Investigation of the conditions for the existence of a leaky Rayleigh wave

The Rayleigh wave, an inhomogeneous surface wave, exists for all isotropic elastic solids. When the free surface of the solid is bounded by a liquid, a leaky Rayleigh wave, or inhomogeneous damped interface wave, may exist. In the limit that the density of the liquid goes to zero, the leaky Rayleigh wave tends to the free Rayleigh wave. However, the leaky Rayleigh wave does not exist for all liquid/isotropic solid systems. A well-known condition for the existence of the leaky Rayleigh wave is that the velocity of sound in the liquid must be less than that of the shear in the elastic solid. Upon investigation of the secular equation for the leaky Rayleigh wave velocity, other necessary conditions for existence become apparent. The conditions are influenced by the density ratio and the ratios of the various velocities in the liquid/solid system. [Work supported by ONR.]