A partial convolution-based deep-learning network for seismic data regularization1

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.

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