I had a similar thing happen, every time i put my foot down there was a loud bang from what seemed to be under the passenger foot well. The car ran fine otherwise. Turned out there was a plug lead shorting out when under load the sound must have been a backfire travelling down the exhaust on that side.
Does the loud thump occur when you take off quite quickly?? Sounds like the transfer chain in the transfer box. Its probably stretched and the box needs a new chain.