A Green's-function method has been used to obtain an expression for the mean free path of a Rayleigh wave propagating along a planar free surface of an isotropic elastic continuum and scattered by a mass defect. The change in density associated with the mass defect is assumed to be $\Delta m\delta (\overrightarrow{\mathrm{x}}-{\overrightarrow{\mathrm{x}}}_0)$, where ${\overrightarrow{\mathrm{x}}}_0$ is the position vector of the defect and $\Delta m$ is the mass change. The Green's function is evaluated for an isotropic elastic continuum with a stress-free planar surface. Using this Green's function, the continuum equations of motion are formally solved for the particle displacement of the scattered wave in terms of the particle displacement of the incident wave. The Poynting vectors are then calculated for the incident wave and the scattered wave. Explicit results for the scattered-wave Poynting vector are obtained in the asymptotic limit of large distance from the mass defect. The mean free path is then obtained from the ratio of the magnitudes of the incident Poynting vector and the asymptotic scattered Poynting vector. The results are compared with those of other workers.

• Received 6 September 1978

DOI:https://doi.org/10.1103/PhysRevB.19.3981