Different radial basis functions and their applicability for regional gravity field representation on the sphere

Global gravity field solutions are commonly modelled in spherical harmonic basis functions. Additionally, radial basis functions on the sphere with quasi-local support are used to model regional refinements of gravity fields. However, these functions are usually not orthogonal on a sphere, which makes the modelling process more complex. In this paper we study and compare different radial basis functions and their performance in regional gravity field modelling on the sphere by making use of simulated data. In addition to the type of radial basis function also the size of the study area on the sphere, the point grid, the margins and the method which is used to solve the singular system have to be taken into account. The synthetic signal, which we use in our simulation, is a residual signal in a bandwidth which corresponds to the bandwidth of GOCE satellite gravity observations. © 2013 Springer-Verlag Berlin Heidelberg.