Anomaly shape inversion via model reduction and PSO

Most of the geophysical inverse problems in geophysical exploration consist in detecting, locating and outlining the shape of geophysical anomalous bodies imbedded into a quasi-homogeneous background by analyzing their effect in the geophysical signature. The inversion algorithm that is currently used creates a very fine mesh in the model space to approximate the shapes and the values of the anomalous bodies and the geophysical structure of the geological background. This approach results in discrete inverse problems with a huge uncertainty space, and the common way of stabilizing the inversion consists in introducing a reference model (through prior information) to define the set of correctness of geophysical models. We present a different way of dealing with the high underdetermined character of this kind of problems, consisting in solving the inverse problem using a low dimensional parameterization that provides an approximate solution of the anomaly via Particle Swarm Optimization (PSO). This methodology has been designed for anomaly detection in geological set-ups that correspond with this kind of problem. We show its application to synthetic and real cases in gravimetric inversion performing at the same time uncertainty analysis of the solution. We have compared two different parameterizations for the geophysical anomalies (polygons and ellipses), showing that we have obtained similar results. This methodology outperforms the common least squares method with regularization.