Uncertainty propagation through integral inversion of satellite gradient data in regional gravity field recovery

Abstract

The Gravity field and steady-state Ocean Circulation Explorer (GOCE) mission, launched by the European Space Agency, provided high-quality gravitational gradient data with near-global coverage, excluding polar regions. These data have been instrumental in regional gravity field modelling through various methods. One approach involves a mathematical model based on Fredholm’s integral equation of the first kind, which relates surface gravity anomalies to satellite gradient data. Solving this equation requires discretising a surface integral and applying further regularisation techniques to stabilise the numerical solution of a resulting system of linear equations. This study examines four methods for modifying the system of linear equations derived by discretising the Fredholm integral equation. The methods include direct inversion, remove-compute-restore, truncation reduction of the integral formula, and inversion of a modified integral for estimating surface gravity anomalies from satellite gradient data over a test area in Central Europe. Since the system of linear equations is ill-conditioned, the Tikhonov regularisation is applied to stabilise its numerical solution. To assess the precision and reliability of the estimated gravity anomalies, the study introduces mathematical models for estimation of biased and de-biased noise variance–covariance matrices of estimated surface gravity anomalies. The results indicate that the signal-to-noise ratio of reduced satellite gradient data in the remove-compute-restore method is smaller compared to other methods in the study, necessitating stronger stabilisation of the model to recover surface gravity anomalies. This, in turn, leads to a more optimistic uncertainty propagation than the other considered methods.