On the propagation of acoustic–gravity waves under elastic ice sheets

Abstract

The propagation of wave disturbances in water of varying depth bounded above by ice sheets is discussed, accounting for gravity, compressibility and elasticity effects. Considering the more realistic scenario of elastic ice sheets reveals a continuous spectrum of acoustic–gravity modes that propagate even below the cutoff frequency of the rigid surface solution where surface (gravity) waves cannot exist. The balance between gravitational forces and oscillations in the ice sheet defines a new dimensionless quantity $\mathfrak{Ka}$. When the ice sheet is relatively thin and the prescribed frequency is relatively low ($\mathfrak{Ka}\ll 1$), the free-surface bottom-pressure solution is retrieved in full. However, thicker ice sheets or propagation of relatively higher frequency modes ($\mathfrak{Ka}\gg 1$) alter the solution fundamentally, which is reflected in an amplified asymmetric signature and different characteristics of the eigenvalues, such that the bottom pressure is amplified when acoustic–gravity waves are transmitted to shallower waters. To analyse these scenarios, an analytical solution and a depth-integrated equation are derived for the cases of constant and varying depths, respectively. Together, these are capable of modelling realistic ocean geometries and an inhomogeneous distribution of ice sheets.

Acoustic–gravity waves from multi-fault rupture

“…The second reason is the neglect of sea-floor elasticity, which turns out to be important for both tsunami and acoustic-gravity wave arrival times (Kadri 2019). For the tsunami, neglecting elasticity results in overestimation of the phase speed (Watada 2013;Watada, Kusumoto & Satake 2014;Abdolali et al 2015bAbdolali et al , 2018. The effect is even more dramatic for acoustic-gravity waves as they can couple to the elastic sea floor and travel at speeds reaching 3900 ms −1 which significantly changes their arrival time (Eyov et al 2013).…”

“…On the other hand, seismic data provide valuable information on the tectonic movements, earthquake size and possible epicentre, though with current technology and analysis they fail to assess the tsunami threat. A complimentary approach has been suggested by a number of authors who considered the slight compressibility of the water in their analysis (Miyoshi 1954;Sells 1965;Yamamoto 1982;Nosov 1999;Stiassnie 2010;Kadri & Stiassnie 2012, 2013bCecioni et al 2014;Kadri 2015;Abdolali et al 2018). In this approach, attention is focused on acoustic-gravity waves that radiate from submarine earthquakes alongside the tsunami, and propagate through the liquid or elastic layers (Eyov et al 2013;Kadri 2016).…”

Teleseismic earthquake wavefields observed on the Ross Ice Shelf

“…Literature on acoustic-gravity waves is extensive but has focused on wave mechanics confined to the water layer. Recent studies have begun to address acoustic-gravity waves in the presence of an ice layer, but have thus far been restricted to inelastic ice caps (Kadri, 2016) or thin ( h ≪ H ) elastic sea ice (Abdolali and others, 2018) and thus do not address coupling between acoustic-gravity and seismic waves.…”

Effect of sea-bottom elasticity on the propagation of acoustic–gravity waves from impacting objects

“…It is now well established that acoustic–gravity waves can travel in the ocean 2–5 for long distances 6 , yet they can also penetrate through the elastic layers such as sea-bottom 7 or ice-sheets 8,9 . The transmission mechanism between layers is still not well developed, though it is believed that it could occur once a critical depth (or frequency) is reached 7 .…”