Computation and Analysis of Geopotential Number in São Paulo, Brazil

Abstract

In recent decades, important steps have been taken to implement the physical concepts of Geodesy in practice, con- cerning height systems. Despite the difficulties involving gravity field modeling, with the establishment of conventions, standards, and computation strategies, the realization of the International Height Reference System (IHRS) is well underway. For a global system, there are constraints for some countries, especially for those with sparse gravity data, mountain regions, and vast areas. In terms of methodology, the computation can be performed directly using the Global Geopotential Models (GGM), recovering existing geoid models, or determining pointwise the gravity potential using integral formulas. In general, the regional gravity modeling is given by numerical integration or least-squares collocation and more recently adopting the spherical radial basis functions. The first approach allows determining the earth’s gravity component at a specific point and adjusting the integral formula according to the gravity coverage. Since so far there is no common sense about the best methodology, computation strategies are been analyzed. In this con- text, the paper aims to contribute to IHRF, computing the geopotential number in the scope of IHRF, using numerical integration to solve the Geodetic Boundary Value Problem and an existing recent quasi-geoid model in four stations in São Paulo state, Brazil. The first approach was performed considering two cases: a radius of 210 km and 110 km of gravimetric data coverage and the Global Geopotential Model GOCO05S truncated at 100 and 200, respectively. The results between solutions have shown a maximum difference of 94 cm, and a minimum difference of 10 cm.