Knowledge Bank

The indirect effects on the geoid computation due to the second method of Helmert's condensation were studied. When Helmert's anomalies are used in Stokes' equation, there are three types of corrections to the free-air geoid. The first correction, the indirect effect on geoid undulation due to the potential change in Helmert's reduction, had a maximum value of 0.51 meters in the test area covering the United States. The second correction, the attraction change effect on geoid undulation, had a maximum value of 9.50 meters when the 10° cap was used in Stokes' equation. The last correction, the secondary indirect effect on geoid undulation, was found negligible in the test area. The corrections were applied to uncorrected free-air geoid undulations at 65 Doppler stations in the test area and compared with the Doppler undulations. Based on the assumption that the Doppler coordinate system has a z-shift of 4 meters with respect to the geocenter, these comparisons showed that the corrections presented in this study yielded improved values of gravimetric undulations.