Print Email Facebook Twitter The choice of the spherical radial basis functions in local gravity field modeling Title The choice of the spherical radial basis functions in local gravity field modeling Author Tenzer, R. Klees, R. Faculty Aerospace Engineering Department Physical and Space Geodesy Date 2008-09-12 Abstract The choice of the optimal spherical radial basis function (SRBF) in local gravity field modelling from terrestrial gravity data is investigated. Various types of SRBFs are considered: the point-mass kernel, radial multipoles, Poisson wavelets, and the Poisson kernel. The analytical expressions for the Poisson kernel, the point-mass kernel and the radial multipoles are well known, while for the Poisson wavelet new closed analytical expressions are derived for arbitrary orders using recursions. The performance of each SRBF in local gravity field modelling is analyzed using real data. A penalized least-squares technique is applied to estimate the gravity field parameters. As follows from the analysis, almost the same accuracy of gravity field modelling can be achieved for different types of the SRBFs, provided that the depth of the SRBFs is chosen properly. Generalized cross validation is shown to be a suitable technique for the choice of the depth. As a good alternative to generalized cross validation, we propose the minimization of the RMS differences between predicted and observed values at a set of control points. The optimal regularization parameter is determined using variance component estimation techniques. The relation between the depth and the correlation length of the SRBFs is established. It is shown that the optimal depth depends on the type of the SRBF. However, the gravity field solution does not change significantly if the depth is changed by several km. The size of the data area (which is always larger than the target area) depends on the type of the SRBF. The point-mass kernel requires the largest data area. Subject local gravity field modellingpenalized least-squaresspherical radial basis functionsvariance component estimationgeneralized cross validation To reference this document use: http://resolver.tudelft.nl/uuid:05302a8b-8d78-4b07-bbbf-099cd1fe6f00 Publisher Springer ISSN 1573-1626 Source Studia Geophysica et Geodaetica, 52 (3) Part of collection Institutional Repository Document type journal article Rights (c) 2008 R. Tenzer; R. Klees Files PDF tenzer_2008_1.pdf 1.08 MB Close viewer /islandora/object/uuid:05302a8b-8d78-4b07-bbbf-099cd1fe6f00/datastream/OBJ/view