K-space dispersion error compensators for the fractional spatial derivatives based constant-Q viscoelastic wave equation modeling.

Unlike the fractional temporal derivatives based constant-Q viscoelastic wave equation, the fractional spatial derivatives based one is preferred for the wavefield simulation due to its tractable memory consumption. This viscoelastic wave equation is often solved by the staggered-grid pseudospectral method, which has the spatial spectral accuracy but temporal low order accuracy. The k-space method is one of the potential remedies for the temporal discretization errors. However, it is difficult to fully remove the temporal dispersion errors by directly applying the elastic k-space error compensators to the viscoelastic wave equation, which contains additional temporal derivatives associated with the amplitude decay terms of the P- and S- waves. To tackle the issue, we have derived a new wavenumber-time domain viscoelastic k-space equation by the eigenvalue decomposition method and by the solution to the matrix differential equations. The error compensation terms inside our k-space equation can simultaneously correct the discretization errors of different types of temporal derivatives and are wave mode adaptive. The accuracy of the k-space wave equation is verified by the viscoelastic Green's function's solution. To further boost the simulation efficiency of the k-space method in heterogeneous media, we have proposed an improved k-space method, which decreases the number of the costly mixed-domain operators. The simulation results from the simple and complex models demonstrate that our two k-space methods are superior to the conventional staggered-grid pseudospectral method for the viscoelastic wave modeling.(c) 2023 Elsevier Inc. All rights reserved.