A new hybrid optimization approach using PSO, Nelder-Mead Simplex and Kmeans clustering algorithms for 1D Full Waveform Inversion

The FWI is formulated as a nonlinear optimization problem that traditionally uses local (derivative-based) minimization to find the scalar field of properties that best represents the field seismic data. This problem has a high computational cost and accuracy limited to local minima, in addition to suffering from a slow convergence rate (Cycle Skipping). Therefore, we developed a two-phase hybrid optimization algorithm based on DFO algorithms. The first use global minimization and clustering technique. The second use local minimization. In phase 1 we adopted the modified PSO and K-means algorithms and in phase 2, we adopted the ANMS. We call the hybrid algorithm of the PSO-Kmeans-ANMS. Where K-means is responsible for dividing swarms of particles into 2 clusters at every instant. This strategy aims to automatically balance the mechanisms of exploration and exploitation of the parameter search space by the hybrid algorithm, allowing one to find more precise solutions and consequently improving its convergence. The PSO-Kmeans-ANMS algorithm was validated on the set of 12 benchmark functions and applied to the FWI 1D problem. We compared PSO-Kmeans-ANMS with classic PSO, modified PSO, and ANMS algorithms. The metrics used were are the average execution time and the success rate (an error of ± 4% of the optimal solution). In all validation experiments and the FWI application, the PSO-Kmeans-ANMS performed well in terms of robustness and computational efficiency. In the case of FWI, there was a significant reduction in computational cost, thus presenting a relevant result.