Numerical simulation of seismic wave propagation in viscoelastic-anisotropic media using frequency-independent Q wave equation

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 1/Q. The frequency-independent Q 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 Grunwald-Letnikov approximation. I evaluate the accuracy of numerical solutions in a homogeneous transversely isotropic (TI) medium by comparing with theoretical Q(P) and Q(S) 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.