Thomsen-type parameters and attenuation coefficients for constant-Q transverse isotropy

Abstract

Transversely isotropic (TI) media with the frequency-independent quality-factor elements (also called "constant-Q" transverse isotropy) are often used to describe attenuation anisotropy in sedimentary rocks. The attenuation coefficients in constant-Q TI models can be conveniently defined in terms of the Thomsen-type attenuation-anisotropy parameters. Recent research indicates that not all those parameters for such constant-Q media are frequencyindependent. Here, we present concise analytic formulae for the Thomsen-type attenuation parameters for Kjartansson's constant-Q TI model and show that one of them (δ Q ) varies with frequency. The analytic expression for δ Q helps evaluate the frequency dependence of the normalized attenuation coefficients of P-and SV-waves by introducing the newly defined "dispersion factors". Viscoacoustic constant-Q transverse isotropy is also discussed as a special case, for which the elliptical condition and simplified expressions for the parameters δ and δ Q are derived. Our results show that in the presence of significant absorption the attenuation coefficients of the "constant-Q" model vary with frequency for oblique propagation with respect to the symmetry axis. This variation needs to be taken into account when applying the spectral-ratio method and other attenuation-analysis techniques.