Rayleigh Waves in Isotropic Viscoelastic Solid Half-Space

Propagation of harmonic plane waves is considered in a linear viscoelastic isotropic medium. Complex-valued velocities define the attenuated propagation of two bulk waves in this medium. The ratio of these velocities, as a complex-valued parameter, decides the number of Rayleigh waves in the medium. An empirical relation is derived to bifurcate the domain of this parameter, which identifies the necessary condition for the existence of an additional Rayleigh wave. In no case, the number of viscoelastic Rayleigh waves can exceed two. The existence of second Rayleigh wave is then explained in terms of real (elastic) Poisson ratio and quotients of the viscoelastic (complex) moduli. Numerical examples are considered to analyze the phase velocity and attenuation coefficient for each of the two viscoelastic Rayleigh waves.