Plane-wave propagation in attenuative transversely isotropic media

Abstract

Directionally dependent attenuation in transversely isotropic (TI) media can influence significantly the body-wave amplitudes and distort the results of the AVO (amplitude variation with offset) analysis. Here, we develop a consistent analytic treatment of plane-wave properties for TI media with attenuation anisotropy. We use the concept of homogeneous wave propagation, assuming that in weakly attenuative media the real and imaginary parts of the wave vector are parallel to one another. The anisotropic quality factor can be described by matrix elements [Formula: see text], defined as the ratios of the real and imaginary parts of the corresponding stiffness coefficients. To characterize TI attenuation, we follow the idea of the Thomsen notation for velocity anisotropy and replace the components [Formula: see text] by two reference isotropic quantities and three dimensionless anisotropy parameters [Formula: see text], and [Formula: see text]. The parameters [Formula: see text] and [Formula: see text] quantify the difference between the horizontal- and vertical-attenuation coefficients of P- and SH-waves, respectively, while [Formula: see text] is defined through the second derivative of the P-wave attenuation coefficient in the symmetry direction. Although the definitions of [Formula: see text], and [Formula: see text] are similar to those for the corresponding Thomsen parameters, the expression for [Formula: see text] reflects the coupling between the attenuation and velocity anisotropy. Assuming weak attenuation as well as weak velocity and attenuation anisotropy allows us to obtain simple attenuation coefficients linearized in the Thomsen-style parameters. The normalized attenuation coefficients for P- and SV-waves have the same form as the corresponding approximate phase-velocity functions, but both [Formula: see text] and the effective SV-wave attenuation-anisotropy parameter [Formula: see text] depend on the velocity-anisotropy parameters in addition to the elements [Formula: see text]. The linearized approximations not only provide valuable analytic insight, but they also remain accurate for the practically important range of small and moderate anisotropy parameters — in particular, for near-vertical and near-horizontal propagation directions.