Modeling of wave propagation in a transversely isotropic attenuative medium based on fractional Laplacian

Modeling seismic wave propagation in anisotropic media is critical in the development of advanced full waveform imaging and inversion. This paper presents a new constitutive equation and the corresponding viscoelastic transversely-isotropic (TI) wave equation based on factional Laplacian operators under the assumption of weak attenuation. The fractional Laplacian operators that are non-local in space can be efficiently computed using the Fourier pseudospectral method. We evaluate the accuracy of numerical solutions in a homogeneous transversely isotropic medium by comparing with theoretical predictions and numerical solutions by an existing viscoelastic anisotropic wave equation based on fractional time derivatives. We found that the proposed formulation is able to improve the efficiency of wave simulation in viscoelastic-TI media by an order with maintaining the accuracy.