In this paper, we present a modified version of the Pereyra–Rosen algorithm to the solution of ill-conditioned linear and nonlinear inverse problems arising in gravimetry. We perform a sensitivity analysis of the solution to the two main tuning parameters of this algorithm, comparing its solution with LSQR and the truncated SVD. First, we show the application to a general-purpose linear system whose system matrix has been created by conditional simulation and whose solution is known and to a synthetic 1D gravimetric problem for two different geological set-ups (smooth Gaussian and blocky geophysical anomalies) in the noise-free and noisy cases. The Pereyra–Rosen algorithm provides very good results using a reduced number of column vectors of the system matrix. We finally show the fast inversion of a real gravity profile in the Atacama Desert (north Chile). The algorithm is well suited for the solution of large-scale ill-conditioned linear problems as the ones encountered in the fine discretization of continuous linear inverse problems in several dimensions and in the iterative linearization of nonlinear inverse problems in several fields of geosciences.
$\bullet$ Implementation of a modified Pereyra–Rosen algorithm and its application to find the solution of linear ill-conditioned systems that arise in integral equations, in different geophysical linear inverse problems, and in the linearization of nonlinear inverse problems.
$\bullet$ Comparation of the modified Pereyra–Rosen algorithm with LSQR and SVD algorithms for different synthetic problems with and without noise in data.
$\bullet$ Sensitivity analysis of the Pereyra–Rosen algorithm, depending to the values of the ORTP and SUPER parameters in order to obtain good solutions.
$\bullet$ Application of Pereyra–Rosen algorithm, LSQR and the truncated SVD algorithms methods to a nonlinear inverse problem in gravity inversion with real data from the Atacama Desert, observing similar results for all of them.
Volume 130, 2021
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