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

Orthometric correction and normal heights for Italian levelling network: a case study

Levelling increments must be corrected for gravity in order to get proper dynamic or orthometric heights. In Italy, most of the levelling lines have no associated gravity observations. Thus, only levelling increments are available, and corrections were computed only on a subset of the existing lines. However, gravity is densely observed, and thus, predictions of gravity along the levelling lines can be computed. This, in principle, would allow the estimation of corrections along the whole Italian levelling network. Furthermore, global model-derived gravity could be used for the same task (e.g. one could use the EGM2008 global geopotential model to get gravity estimates). To check for the reliability of these procedures, a test has been performed along levelling lines in the western Alps area. Both dynamic and orthometric corrections have been computed in order to finally get geopotential numbers, normal heights and orthometric heights from raw levelling increments. The results proved that reliable results can be obtained using the Italian gravity database, while predictions based on the EGM2008 model led to poorer estimates