Prograde Rayleigh-wave particle motion for simple models

The existence of prograde particle motion for fundamental-mode Rayleigh waves is studied systematically in models of increasing complexity by using an exact expression of the ellipticity. The models studied are: the well-known half-space, the impedance surface with Tiersten´s boundary conditions (TBC), layer with fixed bottom (LFB) and layer over half-space (LOH). It turns out that only the models layer with fixed bottom and layer over half-space may support prograde Rayleigh-wave motion on the surface under certain conditions which are analyzed carefully. The exact expression for the ellipticity of Rayleigh waves, together with the secular equation for the phase velocity, are useful to find the most relevant parameters for prograde particle motion, namely Poisson´s ratio in the layer and the shear-wave velocity contrast between the layer and the half-space. The density contrast between layer and half-space, and up to a certain degree Poisson´s ratio in the half-space, are usually less important. The domain of existence of prograde Rayleigh-particle motion is specified for typical combinations of parameters. These considerations are not only of general theoretical interest but they are also important in applying the so-called H/V-method (H/V = ratio between horizontal and vertical displacement components of Rayleigh waves) for seismic hazard assessment.