Inversion of Rayleigh wave dispersion databased on variational modal decomposition football team training algorithm

In view of the triple challenges in the Rayleigh wave dispersion curve inversion algorithm, which has strong sensitivity, low convergence efficiency and poor noise robustness, The Football Team Training Algorithm (FTTA) is applied to the problem of dispersion curve inversion,; and proposes a Variational Football Team Training Algorithm, VFTTA)’s Rayleigh wave dispersion curve inversion method, which introduces variational modal decomposition (VMD) into the FTTA to build a hybrid inversion framework. The core innovation lies in: i) Constructing a three‑stage mapping mechanism for football training – to achieve efficient parameter space search through global collaborative collective training, regional optimization group training, and individual reinforcement additional training; ii) Design a VMD‑FTTA joint preprocessing system, FTTA is used to adaptively optimize VMD parameters to achieve optimal decomposition of the original signal and accurate extraction of the target mode, fundamentally suppressing noise interference and providing high‑fidelity input signals for inversion. This study first tested the performance of FTTA and VFTTA through two complex benchmark functions and then applied it to the inversion of noise‑containing and noise‑free base‑order and higher‑order dispersion curves designed under different geological conditions. The results show the effectiveness and reliability of VFTTA in dispersion curve inversion. Finally, the measured micro‑motion dispersion data in Nanjing area further verified that VFTTA has smaller fitting errors and higher stability compared with FTTA and PSO.