The observation equation of spirit leveling in Molodensky's context

Spirit leveling and surface gravity observations can be expressed as orthometric height differences plus corrections which require the knowledge of the Earth crust density. For leveling increments we can write observation equations in a linearized form, according to the standard Molodensky approach, i.e., intrinsic geodesy, depending on normal height differences plus a correction term. This term is a function of the gravity anomaly at the surface level, thus not requiring any assumption on the crust density, and of the curvature of the normal field force lines, which can not be neglected for leveling profiles directed along meridians. The present work shows how to derive these observation equations. An example is presented to verify the effectiveness of the new approach.