Acoustic wave propagation through porous media revisited

Abstract

In this article a new macroscopic theory for acoustic wave propagation through fluid-saturated porous media will be derived in which losses of the interface type are incorporated. It is argued that in order to explain the occurrence of a slow compressional wave (which is typical for fluid-saturated porous media), a discontinuity in the tangential components of traction and particle velocity at the microscopic fluid/solid interface is essential. The method of spatial volume-averaging will be applied in order to translate the microscopic field equations pertaining to the constituents of the porous medium to the macroscopic level (i.e., several times the wavelength). This method clearly demonstrates the interaction between the fluid and the solid phase at the microscopic fluid/solid interface by means of surface integrals which arise as a consequence of the averaging procedure. These surface integrals are assumed to be linearly related to the volume-averaged state quantities of the phases involved. In this way the interface-type losses are also incorporated. These losses are assumed to be of the inertial type and are triggered by the possible strong fluctuations in the spatial gradients of the microscopic fluid/solid interface (tortuosity). The resulting macroscopic theory, which is assumed to be valid at relatively high frequencies (the frequency range where we observe a slow P wave), mathematically has the same appearance as the most general Biot theory but with a different physical interpretation.