Journal of Mathematical Sciences

, Volume 96, Issue 4, pp 3434–3446 | Cite as

Love waves of SH type in an inhomogeneous transversely isotropic elastic medium

  • Z. A. Yanson


The asymptotics of high-frequency Love waves, which are analogous to transverse surface SH waves, is considered for a special type of anisotropy (transverse isotropy) of elastic media. The wave field is represented as a sum of the space-time (ST) caustic expansion and two additional ST ray series for faster (relative to the transverse surface wave) body waves, decaying exponentially with depth. Near the surface, the coefficients of the ST caustic and ray series, as well as the eikonals of waves, are determined in the form of expansions in a small parameter, which characterizes the proximity of the caustic of the ray field to the surface. With regard for the specific structure of the elasticity tensor of a transversely isotropic medium, the surface is treated as a plane. Interrelations between the parameters of elasticity, which are consistent with the conditions of the positivity of the elastic deformation energy and provide for the origination of the surface waves considered, are obtained.


Surface Wave Isotropy Wave Field Elastic Medium Isotropic Medium 
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© Kluwer Academic/Plenum Publishers 1999

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  • Z. A. Yanson

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