Multi-objective particle swarm optimization for multimode surface wave analysis

Obtaining S-wave velocity profiles by inverting Rayleigh wave dispersion curves is crucial for the Rayleigh wave exploration method. Rayleigh wave inversion is a highly nonlinear and multi-extremum problem; therefore, global optimization algorithms are superior to local optimization methods for this inversion problem. Higher modes of dispersion curves have deeper penetration, which can improve the inversion quality. This study utilizes the multi-objective particle swarm optimization (MOPSO) algorithm, rather than a traditional single-objective optimization algorithm, to obtain S-velocity profiles from Rayleigh wave multimode phase velocity dispersion curves. The uncertainty of the inversion parameters is evaluated through the morphology of the Pareto front and the standard deviation of the Pareto optimal solution set. This is the first application of MOPSO in solving the multimode Rayleigh wave phase velocity dispersion curves joint inversion problem. It inverts three synthetic datasets, compares the inversion results with the synthetic data, and then conducts a comparative analysis with the particle swarm optimization (PSO) algorithm and the multi-objective grey wolf optimization (MOGWO) algorithm in one of these synthetic models to evaluate the accuracy and stability of MOPSO to the joint inversion. In addition, this research inverts observed data from an expressway roadbed in Henan, China, to examine the applicability of MOPSO for the joint inversion of multimode dispersion curves. The MOPSO inversion closely yields S-wave velocity profiles that match the borehole data. The synthetic and observed data inversion results indicated that the MOPSO algorithm accurately inverts multimode dispersion curves.