Rayleigh wave propagation and perturbed boundaries

This paper presents theoretical and experimental studies of the propagation of Rayleigh waves along perturbed boundaries. In the theoretical treatment, the boundary conditions necessary for the propagation of Rayleigh waves are expressed in terms of the shape of the perturbed boundary. Then by applying a perturbation theory, and the Fourier Integral theorem, the perturbed parts of the solutions to the wave equation are obtained in the integral form. The perturbed contributions to the components of strain are obtained by the use of a numerical integration technique. The experiments are conducted on two dimensional ultrasonic models using plexiglass and plaster of paris as the modeling materials. The theoretical and experimental results for the perturbed half-space model and the model of a layer over a perturbed half-space, are in good agreement. In general, the results show an amplification of the strain amplitudes of Rayleigh waves along the Gaussian perturbation in the first model and along the free surface in the second model, in the direction of propagation.