On anelliptic approximations for velocities in transversally isotropic media |

**Sergey Fomel**

sergey.fomel@beg.utexas.edu

I develop a unified approach for approximating phase and group
velocities of
seismic waves in a transversally isotropic medium
with the vertical axis of symmetry (VTI). While the exact phase
velocity expressions involve four independent parameters to
characterize the elastic medium, the proposed approximate
expressions use only three parameters. This makes them more
convenient for use in surface seismic experiments, where estimation
of all the four parameters is problematic. The three-parameter
phase-velocity approximation coincides with the previously published
``acoustic'' approximation of Alkhalifah. The group velocity
approximation is `new and noticeably more accurate than some of the
previously published approximations. I demonstrate an application of
the group velocity approximation for finite-difference computation
of traveltimes.

- Introduction
- Exact expressions
- Muir approximation
- Shifted hyperbola approximation for the phase velocity
- Shifted hyperbola approximation for the group velocity
- Application: Finite-difference traveltime computation
- Conclusions
- Acknowledgments
- Bibliography
- About this document ...

On anelliptic approximations for velocities in transversally isotropic media |

2013-03-02