How do deep-water volcanoes grow?

•We use seismic reflection data to image 13 extinct, deep-water volcanoes in 3D.•The external shapes and internal structures of volcanoes are quantified.•Volcano comprise crater-like base that is larger than overlying conical edifice.•The deep-water volcanic edifices are relatively small but have steep slopes.•Seismic imaging is a powerful tool to unravel volcano growth.