Regularization parameter selection in the 3D gravity inversion of the basement relief using GCV: A parallel approach

Abstract

In this study, we present a computationally efficient automatic method for the optimal selection of the regularization parameter in the 3D inversion of gravity data. We use a linearized inversion method to estimate the depth of a 3D sedimentary basin in which the density contrast varies parabolically with the depth. The sedimentary basin is discretized into rectangular juxtaposed prisms with thicknesses that represent the depths from the surface to the interface and are the parameters to be estimated in the inversion process from the gravity anomaly.To deal with the singularity of the normal equation matrix in the linearized least squares method, standard-form Tikhonov regularization is incorporated in each step. The Generalized cross-validation (GCV) technique, which is capable of finding the optimal regularization parameter in an automatic manner, is adopted in this study. We present the simulation results with a synthetic model of a complex sedimentary basin, taking advantage of a parallel inversion algorithm implemented by adopting the message passing interface (MPI) standard on a multi-core cluster. This makes it possible to reduce the computer time by more than one order of magnitude. The applicability and efficacy of the GCV technique for the selection of the optimum regularization parameter are demonstrated.