An MD-80 Captain reported experiencing a compressor stall after takeoff. He reduced thrust; declared an emergency; and returned to departure airport.

Narrative

We departed VFR in CAVU conditions (First Officer flying) to get the ATC clearance in the air. During climbout; just prior to 4000ft; we heard a loud thud/bang from the right engine and noticed that the right engine thrust had dropped to 1.5~1.6 EPR from the EPR limit. This appeared to be either a compressor stall or bird strike; but after a couple more thuds (within seconds) we decided to treat it as a compressor stall and pulled the power back until it stopped. The First Officer called for a level off at 4500ft and we decided this was significant enough to return to the departure airport. At that point we received a call from a Flight Attendant reporting the loud noise. I quickly told her that we had a partial power loss and would most likely be returning and I would get back to her shortly. At that point; I was concerned that we were still VFR and had not contacted ATC; so I called them just to tell them our situation. They provided some separation services at that time. Shortly thereafter I declared an emergency. I proceeded to complete the checklists. I notified the Flight Attendants and the passengers that we had a partial power loss; but that the engine was still running and that we could 'easily fly on just one if needed;' and that we were returning as a precautionary measure. During approach the First Officer suggested that we test it one more time to see if it would re-occur at a high power setting. It immediately started doing it again so power was quickly reduced. At that point we continued our approach and made an uneventful landing. Emergency vehicles were ready; so after landing I made another PA announcement so that the passengers would not be alarmed.