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

Veronique Farra, Ivan Psencik & Petr Jilek


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.


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

Whole paper

The reprint can be obtained from Ivan Psencik.

Geophysics, 81 (2016), C39-C59.