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A fast algorithm for solving the under-determined 3-D linear gravity inverseproblem based on the randomized singular value decomposition (RSVD) isdeveloped. The algorithm combines an iteratively reweighted approach for$L_1$-norm regularization with the RSVD methodology in which the large scalelinear system at each iteration is replaced with a much smaller linear system.Although the optimal choice for the low rank approximation of the system matrixwith m rows is q=m, acceptable results are achievable with q<<m. In contrast tothe use of the LSQR algorithm for the solution of the linear systems at eachiteration, the singular values generated using the RSVD yield a goodapproximation of the dominant singular values of the large scale system matrix.The regularization parameter found for the small system at each iteration isthus dependent on the dominant singular values of the large scale system matrixand appropriately regularizes the dominant singular space of the large scaleproblem. The results achieved are comparable with those obtained using the LSQRalgorithm for solving each linear system, but are obtained at reducedcomputational cost. The method has been tested on synthetic models along withthe real gravity data from the Morro do Engenho complex from central Brazil.

A fast algorithm for regularized focused 3-D inversion of gravity data using the randomized SVD