Deep Learning for Regularly Missing Data Reconstruction

Inspired by image-to-image translation, we applied deep learning (DL) to regularly missing data reconstruction, aimed at translating incomplete data into their corresponding complete data. With this purpose in mind, we first construct a network architecture based on an end-to-end U-Net convolutional network, which is a generic DL solution for various tasks. We then meticulously prepare the training data with both synthetic and field seismic data. This article is implemented in Python based on Keras (a high-level DL library). We described the network architecture, the training data, and the training settings in detail. For training the network, we employed a mean-squared-error loss function and an Adam optimization algorithm. Next, we tested the trained network with several typical data sets, achieving good performances (even in the presence of big gaps) and validating the feasibility, effectiveness, and generalization capability of the assessed framework. The feature maps for a sample going through the well-trained network are uncovered. Compared with the f-x prediction interpolation method, DL performs better and is capable of avoiding several assumptions (e.g., linearity, sparsity, etc.) associated with conventional interpolation methods. We demonstrated the influences of the network depth, the kernel size of the convolution window, and the pooling function on the DL results. We applied the trained network to dense data reconstruction successfully. The proposed method can overcome noise to some extent. We finally discussed some practical aspects and extensions of the evaluated framework.