I'd think it kind of depends, land druid is probably the closest flavor wise (but you might need to tweak the spell list/ wild shape to focus more on geology), but I could also see something like a warlock working if the stones are a source of arcane power.
I would argue some wizard variant. A wizard is someone who studies magic knowledge. A student is a person who studies regular human knowledge. A geologist is a particular kind of student who studies rocks, so as a class I'd say it's a wizard who focused his magical studies on earth manipulating magic.
I had a geologist friend a while back and she 200% would want to play that character in a campaign. Geo nerds are real into pretty and not so pretty rocks.