Seismic trace interpolation via score-based diffusion model with wavelet convolution

Seismic trace interpolation is a pivotal procedure in seismic data processing. The existing deep-learning interpolation methods necessitate masks during the training process, and the type of mask utilized for training should align with the missing type of test data. Any discrepancy may result in a substantial drop in interpolation performance, or even complete interpolation failure. To overcome this limitation, we leverage the score-based diffusion model, namely the noise conditional score network (NCSN), for seismic trace interpolation. NCSN learns data distribution through score matching, allowing neural networks to capture data priors without being affected by mask forms, thus enabling the recovery of data lost in any form. However, vanilla convolutions in NCSN excel at extracting local features but struggle with capturing global representations. To address this issue, we design a wavelet convolution (WC) operator that can simultaneously capture and process information in both spatial and spectral domains. This WC operator can be seamlessly integrated into any part of NCSN, enabling NCSN to possess both local and global receptive fields. Consequently, the NCSN embedded with WC demonstrates strong representation capabilities for both the details and overall trends of seismic events. Synthetic and field experimental results demonstrate that our WC-NCSN excels in flexibly handling missing forms and achieving high interpolation accuracy, all with just a single maskless training. Nevertheless, the inference process of NCSN leads to relatively low computational efficiency for our method. Future research may focus on reducing computational complexity.