Limits of transversely isotropic elastic parameters for the existence of classical Rayleigh waves

Solutions of P-SV equations of motion in a homogeneous transversely isotropic elastic layer contain a factor exp(±ν _j z), where z is the vertical coordinate and j?=?1, 2. For computing Rayleigh wave dispersion in a multi-layered half space, ν _j is computed at each layer. For a given phase velocity (c), ν _j becomes complex depending on the transversely isotropic parameters. When ν _j is complex, classical Rayleigh waves do not exist and generalised Rayleigh waves propagate along a path inclined to the interface. We use transversely isotropic parameters as α _H , β _V , ξ, ? and η and find their limits beyond which ν _j becomes complex. It is seen that ν _j depends on ? and η, but does not depend on ξ. The complex ν _j occurs when ? is small and η is large. For a given c/β _V , the region of complex ν _j in a ? -η plane increases with the increase of α _H /β _V . Further, for a given α _H /β _V , the complex region of ν _j increases significantly with the decrease of c/β _V . This study is useful to compute dispersion parameters of Rayleigh waves in a layered medium.