Learning Seismic Wavefield Structure from Regional Arrays with Self-Supervised Deep Learning

Miro Ronac Giannone , Stephen Arrowsmith, Eric Larson

Seismic wavefields recorded across regional arrays exhibit spatial structure governed by propagation physics, including phase alignment, apparent slowness, and source directionality. These properties underpin array processing, yet in sparsely sampled arrays the wavefield is only partially observed, making it difficult to determine how information is distributed across sensors. Particularly, it remains unclear which stations provide the strongest constraints on the wavefield and how spatial coherency can be exploited when inter-station redundancy is limited. In this study, we introduce a U-Net–inspired convolutional-Transformer model that learns an implicit representation of the seismic wavefield from partial array observations through self-supervised reconstruction. We show that the model captures physically meaningful, array-consistent structure, across both body and surface waves as evidenced by improved agreement with ground-truth back azimuth from frequency-wavenumber analysis in challenging reconstruction scenarios. The model further demonstrates robustness to complex waveform conditions, including multi-event windows, temporally offset arrivals, and component-specific transient noise, which it suppresses in favor of coherent wavefield energy. Attention-based analysis reveals that spatially isolated sensors contribute disproportionately useful information for reconstruction, reflecting their unique geometric constraints. These results indicate that our model learns a representation of seismic wavefields with implications for sparse array analysis and future sensor network design.