Local gravity field modeling using spherical radial basis functions and a genetic algorithm

摘要

Spherical Radial Basis Functions (SRBFs) can express the local gravity field model of thernEarth if they are parameterized optimally on or below the Bjerhammar sphere. Thisrnparameterization is generally defined as the shape of the base functions, their number,rncenter locations, bandwidths, and scale coefficients. The number/location and bandwidthsrnof the base functions are the most important parameters for accurately representing therngravity field; once they are determined, the scale coefficients can then be computedrnaccordingly. In this study, the point-mass kernel, as the simplest shape of SRBFs, is chosenrnto evaluate the synthesized free-air gravity anomalies over the rough area in Auvergne andrnGNSS/Leveling points (synthetic height anomalies) are used to validate the results. A twosteprnautomatic approach is proposed to determine the optimum distribution of the basernfunctions. First, the location of the base functions and their bandwidths are found using therngenetic algorithm; second, the conjugate gradient least squares method is employed tornestimate the scale coefficients. The proposed methodology shows promising results. On thernone hand, when using the genetic algorithm, the base functions do not need to be set to arnregular grid and they can move according to the roughness of topography. In this way, thernmodels meet the desired accuracy with a low number of base functions. On the other hand,rnthe conjugate gradient method removes the bias between derived quasigeoid heights fromrnthe model and from the GNSS/leveling points; this means there is no need for a correctorrnsurface. The numerical test on the area of interest revealed an RMS of 0.48 mGal for therndifferences between predicted and observed gravity anomalies, and a corresponding 9 cmrnfor the differences in GNSS/leveling points.