Surface waves at an interface between air and an air-filled poroelastic ground

Using a modified Biot theory, employing open pore boundary conditions at the interfaces, and by seeking plane-wave solutions, dispersion equations are derived for a rigid porous half-space, for a poroelastic half-space, and for a layered poroelastic half-space. That for the rigid porous boundary has a single solution. Numerical search shows that, for parameter values characteristic of a dry soil, the dispersion equation for the interface between air and an air-filled poroelastic half-space has three possible solutions corresponding, respectively, to that for the rigid porous case, an air-coupled pseudo-Rayleigh wave, and a new fast surface wave with a speed slightly less than the bulk P-wave speed. The sensitivities of these three surface waves to porosity and elastic parameters are investigated. Of the solutions to the dispersion equation for a system consisting of a single poroelastic layer above a poroelastic half-space, with parameters typical of a dry soil, one is identifiable as an air-coupled pseudo-Rayleigh wave with a phase velocity near to the speed of sound in air. Slower and faster surface waves are predicted also on the layered system when the input parameters for the upper layer are relevant to either a soil or thick snow.