Accurately obtaining subsurface structural information is crucial for various applications such as resource exploration, engineering geological assessment, and seismic hazard prediction. Rayleigh wave dispersion curves, as geophysical data that carry rich information on subsurface medium properties, are widely inverted to estimate shear wave velocity, layer thickness, and other key parameters, thus providing detailed velocity structures of the underground structure. In practical applications, the stability, generalization capability, and computational efficiency of the dispersion curve inversion algorithm directly determine the quality of the reconstructed shear wave velocity profile. Therefore, developing high-precision and efficient inversion methods has long been a key research focus and challenge in surface wave data processing.

This paper proposes an intelligent inversion method for Rayleigh wave dispersion curves by integrating a self-attention mechanism with a Broad Learning System （BLS）. Within the BLS framework, the self-attention mechanism is employed to capture global dependencies, enabling dynamic weighting and deep fusion of the multi-modal features embedded in dispersion curves. This enhances the model’s ability to extract and represent sensitive frequency bands and deep-level features. The introduction of the self-attention mechanism not only improves the discriminative power of feature extraction, but also effectively mitigates the representational bottleneck of traditional shallow neural networks when modeling complex nonlinear mappings. Consequently, it further optimizes the high-dimensional nonlinear mapping relationship between dispersion data and shear-wave velocity parameters.

To systematically validate the effectiveness and reliability of the proposed method, comprehensive numerical simulation tests and real data tests are carried out in this study. Three typical geological models are adoped for numerical simulation: a velocity-increasing model, a model with a low-velocity weak interlayer, and a model with a high-velocity hard interlayer. Theoretical synthetic microtremor data are generated using passive source numerical simulation, and the phase shift method is employed to extract dispersion energy images from the synthetic microtremor data.

Dispersion curves of the fundamental mode alone are insufficient to fully and accurately characterize complex subsurface conditions, especially when resolving sharp velocity contrasts. Higher-mode surface waves, which exhibit distinct sensitivities to subsurface structures at different depths, can provide additional constraints on formation properties. Therefore, joint inversion of fundamental and higher-mode dispersion curves is essential for achieving higher inversion accuracy. Analyses of the cross-correlation functions and dispersion energy distributions of the three models revealed the following characteristics: ① in the velocity-increasing model, the microtremor signal is dominated by the fundamental-mode Rayleigh wave; ② in the model with a low-velocity weak interlayer, fundamental-mode Rayleigh wave energy is concentrated between 3−10 Hz, accompanied by significant higher-mode energy; ③ in the model with a high-velocity hard interlayer, the first higher-mode Rayleigh wave energy dominates whthin specific frequency bands. Based on these observations, a differentiated multi-mode joint inversion strategy was implemented: joint inversion of the fundamental and the first higher modes was applied to the velocity-increasing model and the high-velocity hard interlayer model, whereas joint inversion incorporating up to the third higher modes was adopted for the low-velocity weak interlayer model.

Inversion results for the three typical models were compared among the proposed method, the standard BLS, and the genetic algorithm （GA）. While the dispersion curves forward-calculated from all three algorithms showed good agreement with the theoretical curves, the attention-based BLS method yielded the smallest average relative errors. Furthermore, the average relative errors in both shear wave velocity and layer thickness derived from the multi-mode joint inversion are significantly lower than those obtained using the fundamental mode alone. Field passive source data were also used for surface wave inversion to validate the practical applicability of the proposed method. The results indicate that the attention-based BLS inversion achieves smaller average relative errors and superior stability. More importantly, the inverted shear wave velocity profile shows good consistency with the borehole logging data.

In conclusion, the attention-based BLS inversion method proposed in this paper not only provides a novel approach for the intelligent interpretation of surface wave dispersion curves, but also holds significant potential for engineering applications. This method is expected to be widely applicable in urban subsurface space detection, major engineering foundation evaluation, geohazard identification, and mineral resource exploration.