## Approximate conditions for the off-axis triplication
in transversely isotropic media

**Vaclav Vavrycuk**
### Summary

The presented approximate formulas yield a critical value of anisotropy
parameter *sigma*, for which an incipient off-axis SV-wave triplication
occurs in transversely isotropic media. The formulas are simple but approximate
the exact solution with a high accuracy. The best results are obtained using
the third-order approximation, which yields accuracy at least 30 times higher
than the formulas presented by Thomsen and Dellinger (2003). The formula works
safely for parameters
*kappa*=*a*_{33}/*a*_{44}>2 and
0.2>*epsilon*=(*a*_{11}-*a*_{33})/2*a*_{33}>-0.2,
and yields critical values of *sigma* from 0.1 to 0.7.
Outside this interval, it is recommended to use an exact solution.

### Whole paper

The reprint is available in
PDF (360 kB).

*Stud. geophys. geod.*, **48** (2004), 187-198.

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