Attenuation of Rayleigh waves due to surface roughness.

Rayleigh waves are well known to attenuate due to scattering when they propagate over a rough surface. Theoretical investigations have derived analytical expressions linking the attenuation coefficient to statistical surface roughness parameters, namely, the surface's root mean squared height and correlation length and the Rayleigh wave's wavenumber. In the literature, three scattering regimes have been identified—the geometric (short wavelength), stochastic (short to medium wavelength), and Rayleigh (long wavelength) regimes. This study uses a high-fidelity two-dimensional finite element (FE) modelling scheme to validate existing predictions and provide a unified approach to studying the problem of Rayleigh wave scattering from rough surfaces as the same model can be used to obtain attenuation values regardless of the scattering regime. In the Rayleigh and stochastic regimes, very good agreement is found between the theory and FE results both in terms of the absolute attenuation values and for asymptotic power relationships. In the geometric regime, power relationships are obtained through a combination of dimensional analysis and FE simulations. The results here also provide useful insight into verifying the three-dimensional theory because the method used for its derivation is analogous.