Not only can you get the GS souvenir on Sunday by finding an Earthcache but by travelling 5km to/from it, you get an Geological Society of America one as well:

We are all about helping fellow EarthCachers enjoy the great outdoors.   This year, as part of our 10 year celebrations, we have a special Virtual 5km run in which you can participate as an individual or team.

What you have to do is run or walk (or bike, roll, swim--any human-powered method is great!) a 5km (3.1 miles) path starting at OR ending at an active EarthCache on any of the days over which the run is being held (Friday 3 October through till Monday 13 October 2014). 

You time yourself from start to finish and take a photo of yourself holding a race 'bib' sign with the GC code of the EarthCache, and at the end of your run, complete a simple form and upload your photo.

Everyone who completes the run and uploads a photo will be sent an icon via email that you can display on your caching pages or website.

And it is FREE to participate.