Differential evolution algorithm for nonlinear inversion of high-frequency Rayleigh wave dispersion curves

Abstract

Abstract In recent years, Rayleigh waves are gaining popularity to obtain near-surface shear (S)-wave velocity profiles. However, inversion of Rayleigh wave dispersion curves is challenging for most local-search methods due to its high nonlinearity and to its multimodality. In this study, we proposed and tested a new Rayleigh wave dispersion curve inversion scheme based on differential evolution (DE) algorithm. DE is a novel stochastic search approach that possesses several attractive advantages: (1) Capable of handling non-differentiable, non-linear and multimodal objective functions because of its stochastic search strategy; (2) Parallelizability to cope with computation intensive objective functions without being time consuming by using a vector population where the stochastic perturbation of the population vectors can be done independently; (3) Ease of use, i.e. few control variables to steer the minimization/maximization by DE's self-organizing scheme; and (4) Good convergence properties. The proposed inverse procedure was applied to nonlinear inversion of fundamental-mode Rayleigh wave dispersion curves for near-surface S-wave velocity profiles. To evaluate calculation efficiency and stability of DE, we firstly inverted four noise-free and four noisy synthetic data sets. Secondly, we investigated effects of the number of layers on DE algorithm and made an uncertainty appraisal analysis by DE algorithm. Thirdly, we made a comparative analysis with genetic algorithms (GA) by a synthetic data set to further investigate the performance of the proposed inverse procedure. Finally, we inverted a real-world example from a waste disposal site in NE Italy to examine the applicability of DE on Rayleigh wave dispersion curves. Furthermore, we compared the performance of the proposed approach to that of GA to further evaluate scores of the inverse procedure described here. Results from both synthetic and actual field data demonstrate that differential evolution algorithm applied to nonlinear inversion of high-frequency surface wave data should be considered good not only in terms of the accuracy but also in terms of the convergence speed.