Practical Applications of Global Optimisation Techniques in 2-D Resistivity Inversion

The data collected from 2-D ERT surveys is usually inverted using a nonlinear local optimisation method such as the smoothness-constrained least-squares method. This method attempts to find the minimum of an objective function that consists of the data misfit and model roughness. The least-squares method converges rapidly to a minimum but it might be a non-optimal local minimum. A global optimisation method can locate the optimal global minimum but the calculation time increases exponentially with the number of parameters. A global optimisation method (simulated annealing) is used refine the model obtained by the least-squares method at the regularisation parameter value found by the L-curve method. Inversion of a data set from a 2-D survey over a levee at Colorno (Italy) shows that the simulated annealing method does locate an objective function minimum that is consistently lower than that found the least-squares method. Although the maximum difference is usually less than 10%, the refinement step serves as a check on the model found by the least-squares method. A method to estimate the optimum regularisation parameter using a best fitting analytic function to the numerical L-curve points where conventional methods might give ambiguous results is presented.