An approximate solution for the Rayleigh wave dispersion in materials covered with a thin film

An approximate solution for the Rayleigh wave dispersion in materials covered with a thin film of a different material is developed. The boundary condition determinant is expanded in powers of kh, where k is the wavenumber of the surface wave, and h is the film thickness. As long as kh<<1 expansions to the first order in kh can give Rayleigh wave velocities in very good agreement with numerical calculations based on the complete determinant. The method has been worked out for propagation in high-symmetry directions of various symmetries of substrate and film, including isotropic, cubic, tetragonal, hexagonal and orthorhombic cases. Considerable simplification of the mathematical expressions are obtained as compared to calculations from the complete determinant. Numerical results for various systems are given to illustrate the accuracy of the method.