A Computational Review Of The Line Integral Analytical Formulation Of The Polyhedral Gravity Signal

The generally shaped polyhedron is a widely used model in gravity field modelling and interpretation. Its induced gravity signal - gravitational potential and its derivatives up to second order - has been studied extensively in the geophysical literature. The class of solutions with special interest is the one which leads to closed analytical expressions, as these offer an exact representation of the gravity signal of finite three-dimensional distributions while being at the same time linked to a flexible means of geometric modelling. Of the several mathematical algorithms available, the line integral approach involves no approximations and is, however, connected with certain singularities, occurring for specific relative positions of the computation point with respect to the polyhedral source. The present contribution analyses the algorithmic details of the polyhedral line integral approach focusing on its geometric and computational aspects. Following the definitions of the individual coordinate systems and the two-step application of the Gauss divergence theorem for each face and polygonal boundary of the source, the geometric insight of the algorithm is presented, which permits a deeper understanding of the significance of the involved numerical singular terms. An overview of the line integral analytical approach for the polyhedral gravity signal is presented with emphasis on its geometric and computational aspects. Matlab code and results for the two considered case studies, a prismatic source and asteroid Eros, are provided as electronic supplement.