Cross-gradients joint 3D inversion with applications to gravity and magnetic data

Abstract

We extend the cross-gradient methodology for joint inversion to three-dimensional environments and introduce a solution procedure based on a statistical formulation and equality constraints for structural similarity resemblance. We apply the proposed solution to the joint 3D inversion of gravity and magnetic data and gauge the advantages of this new formulation on test and field-data experiments. Combining singular-value decomposition (SVD) and other conventional regularizing constraints, we determine 3D distributions of the density and magnetization with enhanced structural similarity. The algorithm reduces some misleading features of the models, which are introduced commonly by conventional separate inversions of gravity and magnetic data, and facilitates an integrated interpretation of the models.

3D stochastic inversion of magnetic data

“…(2). By his definition, the total field anomaly caused at point (x 0 , y 0 , z 0 ) by prism j is given by Fregoso and Gallardo (2009): …”

3D stochastic joint inversion of gravity and magnetic data

“…Gravity and magnetic data were inverted also jointly by Pilkington (2006) where the model consists of an interface separating two layers with different, but constant, densities and magnetization. In Fregoso and Gallardo (2009), the authors propose using cross gradients for 3D inversion of gravity and magnetic data. Most of these methods directly, or indirectly, adapt the Tarantola and Valette (1982) techniques to the generalized minimization problem in a Bayesian framework.…”

Lithological Characterization and Its Application Based on Three-Dimensional Structure-Coupled Joint Inversion of Gravity and Magnetic Data

“…The cross-gradients criterion requires the minimization problem to satisfy the condition = 0 τ , which means that any spatial changes occurring in both models must lie in the same or in opposite direction [8] [9] [11]. This implies that if a common boundary exists, their gradients must be sensed in a parallel orientation regardless of the amplitude of the model parameter changes.…”

“…Following the robust statistical optimization algorithm framework developed by Fregoso and Gallardo [11], the inversion problem of minimizing the objective function subject to the given conditions is solved. The data and the discrete models are submitted into a general framework and are processed simultaneously.…”