Near offset reconstruction for marine seismic data using a convolutional neural network

Marine seismic data is often missing near offset information due to separation between the source and receiver cables. To solve this problem, a convolutional neural network is trained on synthetic seismic data to reconstruct the near offset gap. The synthetic data is created using a two-dimensional finite difference method within a heterogeneous velocity model. These synthetics are generated with a source-over-receiver acquisition geometry so that they contain complete near offset data. The convolutional neural network is then trained on input-target synthetic pairs where the inputs are common midpoint gathers with the near offset section removed, and the targets are the same gathers with the near offset section retained. Following training, the robustness of the method is investigated with regards to common midpoint data sorting, normal moveout correction and changes in the velocity model. It is found that training on common midpoint-sorted data results in 2.8 times lower error than training on shot gathers, that normal moveout correction of the training data makes no significant difference in error levels, and that the model can reconstruct realistic near offsets on synthetic data generated 10 km away within the heterogeneous velocity model. In field data testing, first a dataset with source-over-cable acquisition geometry from the Barents Sea is used to compare the reconstructed wavefields to ground truth values. Although the reconstructed amplitudes require minor scaling to match the true values, predictions on this dataset yield 2.5 times lower near offset reconstruction error compared to a simple Radon transform interpolation method. Furthermore, amplitude versus offset gradient and intercept sections from the Barents Sea dataset are estimated with half the error when including the convolutional neural network-predicted near offset data, compared to only using the conventionally-acquirable portion of the data (beyond 112.5 m of offset). In a secondary field data test, a conventional northern North Sea dataset is used to demonstrate how the method may be applied in practice. Here, the convolutional neural network generates more realistic predictions than the Radon method, and the gradient and intercept sections calculated using the convolutional neural network-predicted traces have higher signal-to-noise ratios than the sections calculated using only the original data. The combination of high-quality synthetic training data and interpolation in the common midpoint domain enables near offset reconstruction at significant depth (1 s of two-way traveltime or more), which is demonstrated in both synthetic and field examples.