Slowness vector, ray-velocity vector, traveltime and raypath of seismic body waves in viscoelastic anisotropic media

This paper uses the plane waves in super-space and real space to give the mathematic definitions of the slowness vector, ray-velocity vector, traveltime and raypath of seismic body waves in a viscoelastic anisotropic media (VEAM). Then we explain their physical implications in terms of wave propagation. We show that the slowness vector may be decomposed into the homogeneous and inhomogeneous components, the ray-velocity vector must be a homogeneous complex vector, and the real and imaginary traveltimes represent the wave-phase propagation and wave-energy attenuation, respectively, and the raypaths of wave-phase propagation and wave-energy attenuation are different but both follow Fermat' principle.