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Transversely isotropic (TI) media with the frequency-independentquality-factor elements (also called ``constant-$Q$'' transverse isotropy) areoften used to describe attenuation anisotropy in sedimentary rocks. Theattenuation coefficients in constant-$Q$ TI models can be conveniently definedin terms of the Thomsen-type attenuation-anisotropy parameters. Recent researchindicates that not all those parameters for such constant-$Q$ media arefrequency-independent. Here, we present concise analytic formulae for theThomsen-type attenuation parameters for Kjartansson's constant-$Q$ TI model andshow that one of them ($\delta_{Q}$) varies with frequency. The analyticexpression for $\delta_{Q}$ helps evaluate the frequency dependence of thenormalized attenuation coefficients of P- and SV-waves by introducing the newlydefined ``dispersion factors''. Viscoacoustic constant-$Q$ transverse isotropyis also discussed as a special case, for which the elliptical condition andsimplified expressions for the parameters $\delta$ and $\delta_{Q}$ arederived. Our results show that in the presence of significant absorption theattenuation coefficients of the ``constant-$Q$'' model vary with frequency foroblique propagation with respect to the symmetry axis. This variation needs tobe taken into account when applying the spectral-ratio method and otherattenuation-analysis techniques.

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