## Reflection moveout approximation for a P-SV wave in a moderately
anisotropic homogeneous vertical transverse isotropic layer

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

Description of the subsurface is incomplete without the use
of shear waves. Use of converted waves is one way how to involve
shear waves.
We present and test an approximate formula for the reflection moveout
of a wave converted at a horizontal reflector underlying
a homogeneous VTI (transversely isotropic with
the vertical axis of symmetry) layer. For its derivation, we use the
weak-anisotropy approximation, i.e., we expand the square of the
reflection traveltime in terms of weak-anisotropy (WA) parameters.
Travel times are calculated along reference rays of converted reflected
waves in a reference isotropic medium. This requires the determination
of the point of reflection (conversion point) of the reference ray, at
which the conversion occurs. This can be done either by a numerical
solution of a quartic equation or using a simple approximate solution.
Presented tests indicate that the accuracy of the proposed moveout
formula is comparable with the accuracy of formulae derived in
a weak-anisotropy approximation for pure-mode reflected
waves. Specifically, the tests show that the maximum
relative traveltime errors are well below 1% for models with P- and
SV-wave anisotropy about 10% and below 2% for models with
P- and SV-wave anisotropy of 25% and 12%, respectively. For isotropic
media, the use of the conversion point obtained by numerical solution
of the quartic equation yields exact
results. The approximate moveout formula is used for the derivation
of approximate expressions for the two-way zero-offset traveltime,
the normal moveout velocity and the quartic term
of the Taylor series expansion of the squared traveltime.

### Whole paper

The reprint can be obtained from
Ivan Psencik.

*Geophysics*, **84** (2019), C75-C83.