Propagating Seismic Waves in VTI Attenuating Media Using Fractional Viscoelastic Wave Equation

Seismic velocity and attenuation anisotropy are ubiquitous in the crust and upper mantle, significantly modulating the characteristics of seismic wave propagation in the Earth's interior. Accurate seismic wave modeling of velocity and attenuation anisotropy is essential for the understanding of wave propagation in the Earth's interior as well as constructing global and region-scale seismic full waveform tomography. Here, we derive a decoupled fractional Laplacian (DFL) viscoelastic wave equation to characterize the Earth's frequency-independent Q behavior in the vertical transversely isotropic (VTI) media. We verify the accuracy of the proposed viscoelastic wave equation by 2D synthetic examples; to show its applicability in crustal-scale seismic modeling, we present an example of 3D seismic wave propagation in the realistic Salton Trough model. Through extensive numerical tests, we conclude that the proposed viscoelastic wave equation is superior in four aspects. First, the viscoelastic wave equation takes VTI anisotropy of both velocity and attenuation into account and can describe the strong direction-dependent attenuation. Second, our derivation contains spatially independent Laplacians, and thus the proposed wave equation enjoys higher simulation accuracy for heterogeneous Q media. Third, the new viscoelastic wave equation can decouple the amplitude decay and the phase distortion, which is appealing for improving the resolution in seismic imaging and inversion. Lastly, compared to viscoelastic wave equations with time-fractional operators, our scheme has higher computational efficiency by avoiding substantial wavefield storage.