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

A more direct comparison with Thomsen's approximations uses
equations 24 and 25
to arrive at approximate formulas
for
and analogous to Thomsen's. The resulting expressions,
which may be called ``extended Thomsen formulas,'' are given by

Equations 26 and 27 are the two main

Comparing equations 26 and 27 to equations 6 and 7,
the differences are found to lie in a factor of the form:

and

These results can therefore be used, after deducing some of the elastic constants from field data at near offsets, in order to extend the validity of the equations to greater angles and farther offsets. Inversion of such data is however beyond this paper's scope.

To make the formulas 26 and 27 look as much as possible like Thomsen's formulas -- and thereby arrive at a somewhat different understanding of equations 7 and 8, first eliminate by arbitrarily setting it equal to some value such as , in which case and . Then, the dependence in the denominators goes away, and Thomsen's formulas 7 and 8 are recovered exactly. The particular choice is however completely unnecessary as shall be shown, and furthermore is never valid for any anisotropic medium having .

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

2007-09-15