AN APPROXIMATE APPROACH OF RAY VELOCITY AND ATTENUATION IN VISCOELASTIC ANISOTROPIC MEDIA BASED ON PERTURBATION THEORY

In viscoelastic anisotropic media, the stiffness parameters, slowness vector, phase, and ray velocity are all complex-valued quantities. The solutions are challenging and very complicated where the eikonal equations are difficult to solve. In this contribution, we propose an approximation for calculating the ray velocity vector and quality factor in viscoelastic VTI and ORT media based on the perturbation theory. The real and imaginary parts of the stiffness matrix are regarded as the background quantities and perturbations, respectively. The perturbation part of slowness vector can be determined through the zero-valued Hamiltonian function and the homogenous ray velocity vector. The numerical results show high accuracy for all types, such as qP, qSV and qSH, of seismic waves in models with strong anisotropy and attenuation. This is also valid even in the special propagation directions of qSV-wave where the wave surfaces are folded.