Effect of periodic surface corrugation on the propagation of Rayleigh waves

The Rayleigh wave interaction in an elastically isotropic half space having a free surface with weak sinusoidal corrugations in one direction is investigated for the case of propagation normal to the length of the corrugations. Simple and asymptotically exact analytical expressions are deduced with the help of a singular perturbation procedure for the characteristics of the wave interaction. The theory is applied to obtain the characteristics of the selective reflection of a Rayleigh wave incident on a moderately long periodic array of shallow grooves etched on the free surface. The results obtained from the present asymptotic theory are compared with those previously deduced from an empirical equivalent network approach and a phenomenological coupled mode theory.