Surface Wave Profile Due to Oscillatory Motion of an Asymmetric Block of Ocean Floor

The study of waves generated due to ocean bottom displacements is of great importance. In an underwater earthquake, the ocean bed undergoes movement for a short duration which induces wave motion in the seawater that travels along the surface for a significant amount of time. More than often, such wave propagation creates a tsunami at the shoreline. We here consider a rather simplified problem of the horizontal and rigid ocean floor, a finite chunk of which oscillates in the vertical direction at a rate that varies with respect to space. Such a variation creates an asymmetric floor surface profile of the oscillating block. The impact of ocean water compressibility is introduced by generating acoustic-gravity waves that significantly alter the ocean surface profile. We show the variation in surface profile elevation due to changes in ocean depth, the width of the oscillating ocean floor, and its slope.