Coexistence of gravity waves and elastic waves in unconsolidated sediments

Based on a linear viscoelastic model, we study the coexistence and transiti on of gravity waves and surface elastic waves in a half-space of unconsolid ated sediment. The dispersion relation and surface response are calculated as a function of the period and rigidity of the system. The dispersion rela tion shows two branches. One branch corresponds to a Rayleigh wave for shor t-wave periods, and it becomes a leaky surface wave as the period increases . The second branch shows a linear dependence of the phase velocity with pe riod as expected for gravity waves. As the period increases, this branch ev olves into a leaky surface wave joining the first branch. The surface respo nse function, which is related to the vertical displacement, is also calcul ated, Two distinct peaks are present in the surface response function. One corresponds to a classical Rayleigh wave, while the second is a gravity-dri ven mode whose amplitude is strongly dependent on the wave period and soil rigidity.