Construction of a uniformly valid solution for a Rayleigh wave in a weakly anisotropic elastic medium

When using the perturbation method to investigate surface waves in crystals of differing symmetry, various small parameters are introduced, e.g., the angles by which the planes and direction of propagation of the surface wave diverge from selected planes and directions; a parameter taking account of distortion of elastic symmetry of the crystal; a quantity characterizing the deviation of the anisotropic elastic coefficients from the isotropic ones (materials with such properties are referred to as weakly anisotropic). In this paper we employ the small-parameter method to examine the behavior of surface waves in elastic weakly anisotropic media. We demonstrate that such media exhibit singular directions, in the neighborhood of which direct expansion becomes invalid. The method of extended parameters is employed to construct a uniformly valid solution.