We have trained a supervised deep 3D convolutional neural network (CNN) on marine seismic images for poststack structural seismic image enhancement and noise attenuation. Rather than adding artificial noise to training inputs, the difference in noise levels between the training inputs and labels was created by shot density differences. This design enables the trained CNN to mimic the results and power of stacking to specifically target random and coherent migration artifacts while enhancing low-amplitude reflections. We used field seismic from multiple Gulf of Mexico surveys to train the CNN and the SEG Advanced Modeling (SEAM) phase I synthetic data to evaluate the trained network. The diverse geologic features in the training data are needed to avoid overfitting. The processed outputs of the trained neural network are much cleaner than the inputs, and they highlight geologic structures for easier interpretation. Different scales of geologic structures, from high-resolution faults and diffractors to deep subsalt sediments, are well-preserved by the deep neural network. The trained network can be applied on either prestack gathers or poststack images. The approach is easy to implement and straightforward to parameterize, and it has proven to be an effective and flexible production tool for post-migration data conditioning.