Customizing constraint incorporation in direct current resistivity inverse problems: A comparison among three global optimization methods

Abstract

One-dimensional forward modeling in direct current (DC) resistivity is actually computationally inexpensive, allowing the use of global optimization methods (GOMs) to solve 1.5D inverse problems with flexibility in constraint incorporation. GOMs can support computational environments for quantitative interpretation in which the comparison of solutions incorporating different constraints is a way to infer characteristics of the actual subsurface resistivity distribution. To this end, the chosen GOM must be robust to changes in the cost function and also be computationally efficient. The performance of the classic versions of the simulated annealing (SA), genetic algorithm (GA), and particle swarm optimization (PSO) methods for solving the 1.5D DC resistivity inverse problem is here compared using synthetic and field data. The main results are as follows: (1) All methods reproduce synthetic models quite well, (2) PSO and GA are comparatively more robust to changes in the cost function than SA, (3) PSO first and GA second present the best computational performances, requiring less forwarding modeling than SA, and (4) GA gives higher performance than PSO and SA with respect to the final attained value of the cost function and its standard deviation. From our experience, to put them into effective operation, the methods can be classified from easy to difficult in the order PSO, GA, and SA as a consequence of robustness to changes in the cost function and of the underlying simplicity of the associated equations. To exemplify a quantitative interpretation using GOMs, we compare solutions with least-absolute and least-squares norms of the discrepancies derived from the lateral continuity constraints of the log-resistivity and layer depth as a manner of detecting faults. GOMs additionally provide the important benefit of furnishing not only the best solution but also a set of suboptimal quasisolutions from which uncertainty analyses can be performed.