Approximations to a generalized real ray-tracing method for heterogeneous anisotropic viscoelastic media

The real ray-tracing approach leads to an effective solution in the real space domain using a homogeneous ray velocity vector. However, it fails to yield solutions for quasi-S-waves, which suffer from triplications of the wavefronts. To address this challenging problem, a new real ray-tracing method and its two approximations are developed to solve the complex ray equation. The numerical results indicate that the new real ray-tracing method is superior to the common real ray-tracing method in the presence of triplications of the quasi-S-waves in the computation of ray velocity, ray attenuation, and ray quality factors, as well as the reflection and transmission coefficients in viscoelastic anisotropic media. Based on the assumptions of the real slowness direction and real polarization vectors, two new approximations of the new real ray-tracing method are developed for directly computing the homogeneous complex ray velocity vectors of three wave modes (qP, qS1, and qS2). These approximations sig-nificantly improve computational efficiency by avoiding the iter-ative process required by the new real ray-tracing method that is inherited from the common real ray-tracing method. The compu-tational accuracies are verified through transversely isotropic and orthorhombic models with different strengths of attenuation and anisotropy. Incorporation of the new approximation into the shortest-path method turned out to be efficient and accurate for seismic ray tracing in heterogeneous viscoelastic and trans-versely isotropic media with a vertical axis of symmetry, even in the presence of strong attenuation and anisotropy.