THE SLEPIAN APPROACH REVISITED: DEALING WITH THE POLAR GAP IN SATELLITE BASED GEOPOTENTIAL RECOVERY

摘要

Global gravity field modeling is typically based on spherical harmonic expansion of the potential function. Surface spherical harmonics are globally defined and satisfy the orthogonality relations on the sphere. However, satellite ground tracks often leave out polar areas. Especially for the GOCE (Gravity field and steady-state Ocean Circulation Explorer) mission, a double polar cap with a radius of more than six degrees will not be covered by observation data. Based on recent developments we make use of the Slepian representation, i.e. band-limited base functions that are optimally concentrated within a spherical belt. In particular we review their unique calculation by means of commuting operators. Moreover, this approach results in a simple and fast method to transform to the band-limited base. We apply that approach to a simulated GOCE data set to investigate its benefit for geopotential recovery from satellite gravity gradiometry.