Modelling of viscoacoustic wave propagation in transversely isotropic media using decoupled fractional Laplacians

Abstract

ABSTRACTA new wave equation is derived for modelling viscoacoustic wave propagation in transversely isotropic media under acoustic transverse isotropy approximation. The formulas expressed by fractional Laplacian operators can well model the constant‐Q (i.e. frequency‐independent quality factor) attenuation, anisotropic attenuation, decoupled amplitude loss and velocity dispersion behaviours. The proposed viscoacoustic anisotropic equation can keep consistent velocity and attenuation anisotropy effects with that of qP‐wave in the constant‐Q viscoelastic anisotropic theory. For numerical simulations, the staggered‐grid pseudo‐spectral method is implemented to solve the velocity–stress formulation of wave equation in the time domain. The constant fractional‐order Laplacian approximation method is used to cope with spatial variable‐order fractional Laplacians for efficient modelling in heterogeneous velocity and Q media. Simulation results for a homogeneous model show the decoupling of velocity dispersion and amplitude loss effects of the constant‐Q equation, and illustrate the influence of anisotropic attenuation on seismic wavefields. The modelling example of a layered model illustrates the accuracy of the constant fractional‐order Laplacian approximation method. Finally, the Hess vertical transversely isotropic model is used to validate the applicability of the formulation and algorithm for heterogeneous media.