“The same sort of laws apply in the United States as well. If you find buried treasure on your land, you do not own all of it.”
You most certainly do. You do not usually own stolen property. But if someone hid their own treasure there, you do indeed own it.
Some idiot in Wenathchee, WA a couple years agaon was remodeling their house and cam across $35,000 in silver bars. They went through the property records and found a family member from a previous owner who had hid it there and gave them the silver!