Viscoelastic AVO equations: Born versus Aki-Richards approximations

Shahpoor Moradi, Kristopher A. H. Innanen

Anelastic properties of reservoir rocks are important and sensitive indicators of fluid saturation and viscosity changes due (for instance) to steam injection. The description of seismic waves propagating through viscoelastic continua is quite complex, involving a range of unique homogeneous and inhomogeneous modes. This is true even in the relatively simple theoretical environment of amplitude-variation-with-offset (AVO) analysis. For instance, a complete treatment of the problem of linearizing the solutions of the lowloss viscoelastic Zoeppritz equations, to obtain an extended Aki-Richards approximation (one that is in accord with the appropriate complex Snell’s law) is lacking in the literature. Also missing is a clear analytical path allowing such forms to be reconciled with more general volume scattering pictures of viscoelastic seismic wave propagation. Our analysis, which provides these two missing elements, leads to approximate reflection and transmission coefficients for the P- and types I S- waves as formulated by Borcherdt. These involve additional, complex, terms alongside those of the standard isotropic-elastic Aki-Richards equation. The extra terms are shown to have a significant influence on reflection strengths, particularly when the degree of inhomogeneity is high. The particular AVO forms we present are finally shown to be special cases of potentials for volume scattering from viscoelastic inclusions.