CCNet-5D: 5D convolutional neural network for seismic data interpolation

Abstract

Convolutional neural network (CNN)-based seismic interpolation methods recover missing traces by feeding corrupted data to a trained neural network, whose parameters are obtained by training pairs of corrupted data and their complete labels. Compared with traditional reconstruction approaches, these methods require less human-computer interaction and computation time; therefore, CNN approaches have been popular for 2D/3D seismic interpolation. Five-dimensional seismic data interpolation methods recover missing traces simultaneously in five dimensions, considering all the physical coordinates with high accuracy. Unfortunately, existing deep-learning frameworks (such as TensorFlow and PyTorch) only provide low-dimensional convolution operators (no more than three dimensions), which makes it difficult to generalize to 5D seismic reconstruction directly. To this end, we develop an effective 5D-CNN by cascading low-dimensional convolution to deal with 5D seismic interpolation, referred to as the CCNet-5D. First, based on the definition of convolution and the theory of tensor decomposition, the 5D convolution operator is approximated by the sum of multiple cascading of low-dimensional convolution operators. Then, we determine the CNN architecture for the 5D convolutional operators by cascading the 3D and 2D convolutional layers, called the CC-3D2D module. The final CCNet-5D is constructed by stacking the four resulting CC-3D2D modules. In our setup, 5D-CNN outperforms the existing 5D traditional method and 3D CNN-based method.