On the Optimization of the Inverse Problem for Bouguer Gravity Anomalies

Inverse modeling of gravity data presents a very ill-posed mathematical problem, given that solutions are non-unique and small changes in parameters (position and density contrast of an anomalous body) can highly impact the resulting Earth's model. Although implementing 2- and 3-Dimensional gravitational inverse problems can determine the structural composition of the Earth, traditional inverse modeling approaches can be very unstable. A model of the shallow substructure is based on the density contrasts of anomalous bodies -with different densities with respect to a uniform region- or the boundaries between layers in a layered environment. We implement an interior-point method constrained optimization technique to improve the 2-D model of the Earth's structure through the use of known density constraints for transitional areas obtained from previous geological observations (e.g. core samples, seismic surveys, etc.). The proposed technique is applied to both synthetic data and gravitational data previously obtained from the Rio Grande Rift and the Cooper Flat Mine region located in Sierra County, New Mexico. We find improvements on the models obtained from this optimization scheme given that getting rid of geologically unacceptable models that would otherwise meet the required geophysical properties reduces the solution space.