Satellite gradiometry using a satellite pair

Abstract.

The GRACE mission has substantiated the low–low satellite-to-satellite tracking (LL-SST) concept. The LL-SST configuration can be combined with the previously realized high–low SST concept in the CHAMP mission to provide a much higher accuracy. The line of sight (LOS) acceleration difference between the GRACE satellite pair, the simplest form of the combined observable, is mostly used for mapping the global gravity field of the Earth in terms of spherical harmonic coefficients. As an alternative observable, a linear combination of the gravitational gradient tensor components is proposed. Being a one-point function and having a direct relation with the field geometry (curvature of the field at the point) are two noteworthy achievements of the alternative formulation. In addition, using an observation quantity that is related to the second-instead of the first-order derivatives of the gravitational potential amplifies the high-frequency part of the signal. Since the transition from the first- to the second-order derivatives includes the application of a finite-differences scheme, the high-frequency part of the noise is also amplified. Nevertheless, due to the different spectral behaviour of signal and noise, in the end the second-order approach leads to improved gravitational field resolution. Mathematical formulae for the gradiometry approach, for both linear and higher-degree approximations, are derived. The proposed approach is implemented for recovery of the global gravitational field and the results are compared with those of LOS acceleration differences. Moreover, LOS acceleration difference residuals are calculated, which are at the level of a few tenths of mGal. Error analysis shows that the residuals of the estimated degree variances are less than 10⁻³. Furthermore, the gravity anomaly residuals are less than 2 mGal for most points on the Earth.