Geofyzikální ústav Akademie věd ČR, v.v.i.

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Pšenčík and Farra - 2017 - Reflection moveout approximations for P-waves in a moderately anisotropic homogeneous tilted transverse isotropy layer

Pšenčík and Farra - 2017 - Reflection moveout approximations for P-waves in a moderately anisotropic homogeneous tilted transverse isotropy layer

Ivan Pšenčík, a researcher of the Institute of Geophysics CAS, v. v. i., and Veronique Farra from the Institut de Physique du Globe de Paris, France used the weak-anisotropy approximation to derive approximate P-wave moveout formulae for a homogeneous layer of weakly or moderately anisotropic medium of arbitrary symmetry.

They specified the formulae for the case of a transversely isotropic (TI) medium with arbitrarily oriented axis of symmetry, so-called TTI medium, underlaid by a horizontal reflector. In contrast to the commonly used traveltime formulae, the derived formulae represent an expansion of the traveltime with respect to (small) weak-anisotropy (WA) parameters. WA parametrization is an alternative to the parametrization of generally anisotropic media by a stiffness tensor. WA parameters consist of linear combinations of normalized stiffness-tensor elements. They are dimensionless and can be designed to have the same order of magnitude. They are applicable to anisotropy of any symmetry, strength, and orientation. For the comparison with standard, commonly used moveout formulae, we expressed the derived formulae in the common form of nonhyperbolic moveout, containing normal moveout velocity and a quartic coefficient as functions of the WA parameters. Resulting formulas depend on three P-wave WA parameters specifying the TI symmetry and two angles specifying the orientation of the axis of symmetry. The accuracy of the derived formulae depends strongly on the deviation of ray- and phase-velocity directions (controlled by the deviation of the ray and phase velocities). The errors are negligible for small offsets and generally decrease with increasing offset. The accuracy of the new formulae is comparable with the accuracy of formulae derived for media, in which symmetry elements of considered anisotropy are parallel or perpendicular to the reflector.

Link to the publication.