Focused tsunami waves

Shallower regions in the oceans can act as lenses, focusing the energy of tsunamis, typically onto cusp points where two caustic lines meet. Diffraction theory enables calculation of the profile of a tsunami wave propagating through a cusp. The wave elevation depends on position, time and two main parameters M and B : the large parameter M is the distance of the cusp from the lens, divided by the local wavelength of the tsunami without focusing, and B quantifies the spatial extent of the initial disturbance. Focusing amplifies the wave by a factor A proportional to M 1/4 and can potentially multiply the tsunami energy (proportional to A 2 ) 10-fold over a transverse range of tens of kilometres.