Noise generation in the solid Earth, oceans and atmosphere, from nonlinear interacting surface gravity waves in finite depth

Abstract

Oceanic pressure measurements, even in very deep water, and atmospheric pressure or seismic records, from anywhere on Earth, contain noise with dominant periods between 3 and 10 seconds, that is believed to be excited by ocean surface gravity waves. Most of this noise is explained by a nonlinear wave-wave interaction mechanism, and takes the form of surface gravity waves, acoustic or seismic waves. Previous theoretical works on seismic noise focused on surface (Rayleigh) waves, and did not consider finite depth effects on the generating wave kinematics. These finite depth effects are introduced here, which requires the consideration of the direct wave-induced pressure at the ocean bottom, a contribution previously overlooked in the context of seismic noise. That contribution can lead to a considerable reduction of the seismic noise source, which is particularly relevant for noise periods larger than 10 s. The theory is applied to acoustic waves in the atmosphere, extending previous theories that were limited to vertical propagation only. Finally, the noise generation theory is also extended beyond the domain of Rayleigh waves, giving the first quantitative expression for sources of seismic body waves. In the limit of slow phase speeds in the ocean wave forcing, the known and well-verified gravity wave result is obtained, which was previously derived for an incompressible ocean. The noise source of acoustic, acoustic-gravity and seismic modes are given by a mode-specific amplification of the same wave-induced pressure field near the zero wavenumber.

Hydro-acoustic precursors of gravity waves generated by surface pressure disturbances localised in space and time

“…The physical properties of acoustic-gravity waves in compressible water have been already discussed in the past (Stoneley 1926;Longuet-Higgins 1950;Hasselmann 1963;Guo 1987;Ardhuin & Herbers 2013;. However, except for Hasselmann (1963)'s statistical approach and Guo (1987)'s deep-water attempt, little attention has been paid to the hypothesis that underwater compression waves can be generated together with gravity waves directly by sudden pressure variations and gustiness present in turbulent air masses during storms or cyclones.…”

“…However, except for Hasselmann (1963)'s statistical approach and Guo (1987)'s deep-water attempt, little attention has been paid to the hypothesis that underwater compression waves can be generated together with gravity waves directly by sudden pressure variations and gustiness present in turbulent air masses during storms or cyclones. Previous Authors considered surface pressure patterns caused by second-order interaction of gravity waves, neglecting the first-order effects of compressibility (Ardhuin & Herbers 2013). They showed that nearsurface nonlinear hydrodynamic interactions of gravity waves generate pseudo-Rayleigh waves travelling at large depths and acoustic-gravity modes propagating closer to the ocean surface .…”

“…Such a dynamics strongly depends on the previously neglected first-order compressibility and hence is related to a different phenomenon. We shall refer to the first-order acoustic-gravity modes as "hydro-acoustic" (HA) waves (Stiassnie 2010;Sammarco et al 2013) to distinguish them from the secondorder pseudo-Rayleigh (R) and acoustic-gravity (AG) modes (Ardhuin & Herbers 2013;. On the one hand, R and AG waves are the effect of interacting surface gravity waves.…”

Continental microseismic intensity delineates oceanic upwelling timing along the west coast of North America

“…Because the pressure fluctuations are forced by the standing wave component of the wave-wave interactions, the microseisms occur at twice the frequency of the gravity waves. A subsequent analysis by Hasselmann [1963] showed that seafloor Rayleigh waves are generated when the vector sum, K 12 = k 1 + k 2 , of the nearly identical magnitude and nearly oppositely directed wave numbers k 1 and k 2 of the interacting wave trains matches the wave number K of one of the possible seismic modes for given frequency ω [see also Ardhuin and Herbers, 2013]. This type of microseismic activity is common in coastal regions where onshore propagating trains of gravity waves are reflected from the continental boundary [Bromirski and Duennebeir, 2002;Ardhuin et al, 2011].…”

Large-scale numerical modeling of hydro-acoustic waves generated by tsunamigenic earthquakes

“…Nevertheless a sudden movement of the seabed, triggered by underwater earthquake, compresses the water column and generates pressure waves (hydroacoustic waves) that propagate in the sea at the celerity of sound in water. The present analysis involves only the firstorder effects of compressibility on the generation of surface (tsunami) and hydro-acoustic waves, and does not consider the secondary wave-to-wave interaction (e.g., pseudoRayleigh and acoustic-gravity waves considered in the work of Ardhuin and Herbers, 2013).…”