We have at least three webcams in Arizona that you can argue are geology webcams. Each captures geological scenery, although their purposes are for other reasons.
The Sedona webcams may be the closest to a pure geo-cam because they showcase the scenery to promote tourism. And the scenery is red rock country. [right: webcam view; below: the Sedona webcam
The NAU camera in Flagstaff captures the San Francisco peaks in the background of the campus.
The Grand Canyon camera is actually part of an air quality program so it always seems to be pointed at the haziest areas.