Is there a way to measure the water table level under my yard without
digging a deep hole? Perhaps some sort of radar or sonic equipment?

I'm trying to figure out if my damp crawlspace is caused by high water table
or some other reasons.

Are there any professionals who can do this? I don't know who to call. I
don't want to call just any crawlspace waterproofing contractors because
they are usually interested in selling a service than fully understanding
the problem.