There is a way young grasshopper… Unfortunately I don’t have time to delve into details but I will give you an overview and you can ask for clarification where you’re having trouble.
The basic effect you’re looking for is the Distort > Displacement Map effect. You’ll need a pre-comp, however, to animate the displacement. In this pre-comp you’ll need your graphic that will cause the displacement as well as a solid layer with Simulation > Wave World applied. On your graphic layer apply a Channel > Shift Channels effect and change the RGB channels to Alpha and the Alpha to Full On, then pre-compose this layer moving all attributes to the pre-comp. In the wave world effect set the “Ground” layer to your pre-composed graphic layer. Now animate the height of the floor up until parts of the ground pass through the surface of the wave simulation (or close to the surface, this takes some experimentation) and then back down. This should produce the waves you need, make sure that your Wave World effect is now in View -> Height Map.
Put that composition in your final comp, apply a displacement map effect to the layer you want to displace and point the effect to your height map comp.
There are additional steps that can give you even better results if you process the height map first to produce a poor man’s ‘normal’ map. I can detail that process later if you like.
Darby Edelen
Designer
Left Coast Digital
Santa Cruz, CA