Using Interior Point Method Optimization Techniques to Improve 2- and 3-Dimensional Models of Earth Structures

Abstract:

2- and 3-Dimensional models obtained from the inversion of geophysical data are widely used to represent the structural composition of the Earth and to constrain independent models obtained from other geological data (e.g. core samples, seismic surveys, etc.). However, inverse modeling of gravity data presents a very unstable and 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 model. Through the implementation of an interior-point method constrained optimization technique, we improve the 2-D and 3-D models of Earth structures representing known density contrasts mapping anomalous bodies in uniform regions and boundaries between layers in layered environments. The proposed techniques are applied to synthetic data and gravitational data obtained from the Rio Grande Rift and the Cooper Flat Mine region located in Sierra County, New Mexico. Specifically, we improve the 2- and 3-D Earth models by getting rid of unacceptable solutions (those that do not satisfy the required constraints or are geologically unfeasible) given the reduction of the solution space.