On the propagation of acoustic–gravity waves due to a slender rupture in an elastic seabed

The propagation of waves from a vertical uplift of a slender rectangular fault in a sea of constant depth is discussed, accounting for water compressibility, gravity and seabed elasticity. The compressed water column results in the generation of acoustic–gravity waves that travel at the speed of sound in water. Acoustic–gravity waves are found to terminate after a finite time, with the decay time most influenced by seabed rigidity, which is in contrast to the rigid stationary-phase model where signals persist indefinitely. At certain frequencies acoustic–gravity waves couple with the elastic seabed and travel at the shear velocity (speed of sound in an elastic solid). Improved estimates of the critical frequencies are derived. Moreover, besides the usual tsunami, a second – very small amplitude – surface wave mode travelling at the speed of sound arises under certain frequencies. We derive the cut-off frequency for this mode. The acoustic modes possess a frequency spectrum which depends on the time evolution and spatial properties of the rupture. We find that appropriate filtering of the acoustic–gravity wave signal can reveal characteristic peaks that encode information on the fault's geometry and dynamics.