Significance and behaviour of the homogeneous and inhomogeneous components of linearized viscoelastic reflection coefficients

Shahpoor Moradi and Kris Innanen

ABSTRACT

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 sin 2 θp , where θp is the P-wave incidence angle, however the inhomogeneous term is similarly linear only if normalized by dividing by sinθp. 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 sin 2 θp, however the elastic and homogeneous terms are first and third order in sinθp. 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.

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