Research on the Rayleigh Surface Wave Inversion Method Based on the Improved Whale Optimization Algorithm

Surface wave exploration is widely used in fields such as near‑surface exploration and engineeringsurveys because of its advantages of high resolution near the surface, non-destructive testing, convenient construction, and high-cost performance. Dispersion curve inversion is a key step isurface wave exploration, and the inversion accuracy of subsurface elastic parameters is heavily dependent on the inversion method. Similar to other geophysical inversion problems, dispersion curve inversion has inherent defects such as multiple parameters and multiple extreme values. Therefore, the use of linear methods has certain uncertainties and instability. From the perspective of global optimization nonlinearity, this paper introduces the whale optimization algorithm (WOA) and improves it. The three population update mechanisms of the WOA are independent of each other, so the global exploration and local development processes in the optimization phase can be run and controlled separately. In addition, WOA does not require the artificial setting of various control parameter values, which improves the efficiency of the algorithm and reduces the difficulty of application. However, the WOA application still has slightly lower convergence precision and result accuracy in dispersion curve inversion, so this paper also proposes an improved whale optimization algorithm (IWOA) based on WOA. IWOA optimizes the initialization of the population and adds adaptive weight coefficients to enrich the population information and improve the convergence ability and local search ability of the algorithm. To test the applicability and noise immunity of IWOA for dispersion curve inversion, the noise-free and noise-contaminated dispersion curves of three theoretical models were inverted with IWOA. IWOA was also applied to the study of multi-mode model dispersion curve inversion. At the same time, the particle swarm optimization (PSO) algorithm and WOA were also tested in the same inversion test to compare the performances of the PSO, WOA, and IWOA. The results of the above various experimental analyses show that IWOA has good applicability and noise immunity in the dispersion curve inversion of the theoretical model. The multi-mode dispersion curve inversion results show that IWOA is not only suitable for the inversion of multi‑mode data but also can significantly improve the accuracy of the inversion results. Compared with PSO and WOA, IWOA has a more stable convergence process and higher convergence accuracy. Finally, the measured data from the Arnarbæli area in Iceland (fundamental-mode surface wave data) and the Wyoming area in the United States (multi-mode surface wave data) were inverted to test the practicality of IWOA in inverting measured data. Analysis of measured data shows that IWOA is very suitable for the inversion of dispersion curves and can effectively quantitatively explain and solve practical engineering problems.