A Posteriori Inference of Model Parameters in a Geophysical Inverse Problem Using GA

In this paper we present the application of binary genetic algorithms to the solution and analysis of the Vertical Electrical Sounding (VES) inverse problem. The goal of this technique is to estimate the resistivities and thicknesses of the strata in a multilayered earth, this having important environmental applications. In the inverse problem models are calculated so as to minimize the misfit between observed and theoretical predictions. The VES misfit function usually shows its minima along elongated and narrow valleys in the parameter space. Classical local optimization techniques are very likely to wander impredictably among these equivalent solutions. On the other hand global optimizacion methods can be used to explore the model space following some probabilistic rules. Thus, they could serve to sample the interesting region of the model space according to the ‘a posteriori’ distribution (a.p.d). In a Bayesian framework the a.p.d is related inversely to the misfit function so that models with low misfit are the most likely. We analyze the performance of a binary genetic algorithm for approaching this a.p.d, studying its behavior in some analytical test cases and comparing the results with those obtained by means of Simulated Annealing Finally we focus the results in a decision making framework analysis of a salt water intrusion problem in South Spain.