Seismic anisotropy is the fundamental phenomenon of wave propagation in the earth’s interior. Numerical modeling of wave behavior is critical for exploration and global seismology studies. The full elastic (anisotropy) wave equation is often used to model the complexity of velocity anisotropy, but it ignores attenuation anisotropy. I have presented a time-domain displacement-stress formulation of the anisotropic-viscoelastic wave equation, which holds for arbitrarily anisotropic velocity and attenuation [Formula: see text]. The frequency-independent [Formula: see text] model is considered in the seismic frequency band; thus, anisotropic attenuation is mathematically expressed by way of fractional time derivatives, which are solved using the truncated Grünwald-Letnikov approximation. I evaluate the accuracy of numerical solutions in a homogeneous transversely isotropic (TI) medium by comparing with theoretical [Formula: see text] and [Formula: see text] values calculated from the Christoffel equation. Numerical modeling results show that the anisotropic attenuation is angle dependent and significantly different from the isotropic attenuation. In synthetic examples, I have proved its generality and feasibility by modeling wave propagation in a 2D TI inhomogeneous medium and a 3D orthorhombic inhomogeneous medium.
Numerical modeling of 2D seismic wave propagation in fluid saturated porous media using graphics processing unit (GPU): Study case of realistic simple structural hydrocarbon trap