The Attenuation of Rayleigh Surface Waves by Surface Roughness.

摘要

This paper presents a calculation of the attenuation length of Rayleigh surface waves in the presence of surface roughness. Consider Rayleigh waves on the surface of a semi-infinite isotropic elastic continuum, and the method used produces the contribution to the attenuation rate proportional to the square of the rms amplitude of the roughness. Explicit expressions for the contribution to the attenuation rate are obtained from roughness-induced scattering into bulk transverse and longitudinal acoustic waves, and into Rayleigh waves. The derivation makes use of a Green's function method. When the wavelength lambda of the Rayleigh wave is long compared to the transverse correlation length alpha that characterizes the surface roughness, all contributions to the attenuation rate are proportional to the fifth power of the frequency. When lambda is comparable to or smaller than alpha, the attenuation constant varies more slowly with frequency. For a model of the surface roughness, numerical calculations of the relative magnitude and frequency dependence of the various contributions to the attenuation rate are presented. The Green's function used here may be applied to a number of calculations.