The Rayleigh mode at the plane boundary between a liquid and a double porosity medium

The Rayleigh mode (also called generalized Rayleigh wave) at the flat interface between a liquid and a double porosity medium saturated by the same liquid, is investigated. The double porosity medium obeys the phenomenological model of Berryman and Wang (2000). It allows the simultaneous propagation of three longitudinal waves and a transverse wave. Assuming open pore conditions at the interface, formulas are found for the coefficients of reflection in the liquid and of transmission in the double porosity medium. Considering only the angular variable in the study, numerical simulations based on data for Berea sandstone show the influence of frequency and the two types of porosity on the reflection coefficient and on the velocity of the generalized Rayleigh wave.