Exact seismic velocities for TI media and extended Thomsen formulas for stronger anisotropies |

For purposes of comparison, it is useful to know the exact value and also some related approximations to the exact value of the quasi-SV wave speed at the angle = -- which occurs close to (but not exactly at) the extreme value of over all angles (see discussion after equation 25 in the main text).

Evaluation gives the exact result

And finally, by approximating the square root of this expression and using (14), we have

Equation A-3 can be directly compared to Thomsen's formula for in equation 8. The only difference is a factor of in the final term. This factor could be unity if , but -- since this never happens for anisotropic media -- the factor always differs from unity and can be either higher or lower than unity depending on whether is less than or greater than 45.

Exact seismic velocities for TI media and extended Thomsen formulas for stronger anisotropies |

2007-09-15