A comparison of satellite doppler and gravimetric geoid undulations considering terrain‐corrected gravity data

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Abstract
Geoid undulations from satellite Doppler stations have been compared to geoid undulations computed using three procedures. The first procedure combines potential coefficients with uncorrected 1°×1° free air anomalies in a 10° cap surrounding the computation point. The second procedure uses the Helmert second condensation procedure for anomaly reduction where terrain corrections and topographic indirect effects are considered. The third procedure uses a set of potential coefficients to degree 180. After correcting the original Doppler undulation for a −0.4‐ppm scale change, and a 4‐mZaxis bias, comparisons were made at 10 sites located in mountainous areas of the western United States and 10 sites in the eastern United States where the topography was relatively flat. The mean difference (Doppler minus gravimetric) for the 10 western stations was 1.65 when no corrections were applied to the gravity data, while the difference was reduced to 0.10 m when the terrain corrections and indirect effects were included. For the 10 eastern stations the systematic difference (excluding the negligible terrain effects ) was 0.42 m. For western sites the standard deviation of the differences was ±0.96 m (with no gravity corrections) and ±0.93 m with the correction applied. In the eastern sites the standard deviation was ±0.55 m. Similar results were found with the potential coefficients to degree 180. Our major conclusion is that the neglect of terrain corrections, and to a lesser extent the indirect effect, can cause systematic errors of the order of 1.5 m (for a cap size of 10°) in geoid undulations for stations in mountainous areas.