Determination of the Deflection of the Vertical Using a Gravimetric Approach within the Federal University of Technology Akure, Nigeria

Abstract

Deflection of the vertical is the angle between the true vertical (the direction of gravity) at a point on the Earth's surface and the normal to the reference ellipsoid (the idealized mathematical model of the Earth's shape). It arises due to the Earth's irregular mass distribution, which causes local variations in the direction of gravity. This research investigates the deflection of the vertical at the Federal University of Technology Akure using a gravimetric approach to determine geoidal undulation. Gravity data from 44 geodetic control stations were observed. The geoidal height and deflection of the vertical were calculated through the discrete wavelet decomposition method in MATLAB, with comparisons to ICGEM data. Geoidal heights at each station were also computed using the gravimetric (Stokes integral) approach, with results compared between methods. The study further evaluated high-resolution global geoid models, including EGM 2008, GECO, SGG-UGM-1, SGG-UGM-2, and XGM 2019e_2156. The result reveals that EGM 2008 has the lowest standard deviation of 0.3197m and SGG-UGM-2 with the lowest root mean square error (RMSE) of 0.4787m. For lower-resolution models (GOCO06S, GOSG01S, IGGT_R1, GGM05G, EIGEN 5C), the standard deviation and RMSE differences were also minimal, with EIGEN5C at 0.3180m and IGGT_R1 at 0.3137m. A z-test indicated significant differences between geoidal heights derived from the gravimetric and wavelet methods, leading to the rejection of the null hypothesis. Therefore, discrete wavelet decomposition should be adopted as an alternative method for computing the deflection of the vertical and geoidal heights when using a gravimetric approach.