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We present a workflow for reconstructing missing near offset traces in marine seismic data using a convolutional neural network. We first generate two-dimensional synthetic shot gathers with a finite difference method, and sort them into CMP gathers. From these CMP gathers we form training data of input and target pairs – with the inputs having their near offset traces zeroed out, and the targets retaining their near offset traces. The CNN is trained to transform the inputs to the targets, and reconstruct the missing near offset traces. We test the trained network on synthetic testing data, and compare the results to another network trained on shot gathers, with the CMP-trained network yielding better results. We also demonstrate the robustness of the model to new testing data, which is generated 10 kilometers away from the training data within a heterogeneous velocity model. Finally, the synthetic-trained network is tested on on field data, and we find it yields accurate results compared to a traditional Radon transform method.