## Parameterization of anisotropic media by A-parameters

**Ivan Psencik** **&**
**Veronique Farra**
### Summary

Most common parameterization of anisotropic media is by twenty one
independent elements *a*_{ijkl}
of the density-normalized stiffness tensor or by twenty one
independent elements *A*_{αβ}
of the density-normalized matrix of elastic parameters
in the Voigt notation.
These parameters are commonly of significantly different sizes,
are dimensional, in (km/s)^{2}, often appear in combinations.
We are offering an alternative parameterization
by twenty one A-parameters (anisotropic parameters),
which removes the mentioned
disadvantages and possesses some additional useful properties.
For example, axes or planes of coordinate systems,
in which A-parameters are defined, need not be related to symmetry
axes or planes of the considered anisotropy symmetry as required in
other similar parameterizations.
In combination with the first-order weak-anisotropy approximation,
in which anisotropy is considered as the first-order perturbation of
reference isotropy,
parameterization by A-parameters yields insight into the role of
individual A-parameters in the wave propagation problems.
For example, it turns out that in the first-order
weak-anisotropy approximation, P- and S-wave velocities are each
controlled by fifteen A-parameters.
A set of six of them appears only in the expression for P-wave velocity,
a set of other six A-parameters appears only in S-waves velocity expressions.
Remaining set of nine A-parameters is common for both waves.
We present transformation of A-parameters,
analogue to Bond transformation,
and useful formulae for the weak-anisotropy approximation
for anisotropy of any symmetry and arbitrary tilt.

### Keywords

A-parameters, anisotropy, weak-anisotropy approximation.

### Whole paper

The reprint can be obtained at
https://link.springer.com/article/10.1007/s11200-023-1136-2

*Stud. geophys. geod.*, **68** (2024), in press.