Comment on “Three-dimensional potential field data inversion with L0 quasinorm sparse constraints” by Z. Meng, Geophysical Prospecting 66, 626-646

Abstract

The recent paper of Meng, “3D potential field data inversion with L0 quasi-norm sparse constraints” discuses application of a L0-norm constraint for reconstruction from potential field data. The L0-norm stabilizer makes it possible to reconstruct a sparse solution by the inversion algorithm. While the paper is very interesting, some aspects presented in the paper should be clarified. Most significantly, the L0-norm stabilizer was introduced as the compactness constraint by Last and Kubik (1983) for the inversion of gravity data. The method was further developed by Portniaguine and Zhdanov (1999) through the addition of prior model information, leading to the minimum support constraint. The combination of the L0-norm stabilizer with depth weighting has subsequently been used by a number of authors, as referenced, for example, in Pilkington (2009) and Vatankhah, Ardestani and Renaut (2015). The motivation for the L0-norm constraint presented inMeng (2018) is very close to that of the compactness or minimum support constraints. For the benefit of other readers in the following brief note, we expand on the relationship between these constraint conditions.