Potential Coefficients Recovery from the Spectra of the Full Space-Borne Gravity Gradient Tensor

Abstract

The solution of the satellite gradiometry problem is studied by the space-wise approach. Simple linear relations are derived between the spectral coefficients of six components of the gravity gradient tensor in the local north-oriented reference frame and the harmonic coefficients of the Earth’s potential. These relations are applied for solving numerically two inverse problems. One of them is simulating the spectra of all the gradiometry observables at the altitude h = 250 km of GOCE satellite on the basis of EGM96 geopotential model. The other problem is recovering a geopotential model from the spectrum of each GOCE observable. As a result, EGM96 model is fully “restored” from all the simulated spectra. From these spectra a number of interesting numerical results are obtained characterizing the behavior of the second order derivatives of the geopotential. The elaborated procedures can be propagated to constructing the expansions of the third and higher order geopotential derivatives from a geopotential model. They can be also utilized for modeling the gravity fields of the other planets and the Moon.