Unsupervised anti-aliasing interpolation of regularly sampled seismic data via soft dynamic time warping divergence distance

Due to the lack of labeled data in field seismic data acquisition, unsupervised methods have gained widespread attention in recent years. Most existing unsupervised interpolation methods rely solely on the L₂ norm for loss calculation on the sampled data, lacking appropriate constraints on the interpolated data. This limitation leads to poor performance for regularly subsampled seismic data with strong spatial aliasing. To address this issue, we propose an unsupervised interpolation method based on the Soft Dynamic Time Warping Divergence (SDTWD) distance. The proposed method constrains the interpolated data by minimizing the SDTWD distance. This is a differentiable misfit measurement between the interpolated trace and its neighboring sampled traces. We enhance the network's feature extraction capability by incorporating a Simple, Parameter-Free Attention Module (SimAM) into the conventional UNet architecture. Moreover, we integrate the reinsertion step of Projection Onto Convex Sets (POCS) algorithm into the network's iterative process to further improve interpolation quality. Tests on both synthetic and field datasets demonstrate the superiority of the proposed method compared to the traditional f-x prediction filtering method and unsupervised methods based on deep image priors.