Spaceborne gravimetry and gravity field recovery

As an integrated signal of mass transition and distribution, the Earth's gravity senses the inner and outer mass balance of the Earth. However gravity cannot be measured directly in space but can be derived from other measurements obtained by space vehicles. The dedicated gravity field satellite missions CHAMP, GRACE, and GOCE serve as spaceborne gravimeters by utilizing satellite-to-satellite tracking (SST) and satellite gravity gradiometry (SGG) techniques. In this decade of the geopotentials, these missions will serve different purposes with particular spatial and spectral resolutions. This paper introduces the usefulness of these missions, their impacts on the geosciences the measurement principles, and their implementations. These space sensors will provide a significant number of observations during their mission lifespans. Therefore, global gravity field recovery is a computationally demanding task. Several approaches aimed at this goal are discussed, namely the brute-force approach, the space-wise approach, the time-wise approach, and the proposed torus-based semi-analytical approach. The paper addresses the characteristics of each approach and focuses mainly on the torus-based semi-analytical approach, which can be used to derive the gravity field from any geopotential functional. In this approach, the structure of the normal matrix becomes block-diagonal which leads to a powerful and efficient recovery tool through the use of the fast Fourier transform (FFT). Important issues such as downward continuation, interpolation methods, and regularization approaches are also discussed. To demonstrate the feasibility and efficiency of the torus-based semi-analytical approach of gravity field determination in spaceborne gravimetry, disturbing potential data from CHAMP and GRACE and simulated GOCE gravity gradient tensor data are processed.