Understanding where normal faults are is critical to an accurate assessment of seismic hazard, the successful exploration for and production of natural (including low-carbon) resources, and for the safe subsurface storage of CO2. Our current knowledge of normal fault systems is largely derived from seismic reflection data imaging intra-continental rifts and continental margins. However, exploitation of these data is limited by interpretation biases, data coverage and resolution, restricting our understanding of fault systems. Applying supervised deep learning to one of the largest offshore 3-D seismic reflection data sets from the northern North Sea allows us to image the complexity of the rift-related fault system. The derived fault score volume allows us to extract almost 8000 individual normal faults of different geometries, which together form an intricate network characterised by a multitude of splays, junctions and intersections. Combining tools from deep learning, computer vision and network analysis allows us to map and analyse the fault system in great detail and a fraction of the time required by conventional interpretation methods. As such, this study shows how we can efficiently identify and analyse fault systems in increasingly large 3-D seismic data sets.