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The propagation of Rayleigh waves over curved surfaces at high frequency

Published online by Cambridge University Press:  24 October 2008

R. D. Gregory
R. D. Gregory
Affiliation:
Department of Mathematics, University of Manchester
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Abstract

A formal asymptotic theory, valid at high frequencies, is developed for the propagation of time harmonic Rayleigh surface waves over the general smooth free surface Σ of a homogeneous elastic solid. It is shown that on Σ these Rayleigh waves can be described by a system of surface rays, which are shown to be geodesics of Σ. The amplitude of the waves on Σ is shown to vary in such a way that the energy propagated along a strip of surface rays is constant. The waves are also shown to be dispersive and an explicit first-order dispersion formula is derived.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 70 , Issue 1 , July 1971 , pp. 103 - 121
Copyright
Copyright © Cambridge Philosophical Society 1971

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References

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