A data-adaptive design of a spherical basis function network for gravity field modelling

Abstract

A data-adaptive strategy for the design of spherical basis function (SBF) networks is presented. The strategy comprises a datadriven selection of the SBFs prior to parameter estimation and an automatic selection of the bandwidth of the SBFs. The selection procedure takes the data distribution and the data noise into account. The strategy can be applied to all interpolation and approximation problems that use SBFs. It is particularly suited for the local inversion of magnetic and gravity data acquired by terrestrial, airborne or space-borne sensors. It is shown that for inhomogeneous and scattered data distribution, the method requires significantly less basis functions than commonly used strategies, which range from template networks of SBFs (e.g. from hierarchical subdivision schemes or equal angular grids) to SBFs located below each data point or below a subset of the data points. Moreover, the system of normal equations is much better conditioned, which often make regularization superfluous. Finally, it is shown that the approximation errors are smaller than when using standard SBF networks. © Springer-Verlag Berlin Heidelberg 2007.