Localization of Rayleigh waves

We study the localization of Rayleigh waves propagating in a semi-infinite and isotropic medium with inhomogeneities that are modeled as rods parallel to the incoming wave front and are distributed randomly up to a maximum de pth. For a perfectly smooth surface, the localization length of a Rayleigh wave is predicted to reach a minimum at intermediate wavelength lambda and to diverge for both low and large values of lambda. For large lambda, the d ivergence results from the fact that the strength of each scatterer is prop ortional to omega (2), where omega is the angular frequency of the incident Rayleigh wave. For small lambda, the divergence results from Rayleigh wave s propagating closer to the surface and therefore being sensitive to a decr easing number of impurities.