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

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

We show that it is possible, and often desirable, to accommodate arbitrary
P-wave anisotropy in practical seismic data processing, including migration and
full waveform inversion. We propose a practical concept of arbitrary
P-wave anisotropy, providing a sufficient degree of 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 significantly simplified theory. Here as an example, we use a simple
and transparent formula relating P-wave traveltimes and 15 P-wave A-parameters.
The formula is used in the inversion scheme, which does not require any a priori
information about anisotropy symmetry and its orientation. We test applicability of
the proposed scheme on a blind inversion of synthetic P-wave traveltimes
generated for VSP experiments in homogeneous models. Three
models of varying anisotropy are used: tilted orthorhombic and triclinic models
of moderate anisotropy (~ 10%), and orthorhombic model with a horizontal plane
of symmetry, of strong anisotropy (> 25%). In all cases, the inversion yields
all 15 P-wave A-parameters, which make reconstruction of corresponding phase-velocity
surfaces possible with a high degree of accuracy. The inversion scheme is robust with
respect to noise and source distribution. Its quality depends on the angular
illumination of the medium. 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.

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*Seismic Waves in Complex 3-D Structures*, **28** (2018), 9-44
(ISSN 2336-3827, online at http://sw3d.cz).