Uma nova abordagem de otimização híbrida usando os algoritmos PSO, Nelder-Mead Simplex e o de clusterização K-means para inversão completa da forma da onda 1D

Abstract

Full Waveform Inversion (FWI) is formulated as a nonlinear optimization problem, which traditionally utilizes derivative-based local minimization methods to find the scalar field of physical properties of the subsurface that best represents the field seismic data. However, these methods have a high computational cost and a limited accuracy to local minima, in addition to suffering from a slow convergence rate (Cycle Skipping). Therefore, in this work, a two-phase hybrid optimization algorithm based on Derivative-Free Optimization (DFO) algorithms was developed. In the first phase, global minimization and the clustering technique are used, while in the second phase, local minimization is adopted. In phase 1, Particle Swarm Optimization (PSO) and K-means clustering algorithms were used. In phase2, the Adaptive Nelder-Mead Simplex (ANMS) was used. The new hybrid algorithm was named PSO-Kmeans-ANMS, in which the K-means is responsible for dividing the swarm of particles into two clusters at each iteration. This strategy aims to automatically balance the exploration and exploitation mechanisms of the parameter search space, allowing for finding more accurate solutions and, consequently, improving convergence. The proposed hybrid algorithm was validated on the set of 12 benchmark functions and then applied to the 1D FWI problem. The results of the PSO-Kmeans-ANMS were compared with those obtained by the classic PSO, modified PSO, and ANMS algorithms. The metrics used were the average execution time and the success rate, which accepted errors of up to ±4% of the optimal solution. In all validation experiments and in the application of the FWI, the PSO-Kmeans- ANMS algorithm showed satisfactory performance, providing precise and reliable results, which proves its robustness and computational efficiency. In addition, the application of this hybrid algorithm in the FWI provided a significant reduction in the computational cost, thus representing an important and promising result for the seismic area