Dual-Conditional Diffusion Model for Seismic Data Reconstruction: Integrating Observed Data and Sampling Matrix Constraints

Seismic exploration relies heavily on high-quality data acquisition, but practical limitations often result in incomplete seismic data, violating the Nyquist sampling theorem and introducing aliasing. The completeness and accuracy of data directly influence the effectiveness of subsequent processing and interpretation. Traditional methods rely on various assumptions, facing limitations when dealing with complex or highly sparse datasets. In contrast, recent advances in deep learning (DL), particularly generative models like generative adversarial networks (GANs) and diffusion models, learn the underlying distribution of data, enabling realistic reconstruction from incomplete data by capturing complex patterns. Among these, denoising diffusion probabilistic models (DDPMs) generate high-quality seismic reconstructions with greater stability and flexibility compared with GANs. However, challenges in generalization to new datasets remain. To enhance the generalization performance of DDPM, we propose a dual-conditional DDPM (Dual-CDDPM) that incorporates constraints from both observed data and a sampling matrix. Grounded in machine learning principles, we mathematically demonstrate its potential to improve generalization performance. Experiments conducted on both synthetic and field data further confirm its effectiveness in enhancing generalization and reconstruction accuracy.