Abstract Spatial undersampling is a common problem in actual seismic data due to limitations in seismic survey environments, which can be satisfactorily solved by data regularization. The convolution-based deep-learning reconstruction methods require fewer assumptions than the conventional reconstruction methods (e.g., Curvelet-domain and F-X domain data regularization methods). However, the traditional convolution methods are not suitable for the large percentages of missing data. In this study, we propose an improved partial convolution-based (PConv-based) deep-learning network to reconstruct the missing data, which is evolved from the conventional convolution-based (CConv-based) method. The U-net is used as deep learning network to analyze both PConv-based method and CConv-based method. The PConv-based method adopts a hierarchical, regional-learning mechanism to dynamically update the constrained convolution results for the sample matrix. Hence, the problem of poor amplitude preservation in the data reconstruction has been addressed when multiple consecutive traces are missing. The influence of data loss ratio on reconstruction algorithm is also discussed in this study. The numerical test demonstrates that the trained network is able to process a sample dataset with 50% data lost and largely eliminate the noises in the frequency-wavenumber domain caused by the missing data. This proposed method is further evaluated by actual data, and the results are better than those obtained from the Curvelet-domain method. Moreover, the dataset reconstructed by the PConv-based deep-learning network has a great agreement with the original dataset in terms of amplitude.

中文翻译：

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用于地震数据正则化的基于部分卷积的深度学习网络1

摘要 由于地震勘测环境的限制，空间欠采样是实际地震数据中普遍存在的问题，通过数据正则化可以很好地解决这个问题。基于卷积的深度学习重建方法比传统的重建方法（例如，Curvelet 域和 FX 域数据正则化方法）需要更少的假设。然而，传统的卷积方法不适合大比例的缺失数据。在这项研究中，我们提出了一种改进的基于部分卷积（PConv-based）的深度学习网络来重建丢失的数据，它是从传统的基于卷积（CConv-based）的方法演变而来的。U-net 用作深度学习网络来分析基于 PConv 的方法和基于 CConv 的方法。基于 PConv 的方法采用分层的，区域学习机制来动态更新样本矩阵的约束卷积结果。因此，当多个连续轨迹丢失时，数据重建中幅度保留差的问题已经得到解决。本研究还讨论了数据丢失率对重建算法的影响。数值测试表明，经过训练的网络能够处理丢失 50% 数据的样本数据集，并在很大程度上消除了由丢失数据引起的频波数域噪声。该方法通过实际数据进一步评估，结果优于Curvelet域方法。此外，基于 PConv 的深度学习网络重建的数据集在幅度上与原始数据集有很大的一致性。