Gradient Penalized Regularization for GRACE/GRACE-FO

Abstract:

Gravity estimation from satellite-satellite tracking is an ill-posed problem that requires regularization to stabilize the inversion. The choice of regularizer for a given inverse problem is driven by the nature of ill-posedness and the desired behavior of the regularized solution. The ill-posedness in GRACE/GRACE-FO gravity estimation is primarily driven by two factors: upward continuation of the potential which limits the observability of high frequency components, and orbital geometry that results in poor sensitivity to gradients along East-West direction. The commonly used technique in static and time-variable gravity estimation from GRACE/GRACE-FO is the standard L2-Tikhonov regularization with a heuristic constraint matrix. Here we report results from application of general regularization methods outside of the standard L2-Tikhonov penalty.

Gradient penalty schemes, such as H1-Tikhonov and Total Variation (TV), impose a penalty that naturally increases with higher spatial frequency and allow for greater control of the spectral and directional distribution of the penalty. H1-Tikhonov regularization promotes smoothing behavior, suppressing high-frequency components and spatially smearing the signal. In contrast, TV regularization suppresses stripes while retaining sharp edges without signal smearing but produces a peak-flattening effect since it favors piecewise constant solutions.

We present the results from the search for a hybrid regularizer that could preserve sharp edges and signal localization while avoiding the peak-flattening effect, potentially improving the regularized solutions.