Comparison of least-squares and simulated annealing to estimate fault parameters from airborne gravity gradiometry

Abstract

The inverse problem of estimating parameters (e.g., size, depth) of subsurface structures can be considered as an optimization problem where the parameters of a constructed forward model are estimated from observations collected on or above the Earth’s surface by minimizing the difference between the predicted model and the observations. Traditional solutions based on gradient-based approaches applied to nonlinear and non-unique problems basically depend on the initial conditions and may not always converge to the global minimum of the cost function if the starting model is far away from the true model. Alternatives to these straightforward approaches are innovative methods such as random search techniques that operate directly on the nonlinear models. This study compares a Monte-Carlo optimization method called Simulated Annealing (SA) to the Least-Squares Solution (LESS) within the general Gauss-Helmert formulation to estimate the parameters of a dip-slip fault from gravity gradient measurements as might be collected on profiles surveyed by an airborne system. It is shown that the SA algorithm is a more robust technique with respect to initial conditions in that it proceeds more comprehensively in parameter space and converges to their true values and thus the global minimum of the cost function. The SA algorithm is able to estimate the parameters of the fault as well as or better than LESS, and in the presence of significant background geologic and observation noise.