Numerical Modeling of a Salt Intrusion Problem Inverting Vertical Electrical Soundings Via Global Optimization Methods and Kernel Learning Algorithms

Vertical electrical soundings (VES) is a low-cost geophysical method very well suited to the analysis and monitoring of salt-water intrusion problems, since this interface generates a low resistivity anomaly. One major drawback of all geophysical inverse problems is that they are ill-posed: the objective function has its minimum in a flat elongated valley or surrounded by many local minima. The shape of the cost function depends on the physics of the forward problem and on the signal to noise ratio. Thus, with no regularization methods these data uncertainties are amplified, and transmitted to the model parameters through the optimization algorithm, causing local optimization methods to give unpredictable results (if no prior information is available). This circumstance has traditionally generated mistrust on the practical use of geophysical inverse methods.

Stochastic approach of inverse problems consists in shifting attention to the probability of existence of certain interesting subsurface structures instead of "looking for the true model". The variable of interest is in this case the depth of the intrusion, defined by means of a resistivity threshold.

Global optimisation methods and kernel learning algorithms can be used to sample efficiently the model space and are very robust since they don't solve the optimization problem involved. In this contribution we apply different methods -particle swarm optimization, binary genetic algorithms, simulated annealing, differential evolution, support vector machines- to model a salt water intrusion problem in southern Spain, analyzing how the solution depends on the inversion algorithm used. This methodology is well suited to cases where very little or no prior information is available since the only information input by the modeller is the prismatic search space. This comparison gives important clues about the use of VES for salt water intrusion problems in coastal aquifers.