A systematic approximation to the linear equations for small-amplitude surface waves in an elastic half space, interacting with a residually stressed thin film of different material bonded to its plane boundary, is developed in powers of the film thickness, assuming the latter to be small compared to the wavelength of the disturbance. The theory is illustrated by calculating asymptotic expansions of the wave speeds for Love and Rayleigh waves valid to second order in the dimensionless film thickness for a transversely isotropic film bonded to an isotropic substrate.
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