Pattern search algorithms for nonlinear inversion of high-frequency Rayleigh-wave dispersion curves
Inversion of Rayleigh wave dispersion curves is challenging for most local-search methods due to its high nonlinearity and to its multimodality. In this paper, we implemented and tested a Rayleigh wave dispersion curve inversion scheme based on GPS Positive Basis 2N, a commonly used pattern search algorithm. Incorporating complete poll and complete search strategies based on GPS Positive Basis 2N into the inverse procedure greatly enhances the performance of pattern search algorithms because the two steps can effectively locate the promising areas in the solution space containing the global minima and significantly reduce the computation cost, respectively. The proposed inverse procedure was applied to nonlinear inversion of fundamental-mode Rayleigh wave dispersion curves for a near-surface shear (S)-wave velocity profile. The calculation efficiency and stability of the inversion scheme are tested on three synthetic models and a real example from a roadbed survey in Henan, China. Effects of the number of data points, the reduction of the frequency range of the considered dispersion curve, errors in P-wave velocities and density, the initial S-wave velocity profile as well as the number of layers and their thicknesses on inversion results are also investigated in the present study to further evaluate the performance of the proposed approach. Results demonstrate that pattern search algorithms applied to nonlinear inversion of high-frequency surface wave data should be considered good not only in terms of accuracy but also in terms of the computation effort due to their global and deterministic search process.
pattern search algorithms dispersion curves rayleigh waves surface waves generalized pattern search