## Practical concept of arbitrary anisotropy
applied in traveltime inversion of simulated P-wave VSP data

**Ivan Psencik****,**
**Bohuslav Ruzek** **&**
**Petr Jilek**
### Summary

We have developed a practical concept of compressional wave
(P-wave) traveltime inversion in weakly to moderately anisotropic
media of arbitrary symmetry and orientation. The concept
provides sufficient freedom to explain and reproduce observed
anisotropic seismic signatures to a high degree of accuracy.
The key to this concept is the proposed P-wave anisotropy
parameterization (A-parameters) that, together with the use of
the weak-anisotropy approximation, leads to a significantly
simplified theory. Here, as an example, we use a simple and transparent
formula relating P-wave traveltimes to 15 P-wave
A-parameters describing anisotropy of arbitrary symmetry. The
formula is used in the inversion scheme, which does not require
any a priori information about anisotropy symmetry and its orientation,
and it is applicable to weak and moderate anisotropy. As
the first step, we test applicability of the proposed scheme on a
blind inversion of synthetic P-wave traveltimes generated in
vertical seismic profile experiments in homogeneous models.
Three models of varying anisotropy are used: tilted orthorhombic
and triclinic models of moderate anisotropy (approximately 10%)
and an orthorhombic model of strong anisotropy (>25%) with
a horizontal plane of symmetry. In all cases, the inversion yields
the complete set of 15 P-wave A-parameters, which make
reconstruction of corresponding phase-velocity surfaces possible
with high accuracy. The inversion scheme is robust with respect
to noise and the source distribution pattern. Its quality depends on
the angular illumination of the medium; we determine how the
absence of nearly horizontal propagation directions affects inversion
accuracy. The results of the inversion are applicable, for example,
in migration or as a starting model for inversion methods,
such as full-waveform inversion, if a model refinement is desired.
A similar procedure could be designed for the inversion of
S-wave traveltimes in anisotropic media of arbitrary symmetry.

### Whole paper

The reprint can be obtained from
Ivan Psencik.

*Geophysics*, **85** (2020), C107-C123.