The Geoid and Quasigeoid of São Paulo State Using the Updated Gravimetric Data and the 2018 BVRF

Abstract

The combination of physical and geometric heights, required for geodetic purposes, uses Global Geopotential Models (GGMs), local geoid, or quasigeoid models. The geoid height and the height anomaly, provided by GGMs, are not accurate enough for most engineering applications. Considering the normal height system of Brazil and the physical concepts of the involved reference surfaces, a quasigeoid model is more appropriate than the current Brazilian geoid model MAPGEO2015. This paper shows the determination of the geoid and the quasigeoid models for São Paulo state using the updated gravimetric data and the new system of the normal height of the 2018 Brazilian Vertical Reference Frame (BVRF). The computation of the quasigeoid model was performed by numerical integration through the Fast Fourier Transform (FFT). The Molodensky gravity anomaly was determined in a 5’ grid and reduced and restored using the Residual Terrain Model (RTM) technique and the XGM2019e GGM truncated at degree and order 250 and 720. The geoid model was derived from the Bouguer gravity anomalies. The quasigeoid model validation has shown a Root Mean Square (RMS) difference of 18 cm compared with the Global Positioning System (GPS) measurements in the levelling network.

Computation and Analysis of Geopotential Number in São Paulo, Brazil

“…In addition, T GGM values show significant differences between order and degree 100 and 200. Silva (2021) studied the RMS difference between height anomalies, obtained from the GPS determinations on the leveling network, and the GOCO06S geoidal height of 86 points located in São Paulo state. In the study was observed a difference of 20 cm approximately, between degrees 100 and 200.…”

“…In this paper, a quasi-geoid model of São Paulo (Silva et al, 2021), which has the same database used in Hotine's methodologies, was used. The was computed using the GRAVSOFT package (Forsberg & Tscherning, 2008).…”

“…On the other hand, in Hotine's methodology, the integration area is smaller and with gravity coverage complete in a 5'grid. In addition, for the quasi-geoid model nmax:250 (Silva et al, 2021) the voids were filled with XGM2019 nmax:2190.…”