APPLICATIONS OF VORONOI AND DELAUNAY DIAGRAMS IN THE SOLUTION OF THE GEODETIC BOUNDARY VALUE PROBLEM

Abstract

Voronoi and Delaunay structures are presented as discretization tools to be used innumerical surface integration aiming the computation of geodetic problemssolutions, when under the integral there is a non-analytical function (e. g., gravityanomaly and height). In the Voronoi approach, the target area is partitioned intopolygons which contain the observed point and no interpolation is necessary, onlythe original data is used. In the Delaunay approach, the observed points are verticesof triangular cells and the value for a cell is interpolated for its barycenter. If theamount and distribution of the observed points are adequate, gridding operation isnot required and the numerical surface integration is carried out by point-wise. Evenwhen the amount and distribution of the observed points are not enough, thestructures of Voronoi and Delaunay can combine grid with observed points in orderto preserve the integrity of the original information. Both schemes are applied to thecomputation of the Stokes’ integral, the terrain correction, the indirect effect and thegradient of the gravity anomaly, in the State of Rio de Janeiro, Brazil area.