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 depth. For a perfectly smooth surface, the localization length of a Rayleigh wave is predicted to reach a minimum at intermediate wavelength λ and to diverge for both low and large values of λ. For large λ, the divergence results from the fact that the strength of each scatterer is proportional to ω², where ω is the angular frequency of the incident Rayleigh wave. For small λ, the divergence results from Rayleigh waves propagating closer to the surface and therefore being sensitive to a decreasing number of impurities.