No. The laws vary depending on where you live, but for example, you don't automatically get mineral or oil rights to whatever is beneath your land. Same goes for air rights.
You know... Now I want an apartment in the Earth's core... Why not!?! Electric bill would be high because of the AC... but... Lovely view... And what a way to impress a date... Like... Oh the sunset on a river is nice but... Lava... yeah... Magma... Don't see that every day... And I'll never have to worry about snow again! Yeah... so if anyone's renting bachelor pad down there for about $400/mo. let me know.