Determination of geoidal height difference using ring integration method

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With the advent of artificial satellites, it is possible to determine relative positions of points to an accuracy of a few parts per million (ppm). The coordinate differences ca, in turn, be transformed into differences in latitude, in longitude and in height on an ellipsoid, provided that their positions relative to the geocentric cartesian coordinate system are known. For some applications, such as mappings and vertical crustal movements, orthometric heights or height differences are needed. In order to convert these ellipsoidal heights to orthometric heights, geoidal heights are required. A software has been developed to determine geoidal height differences utilizing terrestrial gravity anomalies. The approach used here is the ring integration which consists of compartments formed by the intersection of rings and lines radiating out from the point of interest. In this approach, the integration is regarded as the summation of all the predicted gravity anomalies at the midpoints of the compartments. The difference of summation of all the predicted gravity anomalies between endpoints of the line is then multiplied by a constant (0.0003 m/mGal) to obtain the geoidal height difference for the inner zone contribution. The remote zone contribution is obtained using the high order geopotential model – RAPP180. The contributions from these two zones are then summed up to obtain a full geoidal height difference. The results generated from this software are compared to the results obtained from other independent methods, such as GPS/Levelling method and the UNB Dec.’86. A mean-relative-accuracy (MRA) of 1.7 ppm was obtained between the ring integration method and the GPS/Levelling method using a cap size of radius. ψ ₒ = 0.6 ° radius. The comparisons showed that an improvement of the geoidal height difference was possible when the inner zone contribution was added to the remote zone contribution – improve from MRA of 4.0 ppm to MRA 1.7 ppm. The mean-relative-accuracy between the ring integration method and the UNB Dec.’86 approach is 0.92 ppm using a cap radius of 0.4 °.