Modeling of Viscoelastic Wave Propagation in Transversely Isotropic Media Using Decoupled Fractional Laplacians

Abstract

Summary We derive a new wave equation involving fractional Laplacians for simulating seismic wave propagation in viscoelastic anisotropic media based on the Kjartansson's constant-Q model. The approximate fractional Laplacian wave equation is developed under the assumptions of or weak velocity and attenuation anisotropy. The formulas can accurately describe the constant-Q (i.e., frequency-independent quality factor) attenuation and attenuation anisotropy behaviours compared to the widely used viscoelastic anisotropic theory based on the generalized standard linear solids (GSLS) model and memory variables. For numerical modeling, we implement the generalized Fourier pseudospectral (PS) method to solve the fractional Laplacian wave equation, which is highly efficient compared to the fractional time wave equation solved by the fractional FD method with the Grunwald-Letnikov (GL) approximation, since it avoids additional memory to store the past wavefields. Numerical results of the homogeneous VTI model validate the accuracy of the proposed equation and illustrate the effect of attenuation and attenuation anisotropy on seismic wavefields, which are consistent with theoretical analysis.