## Determination of the reference symmetry axis
of a generally anisotropic medium
which is approximately transversely isotropic

**Ludek Klimes**
### Summary

For a given stiffness tensor (tensor of elastic moduli)
of a generally anisotropic medium,
we estimate to what extent the medium is transversely isotropic
(uniaxial)
and determine the direction of its reference symmetry axis
expressed in terms of the unit reference symmetry vector.
If the medium is exactly transversely isotropic
(exactly uniaxial),
we obtain the direction of its symmetry axis.
We can also calculate the first-order and second-order
spatial derivatives of the reference symmetry vector
which may be useful in tracing the reference rays
for the coupling ray theory.
The proposed method is tested using various
transversely isotropic
(uniaxial)
and approximately transversely isotropic
(approximately uniaxial)
media.

### Keywords

Elastic anisotropy, stiffness tensor, elastic moduli,
transverse isotropy, approximate transverse isotropy,
reference symmetry axis.

### Whole paper

The reprint is available in
PDF (132 kB).

*Stud. geophys. geod.*, **60** (2016), 391-402.