Inversion of Gravity Anomalies Using Primal-Dual Interior Point Methods

Structural inversion of gravity datasets based on the use of density anomalies to derive robust images of the subsurface (delineating lithologies and their boundaries) constitutes a fundamental non-invasive tool for geological exploration. The use of experimental techniques in geophysics to estimate and interpret differences in the substructure based on its density properties have proven efficient; however, the inherent non-uniqueness associated with most geophysical datasets make this the ideal scenario for the use of recently developed robust constrained optimization techniques. We present a constrained optimization approach for a least squares inversion problem aimed to characterize 2-Dimensional Earth density structure models based on Bouguer gravity anomalies. The proposed formulation is solved with a Primal-Dual Interior-Point method including equality and inequality physical and structural constraints. We validate our results using synthetic density crustal structure models with varying complexity and illustrate the behavior of the algorithm using different initial density structure models and increasing noise levels in the observations. Based on these implementations, we conclude that the algorithm using Primal-Dual Interior-Point methods is robust, and its results always honor the geophysical constraints. Some of the advantages of using this approach for structural inversion of gravity data are the incorporation of a priori information related to the model parameters (coming from actual physical properties of the subsurface) and the reduction of the solution space contingent on these boundary conditions.