## Reference transversely isotropic medium
approximating
a given generally anisotropic medium

**Ludek Klimes**
### Summary

For a given stiffness tensor (tensor of elastic moduli)
of a generally anisotropic medium,
we can estimate
the extent to which the medium is transversely isotropic,
and determine the direction of its reference symmetry axis.
In this paper,
we rotate the given stiffness tensor about this reference symmetry axis,
and determine the reference transversely isotropic (uniaxial) stiffness tensor
as the average of the rotated stiffness tensor
over all angles of rotation.
The obtained reference transversely isotropic (uniaxial) stiffness tensor
represents an analytically differentiable
approximation of the given generally anisotropic stiffness tensor.
The proposed analytic method is compared with a previous numerical method
in two numerical examples.

### Keywords

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

### Whole paper

The reprint is available in
PDF (93 kB).

*Stud. geophys. geod.*, **62** (2018), 255-260.