The scattering formulation presented in 2012 by Stolt and Weglein for isotropic elastic waves, in addition to being a major contribution on its own, represents a jumping-off point for the description of the interaction of seismic waves with a wide range of heterogeneous media. In this paper we extend the scattering picture to include viscoelastic waves, focusing in particular on generalizing the layered medium results of Borcherdt. The main theoretical challenge involves the choice of coordinate system over which to evaluate and analyze the waves, which in the viscoelastic case must be based on complex vector analysis. However, a good candidate system is determined, within which several of Borcherdt's key results for layered media, concerning the reflection and conversion of homogeneous and inhomogeneous P-and S-wave modes, are shown to carry over to general multidimensional scattering. In addition to extending the domain of applicability of this type of viscoelastic wave theory in an intuitive way, the results when incorporated in a Born approximate wave data model are immediately applicable to both direct and full-waveform type inversion calculations.
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