The incompleteness of the seismic data caused by missing traces along the spatial extension is a common issue in seismic acquisition due to the existence of obstacles and economic constraints, which severely impairs the imaging quality of subsurface geological structures. Recently, deep learningbased seismic interpolation methods have attained promising progress, while achieving stable training of generative adversarial networks is not easy, and performance degradation is usually notable if the missing patterns in the testing and training do not match. In this paper, we propose a novel seismic denoising diffusion implicit model with resampling. The model training is established on the denoising diffusion probabilistic model, where U-Net is equipped with the multi-head self-attention to match the noise in each step. The cosine noise schedule, serving as the global noise configuration, promotes the high utilization of known trace information by accelerating the passage of the excessive noise stages. The model inference utilizes the denoising diffusion implicit model, conditioning on the known traces, to enable high-quality interpolation with fewer diffusion steps. To enhance the coherency between the known traces and the missing traces within each reverse step, the inference process integrates a resampling strategy to achieve an information recap on the former interpolated traces. Extensive experiments conducted on synthetic and field seismic data validate the superiority of our model and its robustness to various missing patterns. In addition, uncertainty quantification and ablation studies are also investigated.

翻译：地震数据在空间延伸方向上因障碍物及经济约束导致的缺失道不完整性，是地震采集中的普遍问题，严重削弱了地下地质结构的成像质量。近年来，基于深度学习的地震插值方法取得了显著进展，但生成对抗网络的稳定训练较为困难，且当测试与训练缺失模式不匹配时，性能退化通常十分显著。本文提出了一种新颖的重采样地震去噪扩散隐式模型。模型训练基于去噪扩散概率模型，其中U-Net配备多头自注意力机制以逐步骤匹配噪声。余弦噪声调度作为全局噪声配置，通过加速通过过量噪声阶段，促进已知道信息的高效利用。模型推理阶段利用条件于已知道的去噪扩散隐式模型，以更少的扩散步数实现高质量插值。为增强每个反向步骤中已知道与缺失道之间的连续性，推理过程集成了重采样策略，实现前序插值道的信息回顾。在合成及野外地震数据上开展的大量实验验证了本模型的优越性及其对不同缺失模式的鲁棒性。此外，还进行了不确定性量化与消融研究。