Sparse regularization of inverse gravimetry—case study: spatial and temporal mass variations in South America

Abstract

Sparse regularization has recently experienced high popularity in the inverse problems community. In this paper, we show that a sparse regularization technique can also be developed for linear geophysical tomography problems. For this purpose, we adapt a known matching pursuit algorithm. The main theoretical features (existence, stability, and convergence) of the new method are given. We also show further properties of some trial functions which we use. Moreover, the algorithm is applied to a static and a monthly varying gravitational field of South America which yields spatial and temporal variations in the mass distribution. The new approach represents essential progress in comparison to a corresponding wavelet method, which is not flexible enough for the use of heterogeneous data, and a respective spline method, where the resolution cannot exceed approximately 104 basis functions due to experienced numerical problems with the ill-conditioned and dense matrix. The novel sparse regularization technique does not require homogeneous data and is not limited in the number of basis functions due to its iterative algorithm.