Unsupervised deep learning for 3D interpolation of highly incomplete data

We propose to denoise and reconstruct the 3D seismic data simultaneously using an unsupervised deep learning (DL) framework, which does not require any prior information about the seismic data and is free of labels. We use an iterative process to reconstruct the 3D highly incomplete seismic data. For each iteration, we use the DL framework to denoise the 3D seismic data and initially reconstruct the missing traces. Then, the projection onto convex sets (POCS) algorithm is used for further enhancement of the seismic data reconstruction. The output of the POCS is considered as the input for the DL network in the next iteration. We use a patching technique to extract 3D seismic patches. Because the proposed DL network consists of several fully connected layers, each extracted patch needs to be converted to a 1D vector. In addition, we use an attention mechanism to enhance the learning capability of the proposed DL network. We evaluate the performance of the proposed framework using several synthetic and field examples and find that the proposed method outperforms all benchmark methods.