Attenuation of seismic waves in general viscoelastic media

Propagation of nonstationary seismic waves in a composite (inhomogeneous and anisotropic) viscoelastic medium described by the Volterra linear tensor integral operator with 21 independent components is investigated in terms of asymptotic ray theory. A combined approach based on the main principles of the ray method for isotropic viscoelastic and anisotropic elastic media was used. A recurrent system for terms of the ray series is obtained and its solution is presented in the closed form for the waves of all types. A solution of recurrent system for the computation of reflected and refracted waves is also obtained by using the local principle. Both solutions are based on the theory of plane waves in elastic media. In particular cases, they fit the well known results. All equations are presented in the matrix form convenient for numerical computations. The results can be used for the development of ray algorithms and their modifications for the media of the above-mentioned type. They can be also applied directly to seismic interpretation for the investigation of seismic anisotropy in the presence of viscoelasticity.