An addition to the theory of the Rayleigh surface waves attenuation by surface roughness

Abstract

The problem of the attenuation of Rayleigh surface waves by surface roughness is solved in the first Born approximation of perturbation theory. A technique of the Green function developed by Maradudin and Mills [3] has been used on account of a principal correction whose mathematical treatment is given. When the correlation function of surface roughness has a Gaussian from, the attenuation coefficient in the short-wavelength limit ℷ«ɑ (λ is the wavelength of Rayleigh wave, α is the transverse correlation length of the surface roughness) does not depend on the frequency, it tends to the constant value. The results of this paper coincide with the results for the attenuation constant obtained by the Rayleigh method by Eguiluz and Maradudin [6]. It is shown that the scattering of the Rayleigh wave into other Rayleigh waves in the region ℷ«ɑ is a much more effective attenuation mechanism than scattering into bulk waves. A strong dependence of the attenuation constant on the properties of an elastic medium is found.