A new paper is added to the collection of reproducible documents: On anelliptic approximations for qP velocities in TI and orthorhombic media

Anelliptic approximations for phase and group velocities of qP waves in transversely isotropic (TI) media have been widely applied in various seismic data processing and imaging tasks. We revisit previously proposed approximations and suggest two improvements. The first improvement involves finding an empirical connection between anelliptic parameters along different fitting axes based on laboratory measurements of anisotropy of rock samples of different types. The relationship between anelliptic parameters observed is strongly linear suggesting a novel set of anisotropic parameters suitable for the study of qP-wave signatures. The second improvement involves suggesting a new functional form for the anelliptic parameter term to achieve better fitting along the horizontal axis. These modifications lead to improved three-parameter and four-parameter approximations for phase and group velocities of qP waves in TI media. In a number of model comparisons, the new three-parameter approximations appear to be more accurate than previous approximations with the same number of parameters. These modifications also serve as a foundation for an extension to orthorhombic media where qP velocities involve nine independent elastic parameters. However, as shown by previous researchers, qP wave propagation in orthorhombic media can be adequately approximated using just six combinations of those nine parameters. We propose novel six-parameter approximations for phase and group velocities for qP waves in orthorhombic media. The proposed orthorhombic phase-velocity approximation provides a more accurate alternative to previously known approximations and can find applications in full-wave modeling, imaging, and inversion. The proposed group-velocity approximation is also highly accurate and can find applications in ray tracing and velocity analysis.