The effect of topographical and atmospheric masses on spaceborne gravimetric and gradiometric data

Abstract

Current satellite missions dedicated to global mapping of the Earth’s gravity field are providing accurate global models of the geopotential. Harmonic (Stokes) coefficients of the geopotential derived from satellite observations of its functionals, a potential gradient vector and/or gravity gradient tensor, correspond to the (time-averaged) gravitational potential that is generated by the geoid, topography and atmosphere. The manuscript deals with the effect of static topographical and atmospheric masses on spaceborne observations of the potential gradient vector and gravity gradient tensor that should be applied during their inversion into the geopotential at the geoid level. They would allow for derivation of a harmonic representation of the potential generated only by solid masses inside the geoid and ocean, i.e., harmonicity of the geopotential would apply to the entire space outside the geoid. The geopotential could be then synthesized without problems with diverging harmonic series, i.e., the fundamental condition for application of a truncated harmonic series everywhere outside the geoid would be met. Due to its large numerical values, compensation of topographical masses is outlined using a single-layer potential. Although not entirely sufficient from a geophysical point of view, this model is often applied in geoid-related computations. Corresponding parameters are evaluated in manners that are consistent with spatial resolution and accuracy of current spaceborne data using spherical harmonic representation of topographical heights and corresponding mass distributions. Theoretical formulations are followed by numerical evaluations.