Abstract
Abstract An attempt has been made to evaluate the geoid-quasigeoid separation term over Pakistan by using solutions of terms involving first and second order terrain heights. The first term, involving the Bouguer anomaly, has a significant value and requires being incorporated in any case for determination of the geoid from the quasigoidal solution. The results of the study show that the second term of separation, which involves the vertical gravity anomaly gradient, is significant only in areas with very high terrain elevations and reaches a maximum value of 2–3 cm. The integration radius of 18 km for the evaluation of the vertical gravity anomaly gradient was found to be adequate for the near zone contribution in the case of the vertical gravity anomaly gradient. The Earth Gravity Model EGM96 height anomaly gradient terms were evaluated to assess the magnitude of the model dependent part of the separation term. The density of the topographic masses was estimated with the linear operator of vertical gravity anomaly gradient using the complete Bouguer anomaly data with an initial arbitrary density of 2.67 g/cm3 to study the effect of variable Bouguer density on the geoid-quasigeoid separation. The density estimates seem to be reasonable except in the area of very high relief in the northern parts. The effect of variable density is significant in the value of the Bouguer anomaly-dependent geoid-quasigeoid separation and needs to be incorporated for its true applicability in the geoid-quasigeoid separation determination. The geoid height (N) was estimated from the geoid-quasigeoid separation term plus global part of height anomaly and terrain-dependant correction terms. The results were compared with the separation term computed from EGM96-derived gravity anomalies and terrain heights to estimate its magnitude and the possible amount of commission and omission effects.
Highlights
Most of the modern geodetic boundary value problems provide quasigeoid as its solution
The density of the topographic masses was estimated with the linear operator of vertical gravity anomaly gradient using the complete Bouguer anomaly data with an initial arbitrary density of 2.67 g/cm3 to study the effect of variable Bouguer density on the geoid-quasigeoid separation
The reason behind this difference might be associated with errors in the GPS-leveling data, heights derived from GTOPO5, observed gravity data, and errors in the modeling of density in the determination of the geoid-quasigeoid separation term, in addition to the constant height offset between local and global vertical datums in the Pakistan area
Summary
Most of the modern geodetic boundary value problems provide quasigeoid as its solution. The geoid-quasigeoid separation term is required for the determination of geoid in areas where height datum is based on the orthometric height system. Brief Theoretical Background The geoid to quasigeoid separation term is a function of the geoid and quasigeoid in one sense and orthomeric and normal heights in the other sense This term can be determined with adequate accuracy as a difference of the geoid and quasigeoid using terms to the second power of orthometric heights (Sjoberg, 1995) by the following relationship. Where Np and ζp are the geoid and quasigeoid heights, gB and gF are the Bouguer and free air anomalies, H is the orthometric height, and γis the average theoretical gravity along the ellipsoidal normal between the surface of the geocentric reference ellipsoid and the telluroid.
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