A System of Periodically Alternating Solid and Viscous Fluid Layers: an Exactly Solvable Example of a Biot Medium

Abstract

While the validity of the quasi-static Biot theory of poroelasticity is well established by a large number of theoretical and experimental studies, the theoretical validity of the theory of dynamic poroelasticity and its applicability to earth materials remains a matter of debate. Although equations of dynamic poroelasticity have been re-derived by a number of different methods, all of these methods use some form of averaging or homogenization procedure, coupled with an asymptotic analysis. To shed some more light on the validity of dynamic poroelasticity, I review the results of asymptotic analysis of an exactly solvable example – a periodic system of alternating solid and viscous fluid layers. The results are obtained by the long-wave asymptotic analysis of Rytov’s exact dispersion equation for elastic waves in elastic periodic layered systems. The results are fully consistent with Biot’s theory of dynamic poroelasticity.