Total variation regularized solution of the satellite gravity inverse problem

The Gravity Recovery and Climate Experiment (GRACE) and its successor GRACE-Follow On (GRACE-FO) are satellite-satellite tracking missions which enabled precise measurement of the time-variable gravity and mass change on the Earth and have been critical in improving our understanding of Earth system processes in hydrology, oceanography and the cryosphere. The estimation of time-variable gravity from spaceborne measurements, such as GRACE(-FO), constitutes an ill-posed inverse problem, which results in large errors in the unconstrained solutions. The common approach to stabilizing the inversion has been L₂-Tikhonov regularization using heuristic spatially varying constraint matrices. The design of the constraint matrix requires substantial expertise in interpretation of the signal content in geophysical model outputs or the GRACE(-FO) data. In this dissertation, Total Variation (TV) regularization is demonstrated to be an effective alternative penalty for the GRACE(-FO) gravity estimation problem that does not require the use of an expertly designed constraint matrix. The TV penalty preferentially suppresses the poorly observed high-frequency modes in the solution and promotes edge-preservation and signal localization in the solution. This facilitates the recovery of the mass change signal with limited leakage error, without the need for explicit spatial constraints. Three approaches to regularized estimation of mass change are explored – post-processing of unconstrained estimates, inversion using a spherical harmonic intermediary, and inversion from a direct mapping between mass anomalies and observations. The post-processing framework demonstrates the efficacy of TV regularization in suppressing high-frequency noise and recovering the spatial variability in the mass change signal with limited leakage. TV-regularized estimates of mass anomalies from range rate measurements are derived using a spherical harmonic intermediary. Iterative refinement is performed to reduce signal amplitude loss due to regularization bias, particularly in regions with large trends. The timeseries of mass change estimates generated using TV regularization are consistent with the L₂-Tikhonov mascons presently used by the GRACE(-FO) community in terms of spectral characteristics, long-wavelength modes, spatial distribution of the annual and trend signals, and the temporal evolution of aggregate total mass over basins of interest. TV-regularized estimation using direct mapping between the mass anomalies and range acceleration is also discussed, including results from a simulation performed to assess the behavior of the regularization scheme without being constrained by the limitations of flight data quality. Due to the absence of explicit spatial constraints, the TV regularization scheme exposes the inherent spatial variability in the data, without any preconceptions. While the validation presented here is based on agreement with the L₂-Tikhonov mascons, regional differences between the two solutions could be informative and offers a new pathway for investigation of mass change within the GRACE(-FO) community.