Seismic anisotropy may degrade the quality of seismic images and cause the mispositioning of events within them. Shales have often been observed to be significantly anisotropic, usually with approximately hexagonal symmetry (transverse isotropy) with axis normal to the bedding plane. We investigate the effect of anisotropy on imaging a real data set from offshore Africa, where there are thick shale sequences. We perform, in parallel, isotropic and anisotropic velocity model building and 3D post-stack migration of the same stack volume, We observe that the anisotropic processing improves the focussing of dipping events and that the assumption of isotropy may cause lateral and vertical displacement of the reservoir boundaries, of around 100 and 200 meters respectively, relative to the positions obtained with the anisotropic processing.