Inversion of Rayleigh wave dispersion curve based on beluga whale optimization algorithm

Rayleigh wave exploration is a crucial technique in engineering site investigation for obtaining subsurface stratigraphic information. Inverting its dispersion curve can effectively reveal underground structures. However, traditional global optimization algorithms exhibit significant limitations in dispersion curve inversion, including slow convergence, low accuracy, and a tendency towards premature convergence. These issues hinder the precise interpretation of stratigraphic information and impact the efficiency and reliability of engineering surveys. To address these challenges, this paper introduces a novel global optimization algorithm—Beluga Whale Optimization (BWO)—for Rayleigh wave dispersion curve inversion, aiming to improve inversion effectiveness and enhance performance. BWO achieves optimal solution finding by mimicking beluga whale swimming, predation, and falling behaviours. Compared to other heuristic algorithms, BWO demonstrates favourable performance in solving complex functions, offering superior performance and efficiency while ensuring high solution accuracy, convergence speed, and stability. When testing the theoretical model of BWO applied to dispersion curve inversion, first, four noise-free models were used to verify the feasibility of BWO for dispersion curve inversion; subsequently, 15% random noise was added to the models, demonstrating that BWO has strong anti-interference capability; finally, specific multi-mode dispersion data were used to test that BWO can be applied to multi-order dispersion curve inversion. During the inversion of noise-free, noise-containing, and multi-mode dispersion models, BWO was compared with the Particle Swarm Optimization (PSO) algorithm, which proved that BWO has superior inversion performance and can obtain higher-precision solutions. In the actual data testing, seismic data from Wyoming, USA, were used to verify BWO's capability in processing actual data. Results from theoretical model tests and analysis of field data indicate that BWO possesses characteristics of speed, high accuracy, stability, and strong practicality, making it effectively applicable for the quantitative interpretation of Rayleigh wave dispersion curves.