Recovering the earthʹs potential spectral characteristics from GOCE mission Original Research Article

GOCE mission will allow to measure the diagonal components of the gravity gradient tensor. In order to recover from them the coefficients Cn,m of the Earthʹs disturbing potential T by the space-wise approach different procedures have been elaborated. In particular, the second order derivatives Tij with respect to the local north-oriented coordinates {x, y, z} are expanded in the series of biorthogonal harmonics or pure-spin spherical harmonic tensors. However the derived formulas for Cn,m are complicated for practical implementation. In the present paper an alternative, more simple approach is developed on the basis of the standard spherical functions. The potential derivatives with respect to coordinates x, y, z are expressed in terms of the ones related to the local orbital triad {u, v, w} and then Txx, Tyy and Tzz are treated as the observables. Mathematical models are derived for evaluating Cn,m by the least squares (LS) adjustment on the basis of the observable Txx and the modified observable sin2 θTyy. A basic relation is derived between the spectra of T and of the latter. The spectral coefficients and the degree variances are evaluated for sin2 θTyy at GOCE mission altitude 250 km. The present results will allow, at the next stage, to establish the relationships between the spectrum of T and the ones for Txx and Tyy. On the basis of them one will be able to simulate these observables from a geopotential model and, inversely, recover the potential coefficients from the diagonal potential derivatives.