Plane acoustic waves in linear viscoelastic porous media: Energy, particle displacement, and physical interpretation

Abstract

The poroviscoelastic model, which is asynthesis of the well-known viscoelastic model and Biot’s poroelastic model, is presented in the context of the propagation of plane acoustic waves in linear viscoelastic porous media. Except for the propagation of a second compressional P2 wave in such media, results concerning particle displacement, maximum attenuation, and direction of maximum energy flow are very similar to that obtained by Borcherdt [J. Geophys. Res. 78, 2442–2453 (1973)] in simple viscoelastic media. The energy conservation relation is given explicitly in the case of time harmonic radiation field. From this, expressions of the energy flux, energy densities, dissipated energy, and Q−1 are derived. Furthermore it is demonstrated that the total attenuation Qtotal−1 is equal to the sum of the viscoelastic attenuation Qvisco−1 and Biot’s poroelastic attenuation Qporo−1. This allows a direct comparison between energy dissipated by viscoelasticity and that dissipated by Biot mechanism. For propagation of acoustic waves in infinite natural porous media the latter is always negligible compared to the former. Computed curves and physical interpretations are proposed to illustrate the theoretical derivations.