The performance of various types of Spherical Radial Basis Functions (SRBF) in local gravity field modeling

Global gravity field is commonly modelled in spherical harmonic basis functions to a certain degree of spectral and spatial resolution. Non-uniformdistribution and differentquality data limited these function in local gravity field modeling.Spherical harmonic basis functions show more global property that mean they are suitable for showing low frequency gravityfield. In local-scale studies, radial basis functions on the sphere with quasi-local support can improve gravity fields up to a high spatial/spectral resolution.The local modelsare usually more accurate than global modelsin the desired location.These functions are usually not orthogonal on a sphere, which makes the modelling process more complex.In this study we evaluated the radial basis functions: point-mass kernel, radial multipoles, Poisson and Poisson wavelet and then we compare their performance in regional gravity field modelling on the sphere using real gravity acceleration data in Fars coastal area. A least-squares technique has been used to estimate the gravity field parameters. Iterative Levenberg-Marquardtalgorithm is applied for nonlinear inverse problem solving and minimization of differences between calculated and observed values. These parameters include number, location, depth and scaling coefficients in radial basis function.In order to increase efficiency Levenberg-Marquardt algorithm for solving gravity field modelling, the initial valueof the regularization parameter determined with a relation based on objective function Jacobian and also a method is provided for this parameter updates. The results showed that the accuracy of gravity field modelling for any types of radial basis function would be almost the same, if the depths of SRBFs are chosen properly.