Abstract
The objective of this paper is to minimize the geoid undulation errors by focusing on the contribution of the global geopotential model and regional gravity anomalies, and to estimate the accuracy of the predicted gravimetric geoid.
The geopotential model's contribution is improved by (a) tailoring it using the regional gravity anomalies and (b) introducing a weighting function to the geopotential coefficients. The tailoring and the weighting function reduced the difference (1σ) between the geopotential model and the GPS/levelling-derived geoid undulations in British Columbia by about 55% and more than 10%, respectively.
Geoid undulations computed in an area of 40° by 120° by Stokes' integral with different kernel functions are analyzed. The use of the approximated kernels results in about 25 cm (σ) and 190 cm (maximum) geoid errors. As compared with the geoid derived by GPS/levelling, the gravimetric geoid gives relative differences of about 0.3 to 1.4 ppm in flat areas, and 1 to 2.5 ppm in mountainous areas for distances of 30 to 200 km, while the absolute difference (1σ) is about 5 cm and 20 cm, respectively.
A optimal Wiener filter is introduced for filtering of the gravity anomaly noise, and the performance is investigated by numerical examples. The internal accuracy of the gravimetric geoid is studied by propagating the errors of the gravity anomalies and the geopotential coefficients into the geoid undulations. Numerical computations indicate that the propagated geoid errors can reasonably reflect the differences between the gravimetric and GPS/levelling-derived geoid undulations in flat areas, such as Alberta, and is over optimistic in the Rocky Mountains of British Columbia.
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Li, Y.C., Sideris, M.G. Minimization and estimation of geoid undulation errors. Bulletin Géodésique 68, 201–219 (1994). https://doi.org/10.1007/BF00808101
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DOI: https://doi.org/10.1007/BF00808101