Shear wave transmissivity and wave-induced vorticity diffusion through conversion scattering to slow-shear diffusion wave

Abstract

In the poroelasticity theory of de la Cruz and Spanos, fluid shearing within the viscous boundary layer, i.e. fluid vorticity, manifests as an independent process, namely the diffusive slow shear wave. Quantifying its impact on elastic wave propagation remains a research challenge. We analyse the transmissivity of a horizontally polarized shear wave travelling across a stack of porous fluid-saturated layers. The fluid shearing developed at each contact is captured, in a macroscopic sense, through conversion scattering into this diffusive slow shear wave. Generalizing the reflectivity method for elastic waves to the poroelastic case, we develop semi-analytical results for an arbitrary number of layers. We find that the conversion scattering into this diffusion wave reduces the shear wave amplitude, and this reduction accumulates with the number of layers. In the limit when the layer thickness corresponds to the pore diameter, the resulting wave quality factor is close to the predictions of previously reported attempts to capture the fluid vorticity. However, our approach is distinctively different since it is purely based on a wave-theoretic analysis of interacting waves, acknowledging vorticity diffusion as an independent process, thereby avoiding the problems arising when incorporating a pore-scale phenomenon in a macroscopic wave propagation theory.