Simulation Studies on the Computation of the Gravity Vector in Space from Surface Data Considering the Topography of the Earth

摘要

Three approaches are investigated for the computation of the components of the gravity vector in space considering th topography of the earth: a numerical integration approach based on the application of Green's third identity, the Discrete Dirac approach, and the Least-Squares Collocation approach. Under a spherical approximation, the surface of the earth is assumed to be known through the elevations of its points above a reference sphere. The first technique requires as data gravity disturbances and disturbing potentials on the earth's surface, while the other two techniques requre as data surface gravity anomalies. Two point masses located on the axes of symmetry of two simple terrain models ( a cone and a sphere), generate on their surfaces the synthetic data needed for the simualtions. The agreement between the rigorously computed vetors (from the models), and those from the three techniques, is analyzed in terms of factors such as the inclination of the model's surface, data density, altitude of the space point etc. The application of the Dirac approach is questionable due to its limited acuracy for large data spacing. The Green's approach is recommended for computations above 10 km altitude, while the Collocation approach is suitable for computations at points between the earth's surface and the 10 km level.