Significance and behaviour of the homogeneous and inhomogeneous components of linearized viscoelastic reflection coefficients
Shahpoor Moradi, Kristopher A. H. Innanen
In a recent paper, seismic amplitude-variation-with-offset (AVO) equations describing P-to-P and P-to-S reﬂections from boundaries separating low-loss viscoelastic media, with account taken for variation in attenuation angle, have been derived. We ﬁnd that opportunities now present themselves to use these equations to expose a range of relationships between measured amplitudes and subsurface elastic and anelastic properties. This has signiﬁcant applicability in quantitative interpretation of seismic data in, for instance, reservoir characterization. To facilitate the analysis we decompose the equations into three parts: elastic, homogeneous and inhomogeneous. We show that, for PP modes, the elastic part is sensitive to changes across a reﬂecting boundary in density and P- and S-wave velocities; the homogeneous part is sensitive to changes in density, S-wave velocity and the P-and S-wave quality factors; and the inhomogeneous part is sensitive to changes in density, and P-and S-wave velocities. The latter term is seen to vanish when the attenuation angle vanishes. Elastic and homogeneous terms are linear with respect to sin2p , where p is the P-wave incidence angle, however the inhomogeneous term is similarly linear only if normalized by dividing by sinp. For PS modes, the elastic part is sensitive to changes in density and S-wave velocity; the homogeneous part is sensitive to changes in density, S-wave velocity and the S-wave quality factor; and the inhomogeneous part is sensitive to changes in density and S-wave velocity. This term also vanishes for zero attenuation angle, i.e., in the homogenous limit. For PS modes, the inhomogeneous terms are linear with respect to sin2p, however the elastic and homogeneous terms are ﬁrst and third order in sinp. A further and key result of this expansion of the wave types allowable in AVO analysis is that, for inhomogeneous PS scattering, the viscoelastic AVO equations predict a non-zero reﬂectivity at normal incidence. This is a signiﬁcant deviation from common models of converted wave amplitude analysis.