## Weak-anisotropy moveout approximations for P waves
in homogeneous layers of monoclinic or higher anisotropy symmetries

**Veronique Farra****,**
**Ivan Psencik** **&**
**Petr Jilek**
### Summary

We use the so-called weak-anisotropy (WA) parameterization as an alternative
to the parameterization of generally anisotropic media by stiffness tensor.
WA parameters consist of linear combinations of normalized stiffness tensor
elements controlling various seismic signatures, hence they are theoretically
extractable from seismic data. They are dimensionless and can be designed to
have the same order of magnitude. WA parameters, similarly to Thomsen-type
parameters, have a clear physical interpretation. They are, however, applicable
to anisotropy of any symmetry, strength and orientation. They are defined
in coordinate systems independent of the symmetry elements of the studied
media. Expressions using WA parameters naturally simplify as the anisotropy
becomes weaker or as the anisotropy symmetry increases. We argue that, due
to these useful properties, WA parameterization can potentially provide
a framework for seismic data processing in generally anisotropic media.
Using the WA parameterization, we derive and test approximate P-wave moveout
formulas for a homogeneous layer of up-to monoclinic symmetry, underlaid by
a horizontal reflector coinciding with a symmetry plane. The derived traveltime
formulas represent an expansion of the traveltime with respect to (small)
WA parameters. For the comparison with standard moveout formulas, we express
ours in the common form of non-hyperbolic moveout, containing normal moveout
velocity and a quartic coefficient as functions of WA parameters.
The accuracy of our formulas depends strongly on the deviation of ray-
and phase-velocity directions (controlled by the deviation of ray
and phase velocities). The errors do not generally increase with increasing
offset, nor do they increase with decreasing anisotropy symmetry.
The accuracy of our formulas is comparable to, or better than, the accuracy
of commonly used formulas.

### Keywords

Anisotropy, P-wave, moveout, traveltime, 3D.

### Whole paper

The reprint can be obtained from
Ivan Psencik.

*Geophysics*, **81** (2016), C39-C59.