Theoretical Verification of Homogeneous Seismic Body Waves in Viscoelastic Isotropic and Transversely Isotropic Media

On the basis of real ray path and the newly developed g *‐Hamiltonian method of ray‐velocity vectors, we theoretically investigate three homogeneous body waves (qP, qSV and qSH) in viscoelastic transversely isotropic media and distinguish them from their inhomogeneous situations. We demonstrate theoretical conditions of the Q ‐factors of medium for the three homogeneous body waves and conduct computational experiments with rock samples to validate the analytic derivations and characterizations of the homogenous and inhomogeneous body waves. The theoretical analysis and computational experiments reveal that in a viscoelastic isotropic medium P‐ and S‐wave are always homogeneous; in a viscoelastic transversely isotropic medium, the qP‐ and qSV‐wave are homogeneous only when four Q ‐factors , share a same value, and qSH‐wave becomes homogeneous only when equals These theoretical predictions may significantly simplify the computations of the slowness and ray‐velocity vectors and the complex Snell's law of these body waves at an interface and break the bottleneck of seismic ray tracing in viscoelastic transversely isotropic media, which holds crucial practical significance in enhancing the computational efficiency.