Apple tree

Have a mature apple tree in garden just moved into. Have no idea what kind this is, but it is cooking apples rather than eating.
Understandably, there is no vegetation/grass etc growing under this tree. This is quite a considerable area of mud/earth that extends into lawn of a small garden.
I was thinking of using gravel/stones to cover this area to enable water/drainage etc but was unsure whether this would then be an issue for the health of the tree.
any thoughts?

 

We have gravel under a couple of our apple trees and there are no problems with it, other than cleaning off the fallen leaves i autumn/winter.