Seis-PDDN: Seismic Undersampling Design and Reconstruction Using Prior Distribution and Diffusion Null-Space Iteration

The acquisition and reconstruction of seismic data are fundamental to seismic exploration. The balancing data quality and acquisition cost is essential. To address this challenge, we propose Seis-PDDN, a novel framework that integrates edge-preserving piecewise undersampling design with diffusion null-space iteration, optimizing both survey design and data reconstruction. Seis-PDDN uses the prior distribution of seismic reflectivity to design a linear missing mask operator, guiding the undersampling process. Reconstruction is achieved through a diffusion null-space iteration, combining range-null space decomposition with a pretrained diffusion model, ensuring both consistency and fidelity in the reconstructed data. Extensive experiments on synthetic and public seismic shot gathers demonstrate that Seis-PDDN outperforms traditional random, jittered, and uniform sampling schemes. Further comparisons with other deep learning reconstruction methods confirm that Seis-PDDN achieves higher metrics in seismic reconstruction, especially with a spatial sampling rate as low as 10%. Overall, Seis-PDDN holds significant potential for advancing flexible, economical acquisition and accurate reconstruction in seismic exploration.