Deep Learning for Irregularly and Regularly Missing 3-D Data Reconstruction

Physical and/or economic constraints cause acquired seismic data to be incomplete; however, complete data are required for many subsequent seismic processing procedures. Data reconstruction is a crucial and long-standing topic in the exploration seismology field. We extended our previous works on deep learning (DL)-based irregularly and regularly missing 2-D data reconstruction to 3-D data. A key motivation is that the 3-D convolutional neural network (CNN) can take full advantage of the 3-D nature of the data, and the additional dimension allows more information to contribute to the data reconstruction. DL also avoids many assumptions (e.g., linearity, sparsity, and low-rank) limiting conventional nonintelligent reconstruction methods. We built an artificial neural network (ANN) based on an end-to-end U-Net encoder-decoder-style 3-D CNN. The ANN was trained on large quantities of various synthetic and field 3-D seismic data using a mean-squared-error (MSE) loss function and an Adam optimizer. We demonstrated that the developed 3-D CNN reconstruction method appears to outperform the 2-D CNN for 3-D restoration. We benchmarked the ANN's generalization capacity for recovery of irregularly and regularly sampled 3-D data on several typical seismic data sets, particularly those with high missing percentages or large gaps. An ANN trained with irregularly sampled data can be partly applied to regularly sampled cases. We investigated how a key parameter, i.e., the learning rate, can be experimentally determined. In the context of the presented examples, our methodology provided a substantial improvement over an open-source state-of-the-art rank-reduction-based approach in terms of data fidelity and efficiency.