Particle swarm optimization applied to solving and appraising the streaming-potential inverse problem

Abstract

Water flow in the subsoil generates electrical currents measurable at the ground surface with the self-potential (SP) method. These measured potentials, which result from hydroelectric coupling, are called streaming potentials and are well correlated with the geometry of the water table. The particle swarm algorithm can be used to estimate the water-table elevation from SP data measured at the ground surface. The basic idea behind particle swarm optimization (PSO) is that each model searches the model space according to its misfit history and the misfit of the other models (particles) of the swarm. PSO is a simple, robust, and versatile algorithm with a very good convergence rate (typically before 3000 forward runs), and it can explore a large model space without being time consuming. Based on samples gathered in a low-misfit area, we have computed a fast approximation of the posterior distribution of the water table, the electrokinetic coupling constant, and the reference hydraulic head. Although PSO is a stochastic search technique, our convergence results, based on the stability of particle trajectories, specify clear criteria to tune PSO parameters.