Optimal combination of satellite and terrestrial gravity data for regional geoid determination using Stokes-Helmert’s method
21/09/2016 | 15:30 | Session 3: Regional and Local Geoid Modelling
Author(s): Ismael Foroughi, Petr Vaníček, Pavel Novak, Robert Kingdon, Michael Sheng and Marcelo Santos
Ismael Foroughi, Petr Vaníček, Pavel Novak, Robert Kingdon, Michael Sheng and Marcelo Santos
Geodesist have been using global geopotential models to predict gravity anomalies and/or geoid both globally and regionally. Even though the effective resolution of combined global models—these models are constructed using satellite data as well as global terrestrial data—is at best 5 × 5 arc-minutes, numerous studies have showed that the accuracy of these models in many localities is not good enough to satisfy practical requirements. The omission error of global models is still too large for them to be used for regional modeling, and also their real accuracy varies from place to place. On average, using the full degree/order of a combined global model, the error can reach up to 50 cm. To improve the accuracy of a computed geoid, the global model must be combined with detailed regional terrestrial gravity information.
Combining satellite and regional terrestrial data must be done in Helmert’s space (or some other space that is harmonic between the geoid and the Earth surface) to be able to downward continue satellite and terrestrial data to the geoid in a physically meaningful way. Also, satellite-only global models should be used for this purpose to avoid repeated use of the same terrestrial information. Stokes-Helmert’s method developed at UNB employs both data sets in Helmert’s space to model a precise regional geoid.
Combining the satellite and terrestrial data is done in the Stokes integration step of Stokes-Helmert’s scheme. The satellite field, in its role of a reference field, is removed from terrestrial gravity anomalies in Helmert’s space, resulting in residual Helmert’s anomalies on the Earth surface. Then residual co-geoid is determined by Stokes’s convolution with the downward continued residual anomalies. The removed reference field is put back by adding a reference spheroid of the same degree/order (L) as the reference field to the Helmert residual co-geoid. Stokes convolution is carried out over an integration cap of radius ψ0 . How these two data sets should be best combined is thus determined by the choice of L and ψ0. The proposed methodology in this study is to compute the regional geoid models for all possible combinations of L and ψ0, and to compare these models with local GNSS/levelling points.
The area of Auvergne, France (–1 < λ < 7; 43 < ϕ < 49) was used to test the proposed algorithm and to find the optimal pair of ψ0 and L. The satellite only model of DIR5 was used as the satellite contribution, and 244000 terrestrial gravity anomalies were used for evaluating the local contribution to the geoid. The results revealed that the most precise geoid, in the sense of the L2 norm of differences between the geoid and GNSS/Levelling points, will be achieved for L = 160 and ψ0 = 0.75°.