A hybrid method for geological and geophysical data with multi-peak distributions using the PSO–GRG algorithm

Abstract

To allow peak searching and parameter estimation for geological and geophysical data with multi-peak distributions, we explore a hybrid method based on a combination of the particle swarm optimization (PSO) and generalized reduced gradient (GRG) algorithms. After characterizing peaks using the additive Gaussian function, a nonlinear objective function is established, which transforms our task into a search for optimal solutions. In this process, PSO is used to obtain the initial values, aiming for global convergence, while GRG is subsequently implemented for higher stability. Iterations are stopped when the convergence criteria are satisfied. Finally, grayscale histograms of backscattering electron images of sandstone show that the proposed algorithm performs much better than other methods such as PSO, GRG, simulated annealing and differential evolution, achieving a faster convergence speed and minimal variances.