VES and global optimisation methods: a different perspective to analyze equivalent models in applied geophysics

Abstract

The vertical Electrical Sounding problem is ill posed. Small data disturbances propagate backwards and contaminate notably the solution. Classical interpretation of the inverse problem as a parameter estimation case searches for a unique model. Yet, many models –known as equivalent models- are able to fit data equally well. Local optimization techniques provide unstable solutions, probably very different from the global minimum. Global optimization methods, are probabilistic strategies able to explore the whole model space and to find, asymptotically at least, the global minimum of the problem. Two of these techniques have been programmed, used and are described here: simulated annealing and genetic algorithms. Both are very important in the Bayesian concept of the inverse problem, better issued for practical engineering decision purposes. In the Bayesian framework, the goal is to determine the a posteriori probability distribution of the solution, given data and external a priori information. More interesting yet than their global convergence properties is the fact that, run in a certain way, they provide the sample needed to estimate this a posteriori p.d.f. Justification is given to the use of G.A for these purposes, both through synthetic reasoning and with a practical decision case related to a groundwater coastal intrusion problem in Murcia (Spain).