Rayleigh wave dispersion and attenuation on a statistically rough free surface of a hexagonal crystal

Dispersion and attenuation of Rayleigh surface acoustic waves on a statistically rough free surface of a Z-cut hexagonal crystal were analytically studied using a modified mean-field method within the perturbation theory. Numerical calculations were carried out in the frequency range accessible for the perturbation theory using expressions for the real and imaginary parts of the complex frequency shift of Rayleigh waves caused by a slight surface roughness. The Rayleigh wave dispersion and attenuation in the Z-cut hexagonal crystal were shown to coincide qualitatively with those in an isotropic medium, differing only quantitatively. In the long-wavelength limit λ?a, where a is the lateral roughness correlation length, explicit analytical expressions for the relative change in the phase velocity and the inverse damping depth of Rayleigh waves were derived and used in numerical calculations.