Quality factor (Q) or equivalently attenuation a=1/Q describes the amount of energy lost per cycle as a wave travels through a medium. This is important to correct seismic data amplitudes for near surface effects, to locate subsurface voids or porosity, to aid seismic interpretation or for characterizing other rock and fluid properties. Seismic attenuation can be variable even when there are no discernible changes in seismic velocity or density (Yıldırım et al., 2017) and so provides independent information about subsurface heterogeneity. This study uses ambient noise recordings made on the Ekofisk Life of Field Seismic array to estimate Q structure in the near surface. We employ the method of Liu et al. (2015) which uses linear triplets of receivers to estimate Q – ours is the first known application of the method to estimate the Q structure tomographically. Estimating Q requires an estimate of phase velocity which we obtain using the method of Bloch and Hales (1968) followed by traveltime tomography. The Q structure at Ekofisk has features which can be related to local geology, showing that surface ambient noise recordings may provide a new and robust method to image Q. Our results suggest that there is a nonlinear relationship between Q and compression. They also may explain why it has been found that in the period range of 1s to 2s considered here, ambient noise cross‐correlations along paths that span the North Sea Basin are unreliable: such Q values would attenuate almost all ambient seismic energy during such a traverse.