Marines patrol through strong winds and heavy snow March 2 during a comprehensive bilateral field training exercise as part of Exercise Forest Light 13-3 at the Hokkaido-Dai Maneuver Area in Hokkaido prefecture, Japan. The FTX began with the Marines and JGSDF (陸上自衛隊) patrolling separately on foot and with mechanized vehicles to reach an area where they set up a defensive position. III Marine Expeditionary Force / Marine Corps Installations Pacific. Photo by Pfc. Kasey Peacock
It isn't so much of an occupation as much as it is that the US has bases all around the planet. Japan, S.Korea, Afghanistan, Iraq, Germany, the U.K, you name it, the U.S probably has a military presence there of some sort.
Not just that really, one of the MAIN reasons was to actually help defend Japan from North Korea since the N. Koreans have been trying to threaten everyone around them with missiles and all. And I also agree with SM51, Im sure there was an agreement something similar to that so yeah. So I hope you guys understand why the US military is there.