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 frequency-independent. Here, we present concise analytic formulas for the Thomsen-type attenuation parameters for Kjartansson’s constant-Q TI model and show that one of them () varies with frequency. The analytic expression for helps evaluate the frequency dependence of the normalized attenuation coefficients of P- and SV-waves by introducing the newly defined “dispersion factors.” These factors are frequency-independent and expressed in terms of the Thomsen and Thomsen-type parameters defined at a specified reference frequency. Viscoacoustic constant-Q transverse isotropy is also discussed as a special case, for which the elliptical condition and simplified expressions for the parameters and 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.