Asymptotic Formulation for the Rayleigh Wave on a Nonlocally Elastic Half-Space

This paper deals with the Rayleigh wave, propagating on a nonlocally elastic, linearly isotropic half-space, excited by prescribed surface loading. The consideration develops methodology of hyperbolic–elliptic models for and Rayleigh-type waves, relies effective boundary conditions formulated recently, accounting crucial contributions nonlocal layer. A slow-time perturbation scheme is established, leading to reduced model wave field, comprised singularly perturbed hyperbolic equation longitudinal potential surface, acting as condition elliptic governing decay over interior. An equivalent alternative formulation involving pseudo-differential operator loading terms, parametric dependence depth coordinate, also presented.