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 usual algorithm 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. This method has some drawbacks if the reference model is incorrect, leading to a wrong inverse solution. 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 via Particle Swarm Optimization (PSO). We show its application to a synthetic case in gravimetric inversion, performing at the same time the uncertainty analysis of the solution, which serves to improve the knowledge inferred about the geophysical anomalies. The application in real data to detect cavities has been also performed with excellent results.