## Reflection moveout approximations for P-waves in a moderately
anisotropic homogeneous tilted transverse isotropy layer

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

We have developed approximate nonhyperbolic P-wave moveout formulas
applicable to weakly or moderately anisotropic media
of arbitrary anisotropy symmetry and orientation.
Instead of commonly used Taylor expansion of the square
of the reflection traveltime in terms of the square of the offset,
we expand the square of the reflection traveltime
in terms of weak-anisotropy (WA) parameters.
No acoustic approximation is used.
We specify the formulas designed for anisotropy of arbitrary symmetry
for the transversely isotropic (TI) media
with the axis of symmetry oriented arbitrarily in the 3D space.
Resulting formulas depend on three P-wave WA parameters specifying the
TI symmetry and two angles specifying the orientation of the axis of symmetry.
Tests of the accuracy of the more accurate of the approximate formulae
indicate that maximum relative errors do not exceed 0.3% or 2.5%
for weak or moderate P-wave anisotropy, respectively.

### Whole paper

The reprint can be obtained from
Ivan Psencik.

*Geophysics*, **82** (2017), C175-C185.