DispFormer: A Pretrained Transformer Incorporating Physical Constraints for Dispersion Curve Inversion

TL;DR

DispFormer is a transformer-based neural network that efficiently inverts dispersion curves for subsurface shear-wave velocity estimation, handling variable data lengths and incorporating physical constraints, thus outperforming traditional and existing deep learning methods.

Contribution

This paper introduces DispFormer, a novel physics-informed transformer model for dispersion curve inversion that works with variable-length data and requires minimal labeled data, advancing geophysical inversion techniques.

Findings

Zero-shot DispFormer outperforms interpolated reference models.

Few-shot training surpasses traditional global search methods.

Model generalizes well to real-world dispersion data.

Abstract

Surface wave dispersion curve inversion is crucial for estimating subsurface shear-wave velocity (vs), yet traditional methods often face challenges related to computational cost, non-uniqueness, and sensitivity to initial models. While deep learning approaches show promise, many require large labeled datasets and struggle with real-world datasets, which often exhibit varying period ranges, missing values, and low signal-to-noise ratios. To address these limitations, this study introduces DispFormer, a transformer-based neural network for $v_s$ profile inversion from Rayleigh-wave phase and group dispersion curves. DispFormer processes dispersion data independently at each period, allowing it to handle varying lengths without requiring network modifications or strict alignment between training and testing datasets. A depth-aware training strategy is also introduced, incorporating physical constraints derived from the depth sensitivity of dispersion data. DispFormer is pre-trained on a global synthetic dataset and evaluated on two regional synthetic datasets using zero-shot and few-shot strategies. Results show that even without labeled data, the zero-shot DispFormer generates inversion profiles that outperform the interpolated reference model used as the pretraining target, providing a deployable initial model generator to assist traditional workflows. When partial labeled data available, the few-shot trained DispFormer surpasses traditional global search methods. Real-world tests further confirm that DispFormer generalizes well to dispersion data with varying lengths and achieves lower data residuals than reference models. These findings underscore the potential of DispFormer as a foundation model for dispersion curve inversion and demonstrate the advantages of integrating physics-informed deep learning into geophysical applications.