Propagation of underwater wave groups in a compressible ocean coupled with an elastic seafloor

Abstract

The overall system of interest is an infinite half-space in which a compressible ocean is the top layer and an elastic seafloor (together with the crust beneath) forms a semi-infinite bottom layer. Whereas water-column compression waves and seafloor waves individually have received considerable attention, not much is known about their propagation as groups. This work utilizes the group behaviour of these waves to derive energy balance relations for wavenumber spectra for wave groups propagating through a mildly non-uniform water-column–seafloor system. Dispersion relations for the coupled system are derived using known kinematic and kinetic conditions at the interface, and free and forced wave solutions for the wavenumber spectra are obtained, with particular attention to the case when certain frequency–wavenumber combinations in the forcing excite the two-media system into resonance. Wavenumber spectra predicted using the theory for mildly non-uniform media are found to be close to those predicted assuming uniform media, though the effect of non-uniformity becomes more noticeable as the groups propagate farther from the generation area. Here, nonlinear interactions among stationary, random multi-directional surface-wave fields provide the forcing for groups of compression waves in the water and surface waves on the seafloor. The formulation includes the cumulative effect of multiple generation areas along the group propagation direction. Comparisons with observational data from a sensor array in the Atlantic Ocean indicate that the theory can be applied to reconstruct plausible combinations of generation areas and interaction times that are consistent with the measured data, for deriving approximate predictions at down-wave distances along the group propagation directions. Implications of this and other findings are discussed for (i) the potential for energy conversion from water-column compression waves on the seafloor, (ii) tracking of tropical cyclones from the seafloor, and (iii) quantification and comparative assessment of low-frequency mid-ocean ambient noise and microseism activity.