T-Recs creators of time lapse photography post a short tutorial on how you are able to create a “zolly” or Dolly Zoom Effect (as seen in the movie vertigo, poltergeist and many others) where the background of the shot appears to get further away as the camera gets close. This is usually created by widening the lens as the camera is moving in.

It is relevant to not that this effect is not entirely created in After Effects, so this will NOT work with a static timelapse shot – The time lapse is actually a shot moving, or walking forward with the camera with the zoom on the lens is changing.

Then in After Effects you are able to stabilize the shot and animate the area of interest pretty simply by adding scale and position keyframes for a pretty great result.