The H-factor in regional geoid modelling: a case study with different scenarios

In order to satisfy the Stokes’ solution to the Robin’s problem, the masses above the geoid are removed using an appropriate reduction scheme. This requires heights of the gravity station and at the integration or running points to be known with reasonable accuracy. The height data is used to compute the topographic, atmospheric, and downward continuation effects—essential elements of any geoid model—as well as to estimate free-air gravity anomalies. The height of the gravity station is usually tied to the local vertical network using standard heighting methods, ideally spirit levelling, while a Digital Elevation Model (DEM) is used to derive the heights at the integration points. In most developing countries, the gravity station heights are either not available or are unreliable for geoid modelling applications, since they were mostly observed to cater for the needs of geophysical exploration. By the end of the day, the geodesist has to accommodate the height information in the integral equations for computing topographical effects using the data available in the country. In this study, the different options for height information are investigated using the data available in Auvergne, central France. Geoid models are computed using different height data combinations to represent different scenarios which exist in different countries. Spherical one-dimensional (1D) Fourier transform is used to evaluate the Stokes’ integral in the framework of the Remove-Compute-Restore (RCR) technique. Results show that orthometric heights derived from a high-resolution Global Geopotential Model (GGM) with ellipsoidal heights may be as good as, if not better than, spirit-levelled heights, when used at the gravity station.