1st Joint Commission 2 and IGFS Meeting
International Symposium on
Gravity, Geoid and Height Systems 2016

September 19-23, 2016
Thessaloniki, Greece

Rigorous evaluation of satellite-only gravitational models

19/09/2016 | 17:30 | Session 2: Global gravity field modelling


Michael Sheng, Petr Vanicek, Robert Kingdon and Ismael Foroughi


This paper provides an algorithm for formulating a gravitational model that accounts for topographical density above the geoid using the ESA-produced Release 5 gravitational models based on GRACE, GOCE, and Lageos observations. Due to the limited spectral content of the observations, the resulting model is truncated to degree and order 300, sufficient for providing a satellite-only reference field for computing regional high-precision geoids.

The spherical harmonic coefficients are evaluated on the Brillouin sphere, a geocentric sphere of the smallest radius R encapsulating all the masses of the Earth. For various applications, we need to know the potential field on the geoid;. this complicates matters as the field cannot be simply continued downward to the geoid because there are topographical masses located in that space making it non-harmonic yet we can only downward continue the field in a harmonic space.

By making use of Helmert’s second condensation method, it is possible to, more or less rigorously (the topographical density is known only to a certain degree) account for the effects of topographical masses and make the space harmonic. The difference between the topographical and the condensed topographical potentials – the direct topographical effect (DTE) – is expressed in spectral form derived by Vanicek et al. (1995). Its addition transforms the gravity potential from the real to Helmert’s space.

Once we have obtained Helmert’s gravity potential, the normal potential of the GRS80 ellipsoid of revolution is subtracted from it to get Helmert’s disturbing potential. This potential is then downward continued simply by using the spherical harmonic series. Helmert’s disturbing potential on the geoid will be used to get the Helmert co-geoid (the geoid in Helmert space). The Helmert co-geoid will be transformed to the real space by accounting for the difference between topographical and the condensation layer’s effects. Numerical values of the real potential coefficients will be compared to EGM2008, GGM05G, and SPW-r4; the resulting geoid will be compared to GPS-levelling benchmarks over North America and central Europe after estimating the omission error.

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