## P-wave reflection moveout approximation
for horizontally layered media of arbitrary moderate anisotropy

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

We present an approximate nonhyperbolic P-wave moveout
formula applicable to horizontally layered media of moderate
or weak anisotropy of arbitrary symmetry and orientation.
Anisotropy symmetry and its orientation may differ from layer
to layer. Instead of commonly used Taylor-series expansion
of the square of the reflection traveltime in terms of the square
of the offset, we use the weak-anisotropy approximation, in
which the square of the reflection traveltime is expanded in
terms of weak-anisotropy (WA) parameters. The resulting formula
is simple, and it provides a transparent relation between
the traveltimes and WA parameters. Along an arbitrarily
chosen single surface profile, it depends, in each layer, on
the thickness of the layer, on the reference P-wave velocity
used for the construction of reference rays, and on three
WA parameters specified in the Cartesian coordinate system
related to the profile. In each layer, these three “profile”
WA parameters depend on “local” WA parameters specifying
anisotropy of a given layer in a local coordinate system and on
directional cosines specifying the orientation of the local coordinate
system with respect to the profile one. The number of
local P-wave WA parameters may vary from three for transverse
isotropy or six for orthorhombic symmetry to nine for
triclinic symmetry. Our tests of the accuracy indicate that the
maximum relative traveltime errors do not exceed 0.5% or
2.5% for weak or moderate P-wave anisotropy, respectively.

### Whole paper

The reprint can be obtained from
Ivan Psencik.

*Geophysics*, **85** (2020), C61-C70.