Comment on: 'Improving compact gravity inversion based on new weighting functions', by Mohammad Hossein Ghalehnoee, Abdolhamid Ansari and Ahmad Ghorbani

The recent paper of Ghalehnoee et al., 'Improving compact gravity inversion based on new weighting functions', discusses weighting functions for the compact inversion of gravity data. We studied the paper with great interest but deduced that the paper presents minor changes to already published methods. In the manuscript, the model weighting function is the product of three diagonal matrices, that is, a depth weighting matrix, a compactness constraint and a scaling matrix. The authors claim that the scaling matrix is new and introduce the notation 'kernel weighting'. Based on our knowledge and understanding of the ideas, not only all the matrix weighting matrices have been used before but also their combination has been used in many published research papers. Here we explain why we believe that the ideas in Ghalehnoee et al. are not new.