DEVELOPMENT OF A HIGH RESOLUTION GRAVIMETRIC GEOID FOR CENTRAL INDIA

Abstract

Earth's gravity field can be described by continuous smooth and convex surfaces of the constant potential. Among these equipotential surfaces there is one surface called as geoid, which is considerable important in geodesy and geosciences. The geoid plays an important role for the establishment of vertical datum for a country. The GPS technique, which has now become an integral part of surveying and mapping, necessitates the requirements of a precise geoid model in order to offer an alternative and cost effective method for providingorthometric heights. In India, during the last few years, the demand for a high resolution geoid model has also gained momentum due to extensive use of GPS by Indian surveyorcommunity. Nowadays, the GPS users need to transform the GPS- derived ellipsoidal heights into physically meaningful orthometric heights, which refer to the local vertical datum. Therefore, to meet the user's requirement, the geoid model must be known to an accuracy of few centimeters. Theoretically, Stokes' formula for geoid determination is applicable to the global coverage of gravity anomalies. The requirement of gravity coverage over the entire Earth cannot be met anyway due to inaccessibility and confidentiality. This irresolvable constraint has precluded on accurate determination of geoid using Stokes' formula, instead an approximate solution is used in practice. This problem is overcome partly by the inclusion of a global geopotential model (GGM) and partly by some modification of Stokes' integral. The GGM offers a superior information source of low frequency component of geoid via a set of spherical harmonic coefficients and when combined with local terrestrial gravity data, gives a reasonable estimate of regional geoid. This process can easily be implemented in most commonly adopted and applied approach to regional gravimetric geoid determination called as Remove-Compute-Restore (RCR) technique (e.g., Schwarz et. al, 1990), where the complete expansion of the GGM is used in conjunction with regional terrestrial gravity data. In practice, the solution of Stokes' formula is derived by performing the integration over a surface defined by a circle of fixed radius centered at the computation point, which gives rise to a truncation error. The recent trends in application of the modified Stokes' formula have shown that the modification procedure must be able to minimize not only the truncation error but also suitably treat the errors stemming from erroneous potential coefficients of GGM and inadequate compensation of topographic effect. The main goal of u this study therefore is to design an appropriate methodology for computation of gravimetric geoid for central region of Indian subcontinent using modified form of Stokes' integral. The study area (data) is bounded by the parallels 22° N to 30° N and the meridians 72°E to 84°E. The target area, which is used for computation of geoid, extends from 24° to 29° north latitude and from 76° to 82° east longitude. Geoid determination by Stokes' formula requires that there are no masses outside the geoid. This condition is implemented by applying corrections related to topography to raw free-air gravity anomaly data and incorporating the associated indirect effect in geoid computation process. The Helmert's second method of condensation has been used to account for the topographic mass effect on the geoid. The RCR procedure has been applied to combine the GGM, high frequency height data from a DEM and local terrestrial gravity anomaly data. Two global DEM namely ETOP02 and GLOBE are tested in this study in order to determine the most appropriate representation of topography of the study area. GLOBE model has been selected after testing it empirically with the help of available observed height data. EIGEN-GL04C and GGM02-EGM96 combined GGMs are found to be best fit for representing the long wavelength part of the geoid signals in the study area. Finally, EIGEN- GL04C model is used for the computation of geoid. Wong& Gore (1969) modification approach to Stokes' kernel with a truncations radius of 2.3° and degree of modification 90 is found to be best approach amongst all the kernel modification techniques considered in this study. The gravimetric geoid model developed for the study area has been validated by 72 GPS/ levelling points. A mean bias of approximate 5 cm and a standard deviation of 9 cm have been detected, which is most likely due to the long wavelength effect of the GGM and inconsistencies in Indian height datum (IHD). In order to further improve the fit to GPS/ Levelling data a hybrid geoid is computed by applying a corrector surface to gravimetric geoid. The corrector surface is developed using residuals of gravimetric geoid as basic input in a four parameter-least square collocation combined solution. The hybrid geoid may not necessarily represents the Earth's gravity field but it is most suitable for conversion of GPS ellipsoidal heights to orthometric heights. The hybrid geoid model has shown considerable improvement over gravimetric geoid, and standard deviation of post fitting residuals is improved to approximately 5 cm. Thus, the hybrid model would provide an important geodetic infrastructure, which maywork satisfactorilyfor most of the large scale mapping and engineering survey applications.