The real raytracing approach leads to an effective solution in the real space domain using a homogenous ray velocity vector. However, it fails to yield solutions for quasi-shear waves, which suffer triplication of the wavefronts. To address this challenging problem, a generalized real ray-tracing method and its new approximations are presented to solve the complex ray equation. The numerical results show that the generalized ray-tracing method is superior to the real ray-tracing method in the presence of triplications of the quasi-shear 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 generalized 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 significantly improve the computational efficiency by avoiding the iterative process required by the generalized real ray-tracing method that is inherited from the real ray-tracing method. The computational accuracies are verified through transversely isotropic models and orthorhombic models with different strengths of attenuation and anisotropy. The incorporation of the new approximation into the shortest-path method turned out to be an efficient and accurate method for seismic ray tracing in heterogeneous viscoelastic and transversely isotropic media with a vertical axis of symmetry, even in the presence of strong attenuation and anisotropy.
Microseismic source location using a 3D velocity model: From the ray tracing method to waveform inversion
