A multidirectional deep neural network for self-supervised reconstruction of seismic data

Seismic studies exhibit gaps in the recorded data due to surface obstacles. To fill in the gaps with self-supervised deep learning, the network learns to predict different events from the recorded parts of data and then applies it to reconstruct the missing parts of the same dataset. We propose two improvements to the task: a rearrangement of the data, and a new deep-learning approach. We rearrange the traces of a 2-D acquisition line as 3-D data cubes, sorting the traces by the source and receiver coordinates. This 3-D representation offers more information about the structure of the seismic events and allows a coherent reconstruction of them. However, learning the structure of events in 3-D cubes is more complicated than in 2-D images while the size of the training dataset is limited. Thus, we propose a specific architecture and training strategy to take advantage of 3-D data samples, while benefiting from the simplicity of 2-D reconstructions. Our proposed multidirectional convolutional neural network has two parallel branches trained to perform 2-D reconstructions along the vertical and horizontal directions and a small 3-D part that combines their results. We use our method to reconstruct data gaps resulting from several missing shots in a benchmark synthetic and a real land dataset. Compared to a conventional 3-D U-net, our network learns to reconstruct the events more accurately. Compared to 2-D U-nets, our method avoids the discontinuities that arise from the 2-D reconstruction of each trace of the missing shot gathers.