Roughness-trapped shear horizontal surface acoustic waves

Shear horizontal surface acoustic waves do not exist on the flat surface of a semi-infinite elastic medium. It has been shown by several authors recently that such waves can exist on a periodically corrugated, planar surface. We show here on the basis of the Rayleigh method that shear horizontal surface acoustic waves exist on a randomly rough planar surface of an isotropic elastic medium. These waves are only weakly localized to the surface and they have a lifetime that is long due to their roughness-induced scattering into other surface acoustic waves and into bulk waves.