A second-order asymptotic model for Rayleigh waves on a linearly elastic half plane

We derive a second-order correction to an existing leading-order model for surface waves in linear elasticity. The same hyperbolic-elliptic equation form is obtained with a correction term added to the surface boundary condition. The validity of the correction term is shown by re-examining problems which the leading-order model has been applied to previously, namely a harmonic forcing, a moving point load and a periodic array of compressional resonators.