This is the hero fedora worn on screen by Harrison Ford during the majority of the film. A different hat is used during the first scene when Indy acquires the idol, along with potentially a few other scenes. There are many very specific marks along with folds and loose threads in the ribbon and bow that are an exact match. Over the years, some of the original dirt has fallen off - as well, you can see the hat looks like a different color depending on the lighting for the scene.
For more details on the fedoras used in all the Indy films, along with a writeup on this fedora, click on the following link (opens in a new window):
Indy Gear Website