Effect of great lakes on gravity reduction and geoid determination caused by unclassified DTMs: case study for Lake Victoria, Africa

Abstract

The determination of the gravimetric geoid is based on the magnitude of gravity observed at the topographic surface of the Earth. In order to satisfy Laplace’s equation, the masses between the surface of the Earth and the geoid must be removed or shifted inside the geoid. Then the gravity values have to be reduced to the geoid, forming the boundary values on the boundary surface. Gravity reduction techniques with unclassified height models usually presume that positive elevations are reserved for positive rock topography. Great lakes, however, are filled with water and may be situated partially or fully above sea level. In case of Lake Victoria, the whole lake including its bed floor is situated above sea level, i. e., having positive elevation (orthometric height). This leads to an obvious error in the topographic-isostatic reduction using, for example, the TC program (Forsberg in A study of terrain reductions, density anomalies and geophysical inversion methods in gravity, 1984; Forsberg and Tscherning in Sanso F, Rummel R (eds) Geodetic boundary value problems in view of the one centimeter geoid, Lecture notes in earth sciences. vol 65, pp 239–272, 1997. https://doi.org/10.1007/BFb0011707 ) by assuming rock topography filling the lake instead of water. The aim of this paper is to determine the effect of Lake Victoria on gravity reduction and geoid computation in Africa, as a prototype of the effect of great lakes on gravity reduction and geoid determination. The results prove that the masses of Lake Victoria have significant effect both on the reduced anomalies and on the computed geoid, which then have to be considered for precise geoid determination with correct density values.