REAL EARTH BASED SPLINE FOR GRAVITATIONAL POTENTIAL DETERMINATION

Abstract

For computational reasons, the spline interpolation of gravitational potential is usually done in a spherical framework [3]. However, the increasing observational accuracy requires mathematical methods for geophysically more relevant surfaces. We propose a spline method with respect to the real Earth. The spline formulation reflects the specific geometry of a given regular surface. This is due to the representation of the reproducing kernel as a Newton integral over the inner space of a regular surface. The approximating potential functions have the same domain of harmonicity as the actual Earth’s gravitational potential. Moreover, this approach is a generalization to spherical kernels.