Identification of Higher-Mode Numbers in Dispersion Curves for Rayleigh Wave Inversion

Shear-wave velocity is a key parameter for subsurface material characterization, and Rayleigh wave inversion is widely used to retrieve S-wave velocity profiles in near-surface imaging and ambient noise tomography. While the fundamental mode is typically observable, higher modes are often absent or limited due to field conditions, complicating the inversion process. Existing frameworks require prior identification of mode numbers, which traditionally relies on either manual supervision or repeated inversions. Manual identification is susceptible to subjective errors and inefficiency, whereas repeated inversions depend heavily on the accuracy of the initial model, reducing robustness. To address these limitations, this study proposes a novel automatic method for higher-mode identification in Rayleigh wave dispersion curves using a broad learning network. The proposed method directly models the relationship between higher-mode dispersion curves and their corresponding mode numbers, leveraging the known mode number of the fundamental mode. Validation through numerical simulations and field data applications demonstrates its effectiveness in accurately identifying higher-mode numbers. Furthermore, inversion tests incorporating the identified mode numbers confirm that the proposed method enhances inversion reliability, mitigating the adverse effects of mode misidentification on S-wave velocity estimation. Although the method identifies only one mode number at a time and requires retraining when applied to new field data, the high training efficiency of the BL network enables rapid adaptation to different dataset. By providing a scalable and computationally efficient solution for multimodal dispersion curve inversion, this study advances subsurface exploration in geophysical applications.