Dispersion and attenuation of Rayleigh waves at a one-dimensional random roughness of the free surface of a hexagonal crystal

Abstract

Analytical expressions are derived for dispersion and attenuation of Rayleigh waves propagating along the statistically rough free surface of a hexagonal crystal (Z cut). The roughness under consideration is one-dimensional (the profile function of the roughness depends on one coordinate) and has the form of hollows of a random lattice. The results obtained earlier in the solution of an analogous problem for a two-dimensional roughness are used in the one-dimensional case. The relationships derived for the dispersion and attenuation of Rayleigh waves are treated analytically and numerically over the entire range of frequencies acceptable in the framework of the perturbation theory. It is shown that the dispersion and attenuation of Rayleigh waves are qualitatively similar to those observed in an isotropic medium.