GNGTS 2018 - 37° Convegno Nazionale

726 GNGTS 2018 S essione 3.3 for each method from which we select the best results. The results (Fig. 2) show that the FA clearly outperforms the other methods, since this algorithm is always able to provide a final CMP very similar to the reference CMP. In particular, the FA-CMPs could be used as a valid starting model for any local optimization method for a further refinement of the residual statics estimation. Differently, the ICA and QPSO outcomes are affected by many misalignments of the reflections and cycle-skipped traces especially for the 40-and 60-trace examples. In Fig. 3, we observe that the energy of the stack trace associated to the FA-CMP is always very close to the energy of the stack trace pertaining to the reference CMP, and also that the FA shows a rapid convergence toward the optimal solution. Differently, QPSO is always affected by premature convergence and entrapment in local minima, whereas ICA shows a much slower convergence rate than the other two methods. Conclusions. We tested three relatively new global optimizations methods on analytic objective functions and residual statics corrections. The three methods are the firefly algorithm, imperialist competitive algorithm and quantum particle swarm optimization. The tests on the analytic functions demonstrated that all the approaches are able to find the global minimum in case of regularly distributed minima, whereas the QPSO and particularly the ICA suffer in case of objective functions with complex topology (i.e. irregularly distributed minima). In addition, the ICA is characterized by a much slower convergence rate with respect to the other two algorithms. In the residual statics corrections, the FA clearly outperforms the other two methods. Indeed, this algorithm successfully converges even in high-dimensional model spaces and is also characterized by a very fast convergence rate. Currently, other tests are ongoing to compare the algorithms in other analytic objective functions and in other seismic optimization problems. References Atashpaz-Gargari, E., and Lucas, C. (2007). Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition. In Evolutionary computation Congress 2007, 4661-4667. Eberhart, R., and Kennedy, J. (1995). A new optimizer using particle swarm theory. In Proceedings of the sixth international symposium on micro machine and human science, 39-43. Hosseini, S., andAl Khaled,A. (2014).Asurvey on the imperialist competitive algorithmmetaheuristic: implementation in engineering domain and directions for future research. Applied Soft Computing, 24, 1078-1094. Sajeva, A., Aleardi, M., Galuzzi, B., Stucchi, E., Spadavecchia, E., and Mazzotti, A. (2017). Comparing the performances of four stochastic optimisation methods using analytic objective functions, 1D elastic full-waveform inversion, and residual static computation. Geophysical Prospecting, 65, 322-346. Sen, M. K., and Stoffa, P. L. (2013). Global optimization methods in geophysical inversion. Cambridge University Press. Sun, J., Feng, B., and Xu, W. (2004). Particle swarm optimization with particles having quantum behavior. In Evolutionary Computation, 2004, 1, 325-331. Yang, X. S. (2008). Firefly algorithm. Nature-inspired metaheuristic algorithms, 20, 79-90. Fig. 3. Energy curves representing the evolution of the energy of the stack trace (computed on the predicted CMP) over iterations for the three different algorithms and for the 20-, 40- and 60-trace tests.