domain decomposition strategy in improving the accuracy of solving fractional Laplacians in the viscoelastic wave equations.