Surface waves at a fluid/double-porosity medium interface

We consider surface-wave propagations at an interface separating a fluid layer and a double-porosity medium embedded with cracks. The theory is based on a generalization of the Biot-Rayleigh model from spherical cavities to penny-shaped cracks randomly embedded into a host medium, where mesoscopic local fluid flow (LFF) plays an important role. We derive closed-form dispersion equations of surface waves, based on potentials and suitable boundary conditions (BCs), to obtain the phase velocity and attenuation by using numerical iterations. Two special cases are considered by letting the thickness of the fluid (water) layer to be zero and infinity. We obtain pseudo-Rayleigh and pseudo-Stoneley waves for zero and infinite thickness and high-order surface modes for finite nonzero thickness. Numerical examples confirm that the LFF affects the propagation at low frequencies, causing strong attenuation, whereas the impact of BCs is mainly observed at high frequencies, due to the propagation of slow wave modes. The crack density mainly affects the level of attenuation, whereas the aspect ratio the location of the relaxation peak. The fundamental mode undergoes a significant velocity dispersion, whose location moves to low frequencies as the thickness increases. In all cases, there also exist two slower surface modes that resemble the two slow body waves, only present for sealed BCs.