Generalization techniques to reduce the number of volume elements for terrain effect calculations in fully analytical gravitational modelling

Beyond rectangular prism polyhedron, as a discrete volume element, can also be used to model the density distribution inside 3d geological structures. the calculation of the closed formulae given for the gravitational potential and its higher-order derivatives, however, needs twice more runtime than that of the rectangular prism computations. although the more detailed the better principle is generally accepted it is basically true only for errorless data. as soon as errors are present any forward gravitational calculation from the model is only a possible realization of the true force field on the significance level determined by the errors. so if one really considers the reliability of input data used in the calculations then sometimes the “less” can be equivalent to the “more” in statistical sense. as a consequence the processing time of the related complex formulae can be significantly reduced by the optimization of the number of volume elements based on the accuracy estimates of the input data. new algorithms are proposed to minimize the number of model elements defined both in local and in global coordinate systems. common gravity field modelling programs generate optimized models for every computation points (dynamic approach), whereas the static approach provides only one optimized model for all. based on the static approach two different algorithms were developed. the grid-based algorithm starts with the maximum resolution polyhedral model defined by 3–3 points of each grid cell and generates a new polyhedral surface defined by points selected from the grid. the other algorithm is more general; it works also for irregularly distributed data (scattered points) connected by triangulation. beyond the description of the optimization schemes some applications of these algorithms in regional and local gravity field modelling are presented too. the efficiency of the static approaches provide even more than 90% reduction in computation time in favourable situation without the loss of reliability of the calculated gravity field parameters.