Inversion of Rayleigh Wave Dispersion Curves via BP Neural Network and PSO

Abstract

Rayleigh wave analysis serves as a critical tool for subsurface characterization in geotechnical engineering and geophysical exploration, while reconstructing stratigraphic velocity profiles from dispersion curves remains challenging due to inherent nonlinearity and solution multiplicity. This study proposes a hybrid inversion framework integrating a backpropagation (BP) neural network with particle swarm optimization (PSO). A statistically representative training database encompassing realistic stratigraphic configurations is systematically established through random perturbation of shear-wave velocity profiles. Then, a BP neural network is employed to establish the nonlinear correspondence between dispersion curves and stratum-specific shear-wave velocity profiles. The trained BP neural network demonstrates computational efficacy in generating geophysically plausible velocity estimates, albeit with limited spatial resolution. These network-derived models serve as physics-informed initial inputs for the subsequent PSO inversion framework, forming a dual-phase inversion framework. This synergistic methodology specifically targets two persistent challenges in geophysical parameter estimation: (i) the non-iterative nature of standard BP architectures that restricts progressive model improvement, and (ii) the suboptimal search efficiency of standalone PSO implementations when initialized without physically meaningful constraints. Benchmark synthetic experiments confirm the enhanced robustness of the dual-phase inversion framework, exhibiting a significant reduction in mean relative error compared to BP neural network and PSO under controlled noise conditions. Furthermore, field implementation at the Baotou–Yinchuan railway site successfully identified weak interlayers, as confirmed by the borehole data.