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%.
The paper is available in PDF (294 kB).