3D smooth inversion of gravity data and estimation of optimum regularization parameter by unbiased predictive risk estimator (UPRE) method, case study: San Nicolas Sulfide Deposit, Mexico

Inversion of gravity data is one of the important steps in the interpretation of practical gravity data. The goal of 3D inversion is to estimate the density distribution of an unknown subsurface model from a set of known gravity observations measured on the surface. The inversion result can be obtained by minimization of Tikhonov objective function. Inversion of gravity data is an underdetermined and ill-posed problem. In addition, the non-uniqueness of the solution is the main issue of the inversion. One way to achieve a suitable model result in the inversion is to carry out the inversion with smoothness and smallness constraint. The determination of an optimal regularization parameter is highly important in gravity data inversion. Regularization parameter makes a trade-off between misfit and regularization function. In this paper, an attempt has been made to use Unbiased Predictive Risk Estimator (UPRE) method in selecting the best regularization parameter for 3D inversion of gravity data using Lanczos bidiagonalizatoin (LSQR) algorithm. The UPRE method has been adapted for the solution of inverse problems. The UPRE method is based on a statistical estimator of the mean squared norm of predictive value. In this method, the optimal regularization parameter minimizes the UPRE function. We have developed an algorithm for 3D inversion of gravity data that uses the UPRE method for choosing optimal regularization parameter, and then, the inverse problem is solved by the LSQR algorithm. To evaluate the reliability of the introduced method, the gravity data of a synthetic model contaminated by 5 percent random noise has been inverted using the developed method. The discrepancy principle method was also applied for comparison of its results with the UPRE results. Then, the algorithm was used for inversion of real gravity data obtained from San Nicolas deposit in Mexico. The results of three-dimensional (3D) inversion of gravity data from this sulfide deposit show that the LSQR algorithm can provide an adequate estimate of gravity density and geometry of subsurface structures of mineral deposits. A comparison of the inversion results with geological information clearly indicates that the proposed algorithm can be used for 3D inversion of gravity data to estimate precisely the density distribution and geometry of ore bodies. The obtained results indicate that the discrepancy method is weaker than UPRE method to choose regularization parameter, but the UPRE method finds a unique optimal regularization parameter. Finally, the introduced algorithm has been used for 3D inversion of gravity data from sulfide deposit in San Nicolas. The results are consistent with geological information.