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

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

We use the so-called WA parameterization as an alternative
to the parameterization of generally anisotropic media by
stiffness tensor. WA parameters have important advantages.
They 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 of the same order of magnitude. WA parameters
have a clear physical interpretation, similarly to Thomsen-type
parameterizations, however, they are applicable to anisotropy of
arbitrary symmetry and strength. They are defined in coordinate
systems independent of symmetry elements of studied media.
Expressions using WA parameters naturally simplify as the anisotropy
becomes weaker or anisotropy symmetry increases. We argue that,
due to these useful properties, WA parameterization is well-suited
for solving forward and inverse problems, and 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 formulae for anisotropic media
up-to monoclinic symmetry underlaid by a horizontal reflector
coinciding with a symmetry plane. Derived traveltime formulae
represent an expansion of the traveltime with respect to (small)
WA parameters. We express the moveout formulae in the common form
of non-hyperbolic moveout, containing normal moveout velocity
and a quartic coefficient as functions of WA parameters. All
the resulting formulae are simple, transparent, and described by
only a few WA parameters. The accuracy of the formulae depends
strongly on the deviation of ray- and phase-velocity directions,
which is more pronounced for strongly anisotropic media. The errors
do not generally increase with increasing offset, neither they
increase with decreasing anisotropy symmetry. The accuracy of our
formulae is comparable to, or better than, the accuracy of commonly
used formulae. For anisotropy with a non-negligible strength of 25%,
the relative traveltime errors do not exceed 1%.

### Whole paper

The paper is available in
PDF (294 kB).

*Seismic Waves in Complex 3-D Structures*, **25** (2015), 51-88
(ISSN 2336-3827, online at http://sw3d.cz).