Accurately propagating P- And S-waves in attenuation media using spatial-independent-order decoupled fractional Laplacians

To accurately simulate wave propagation in the earth, the dispersion and dissipation caused by attenuation should be taken into account during wavefield extrapolation. In this study, we derive a spatial-independent-order decoupled fractional Laplacian (DFL) viscoelastic wave equation based on the dispersion relation of the constant-Q model. The proposed DFL viscoelastic wave equation similar to DFL wave equations show the decoupled anelastic effects. In addition, the proposed formulation has a superiority that the power orders of DFL operators are constant. For numerical simulations in heterogeneous attenuation media, our scheme is free of suffering from the mixed-domain problem and thus maintain the numerical accuracy. Numerical examples in 2D and 3D demonstrate the accuracy and the feasibility of the proposed scheme for seismic modelling problems. valuable wavefield information. Different from the DFL in Zhu and Harris (2014) that obtained by approximating the fractional time derivative, the proposed scheme is derived with an approximated dispersion relation of the original constant-Q model (Kjartansson, 1979), in which the mixed-domain problem is avoided while the decoupled effects still preserved (Xing and Zhu, 2018). Here, we investigate whether the new viscoelastic wave equation has the capability of simulating seismic wave propagation in heterogeneous media with higher accuracy and efficiency than simulations by the original DFL viscoelastic wave equation (Zhu and Carcione, 2014). The layout of this paper is as follows. First, we give a detailed derivation process of the proposed scheme. Then, we verify the accuracy by performing two 2D numerical examples and show the generality and feasibility by a 3D simulation. Finally, we draw the conclusion.