On the propagation properties of surface waves

Abstract

Surface waves were discovered by Rayleigh at the end of the last century [1]. He considered a homogeneous and isotropic elastic half-space R ₊ ³ = (x, ξ), x ≥ 0, ξ ∈ R ², whose boundary surface x = 0 is free of traction. He discovered that there are two types of solutions of the respective boundary value problem:

• (i) Solutions which are oscillating and nondecaying in all variables. They are called the volume (bulk) waves.

• (ii) Solutions which are the plane waves in the longitudinal variables ξ and which are exponentially decaying in the transverse variable x. These solutions are called the surface (grazing) waves. They propagate only in the longitudinal directions, with the velocity slightly smaller than the velocity of the volume waves.