## Determination of rock-sample anisotropy
from P- and S-wave traveltime inversion

**Ivan Psencik,**
**Bohuslav Ruzek,**
**Tomas Lokajicek** **&**
**Tomas Svitek**
### Summary

We determine anisotropy of a rock sample
from laboratory measurements of P-and S-wave
traveltimes using weak-anisotropy approximation
and parametrization of the medium by a
special set of anisotropy parameters.
For the traveltime inversion, we use first-order velocity
expressions in the weak-anisotropy approximation,
which allow to deal with P and S waves
separately. Each wave is described by 15 anisotropy
parameters, 9 of which are common for
both waves. The parameters allow an approximate
construction of separate P-or common
S-wave phase-velocity surfaces. Common S-wave
concept is used to simplify the treatment
of S waves. In order to obtain all 21 anisotropy
parameters, P-and S-wave traveltimes must
be inverted jointly. The proposed inversion
scheme has several advantages. As a consequence
of the use of weak-anisotropy approximation
and assumed homogeneity of the rock sample,
equations used for the inversion are linear.
Thus, the inversion procedure is non-iterative. In the
approximation used, phase and ray velocities
are equal in their magnitude and direction. Thus,
analysis whether the measured velocity is the
ray or phase velocity is unnecessary. Another
advantage of the proposed inversion scheme is
that, thanks to the use of the common S-wave
concept, it does not require identification of
S-wave modes. It is sufficient to know the two
S-wave traveltimes without specification, to
which S-wave mode they belong. The inversion
procedure is tested first on synthetic traveltimes
and then used for the inversion of traveltimes
measured in laboratory. In both cases,
we perform first the inversion of P-wave traveltimes
alone and then joint inversion of P-and S-wave
traveltimes, and compare the results.

### Keywords

Body waves, seismic anisotropy, seismic tomography.

### Whole paper

The reprint can be obtained from
Ivan Psencik.

*Geophys. J. int.*, **214** (2018), 1088-1104.