## Weak-anisotropy approximation of P-wave reflection coefficient
in anisotropic media of arbitrary symmetry and tilt

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

Applicability of the approximate expression for the P-wave
reflection coefficient at a weak-contrast reflector separating
two weakly anisotropic half-spaces of arbitrary symmetry is
extended to media of arbitrary symmetry and tilt. The reflection
coefficient consists of the approximate P-wave reflection
coefficient at a weak-contrast interface separating two reference
isotropic half-spaces and a correction term due to
anisotropy. Along an arbitrarily chosen profile, the "isotropic"
term depends on the density and P- and S-wave contrasts,
and the correction term depends linearly on the contrasts of
four profile weak-anisotropy (WA) parameters specifying
anisotropy along the profile. In addition, both terms depend
on the polar angle of incidence. In each half-space, the four
profile WA parameters can be expressed as a linear combination
of 12 of 21 global WA parameters specifying anisotropy of
the half-space. Coefficients of this linear combination are functions
of the azimuth of the profile. WA parameters are a generalization
of Thomsen parameters to arbitrary anisotropy and
represent an alternative to 21 independent elements of the stiffness
tensor. WA parameters can be used for the approximation
of other related concepts such as the reflection moveout or the
geometric spreading. Presented tests illustrate high accuracy
and flexibility of the proposed formula for the P-wave reflection
coefficient. They also show that very accurate results can be
obtained for contrasts and anisotropy, which cannot be considered weak.

### Whole paper

The reprint can be obtained from
Ivan Psencik.

*Geophysics*, **87** (2022), C39-C48.