Considering that depth denotes the distance below sea-level to a point on an object located below sea level, and considering that height denotes the distance to some point above the surface of the earth as measured from a point on surface of the earth, it seems there ought to be a term that denotes the distance to some point below the surface of the earth as measured from a point on the surface of the earth.
For example, suppose someone dug a mine shaft down into the earth from an elevated point, but not so far down that it descends below sea-level; what term ought we use to denote the points below the surface of the earth?