Representation of Regional Gravity Fields by Radial Base Functions

Abstract

The research aims at an investigation of the optimal choice of local base functions, to derive a regional solution of the gravity field. Therefore, the representation of the gravity field is separated into a global and a residual signal, which includes the regional details. To detect these details, a superposition of localizing radial base functions is used. The base functions are developed from one mother function, and modified by four parameters. These arguments can be separated into two coordinates, one scale factor and a shape parameter. The observations of a few residual gravity fields are simulated by orbit integration and the energy-balance technique, in order to test the current approach. After selecting a region of interest, the parameters of the base functions are estimated. In order to get the optimal positions, two searching algorithms are compared. In the first algorithm the scale factors are estimated, while the positions and shape parameters are fixed. This method requires no initial values, because of the linear, but ill-posed and maybe ill-conditioned problem, but usually a regularization is necessary. The second algorithm searches possible positions for one base function in each step, until a termination condition is fulfilled, and improves the positions and scale factors in one adjustment. The results in the second case are better and faster for the test fields, but they depend on the initial values, the number of iterations and an assumption of an approximate constant orbit height