A Fast and Stable Projected Space Algorithm for Sparsity Inversion of Gravity Data

We develop a fast and stable inversion method to solve the underdetermined linear sparsity gravity inversion problem. A new sparsity constraint based on $L0$ norm is studied to improve the accuracy of the recovered block density. A projected space algorithm avoids the update of forward matrix in the general reweighted iterative method, whose operations are complex and time consuming. Another advantage of the proposed projected algorithm is that it is compatible with other fast gravity methods. A general iterative algorithm is applied to solve the general gravity inversion. This space algorithm projects the recovered density on the sparsity constraint. With the application of space algorithm, the large forward matrix is calculated once. A test of synthetic example demonstrates the advantages of inversion efficiency and accuracy. The application of real gravity obtained from Mobrun ore, northeast of Noranda, QC, Canada shows the practical value of the proposed inversion method. This novel study can be used in other geophysical inversions.