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

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 (delta Q) varies with frequency. The analytic expression for delta Q 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 delta and delta 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.