The Earth’s hum: the excitation of Earth normal modes by ocean waves

S U M M A R Y The recent discovery that the seismic normal modes of the Earth are excited to a nearly constant level during seismically quiet days (‘the hum of the Earth’) has lead to much speculation as to what drives the observed background in the absence of large earthquakes. Other authors have shown that the hum cannot be explained by the many small earthquakes occurring each day and have also precluded excitation by ‘slow’ earthquakes as the source. The non-linear interaction of low frequency ocean waves (infragravity waves) generates high phase velocity components that excite the seismic normal modes of the Earth. I show the forcing of the normal modes of the Earth by infragravity waves interacting over the continental shelves and over the deep ocean basins is sufficient to explain the background seismic acceleration spectrum observed during seismically quiet days. Atmospheric turbulence is shown to be a negligible source of the Earth’s hum. Observations suggesting enhanced spectral levels for two seismic modes that couple strongly with atmospheric modes (0S27 and 0S39) have been cited as evidence that the source of the hum lies in the atmosphere. However, the wave interaction mechanism also couples energy into infrasound and thus may explain these observations. A calculation of the coupling between ocean waves and normal modes expected from ocean waves interacting over the shelves reproduces the vertical acceleration spectrum observed at quiet seismic sites from 2 to 40 mHz including the small ‘hump’ between 5 and 15 mHz and the observed rise at higher frequencies. The model diverges above 40 mHz because the ‘single frequency’ microseism peak is generated by a different mechanism. The shape of the hum spectrum is controlled primarily by the elastic properties of the Earth with the attenuation structure controlling mode amplitudes. A second calculation shows the excitation of Earth’s normal modes by infragravity waves interacting over the deep ocean basins can also explain the observed spectrum of the Earth’s hum. Infragravity waves are less energetic and the forcing mechanism weaker over deep water, but the integrative effect of forcing over a large area offsets the weaker forcing per unit area. It is likely that both pelagic and shelf ocean wave sources contribute significantly to the forcing of the Earth’s hum and both coastal and pelagic source regions have been identified using seismic techniques. Infragravity wave spectra in deep water over the Pacific basin vary little, thus explaining the small variation in the hum that is observed. However, time varying source regions are also observed in the hum, and may be best explained by intense near shore sources. The great similarity between the spectra predicted from continental shelf forcing and from forcing over the deep ocean basins precludes discriminating between coastal and pelagic sources based on the shape of the spectrum. A more complete knowledge of the climatology of infragravity waves coupled with better seismic observations are needed to resolve this question.