Hybrid Model for Vertical Deflection Component Determination
Abstract
Observations (Horizontal and vertical angles, azimuth, and zenith distances) made by Surveyors and geodesists in their quest to solve spatial problems in the mapping of the earth's surface are with respect to the earth's gravity field (geoid). The irregularity as a result of the inhomogeneity in the earth's mass-density distribution has made the geoidal surface unsuitable for computation and adjustment of spatial data. Hence, the ellipsoid has been adopted as an approximation of the geoid surface for mathematical computation. The non-coincidence of the normal between these surfaces (the geoid and ellipsoid) underscores the criticality of the deflection of the vertical for the reduction of these observations to the ellipsoid. The need to provide a framework that will ensure the seamless transformation and conversion of coordinates of varying reference surfaces (geoid and reference ellipsoid) and the reduction of astronomical quantities to the ellipsoid underscore the problem of this research. Hence, a hybrid model was developed for the determination of the component of the deflection of the vertical in Rivers state. This involves the integration of the integration of geoid height difference obtained from GPS/Levelling and that obtained from the spherical harmonic coefficient of the earth gravity field (EGM 2008). Using the method of least Squares, the component of the deflection of the vertical for fifteen stations was found to be within between -0.0552? to 0.0784? in the north-south component and -0.05940? to 0.21530? in the east-west component. The component of the deflection of the vertical computed using the various models gives ? = 0.0473?, ? = -0.0393?; ? = 0.0404?, -0.0345?; ? = 0.0157?, ? = 0.0157? for the geometric, hybrid and the EGM 2008 Model respectively. A map of the deflection of the vertical for the study area was developed and a Graphic User Interface (GUI) to aid in the determination of the deflection of the vertical for any point within the study area using MAT Lab 4th Level Programming Language.