This work is analyzing the contribution of surface waves into the overall dynamic response. The cases of surface Rayleigh wave and interfacial Stoneley and Scholte - Gogoladze waves are considered. The asymptotic models of surface waves are obtained through slow-time perturbation approach and formulated in terms of potentials of the continuum media. The introduction of small parameter corresponds to the small deviation between the speed of the travellign wave and the surface wave speed. In case of the Rayleigh surface wave the asymptotic model is obtained both in 2D and 3D formulations. In case of the interfacial waves the plain strain problem is considered.
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