I created this animation with the GIMP by running Script-Fu / Animators / Waves on the original image (a photograph of me, in case you are wondering).

This is a nice animation, but it would be better if only the sea was moving...

Taking the original (static) image again, I created the mask by erasing some parts of it. Instead of clearing all the areas occupied by the sea, I made the holes a bit smaller so that the edges of the sky and rocks are not affected by the movement.

After the merge, the sea appears to be moving and everything else is static.

The same technique can be used in other cases where you want to animate some parts of an image, but you only have a script or plug-in that animates the whole image.