It seems the mathematical analyses of waves generated by sea surface or bottom disturbances may be related with a single transformation, although I don't know that. There is a hint of this kind of observation in the 'surface wave' chapter by Weahausen and Laitone in Handbuch der physik. I have been trying to do some work in tsunami wave dynamics with very little success though for the last 5-6 years.
Another point I wish to make about the classical Cauchy Poisson problem, has it got any deep rooted point to establish in the generation of tsunami waves? Why is it so that the warning systems are failing so miserably?