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

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

We present approximate nonhyperbolic P-wave moveout formula applicable to horizontally
layered, weakly or moderately anisotropic media of arbitrary anisotropy symmetry and
orientation. Symmetry and 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 expand the square of the reflection traveltime in terms of
weak-anisotropy (WA) parameters. Resulting formula yields the square of traveltime
as a function of the square of the offset along a surface profile. It depends,
in each layer, on the thickness of the layer, on the reference P-wave velocity used
for the construction of a reference ray, and on three weak-anisotropy (WA) parameters
specified in the global Cartesian coordinate system. These three parameters can be expressed
in terms of local WA parameters specifying anisotropy of a given layer, specified in
a local coordinate system, and on directional cosines specifying the orientation of
the local coordinate system with respect to the global one. The number of local WA
parameters may vary from three for transverse isotropy, six for orthorhombic symmetry
to fifteen for triclinic symmetry. Tests of the accuracy of the more accurate of
the approximate formulae indicate that maximum relative errors do not exceed 0.5%
or 2.5% for weak or moderate P-wave anisotropy, respectively.

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*Seismic Waves in Complex 3-D Structures*, **28** (2018), 45-60
(ISSN 2336-3827, online at http://sw3d.cz).