Abstract
Traditionally, geoid determination is applied by Stokes’ formula with gravity anomalies after removal of the attraction of the topography by a simple or refined Bouguer correction, and restoration of topography by the primary indirect topographic effect (PITE) after integration. This technique leads to an error of the order of the quasigeoid-to-geoid separation, which is mainly due to an incomplete downward continuation of gravity from the surface to the geoid. Alternatively, one may start from the modern surface gravity anomaly and apply the direct topographic effect on the anomaly, yielding the no-topography gravity anomaly. After downward continuation of this anomaly to sea-level and Stokes integration, a theoretically correct geoid height is obtained after the restoration of the topography by the PITE. The difference between the Bouguer and no-topography gravity anomalies (on the geoid or in space) is the “secondary indirect topographic effect”, which is a necessary correction in removing all topographic signals. In modern applications of an Earth gravitational model (EGM) in geoid determination a topographic correction is also needed in continental regions. Without the correction the error can range to a few metres in the highest mountains. The remove-compute-restore and Royal Institute of Technology (KTH) techniques for geoid determinations usually employ a combination of Stokes’ formula and an EGM. Both techniques require direct and indirect topographic corrections, but in the latter method these corrections are merged as a combined topographic effect on the geoid height. Finally, we consider that any uncertainty in the topographic density distribution leads to the same error in gravimetric and geometric geoid estimates, deteriorating GNSS-levelling as a tool for validating the topographic mass distribution correction in a gravimetric geoid model.
Highlights
Stokes’ formula [1] is fundamental for gravimetric geoid determination
The topographic corrections direct topographic effect (DITE) and primary indirect topographic effect (PITE) are added as a combined topographic effect for the geoid height, and the dwc effect is directly computed as another correction to the geoid height
Similar to the gravimetric geoid height one error source to this geoid height solution is the uncertainty in the topographic density distribution, say dμ, which affects the orthometric height by the error dH
Summary
Stokes’ formula [1] is fundamental for gravimetric geoid determination As it requires no masses outside the sphere of computation, traditionally ([2], Chapter 3) the topographic signal on gravity is removed or reduced by a compensation mass below or by a density layer at sea-level (direct topographic effect; DITE on gravity). Another topographic correction is the free-air correction, which provides a downward continuation (dwc) of gravity from the Earth’s surface to sea level. To make the presentation more transparent, the methods are given without corrections for atmospheric masses and ellipsoidal effects (e.g., [11,12])
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