The anomalous splitting of some core-sensitive eigenmodes suggests the presence of a structure in the liquid core. Geodynamical considerations rule out density heterogeneities, however they do not rule out the possibility of anisotropy in the liquid core. The seismic polar paths through the anisotropic inner core, which are anomalously fast, also sample the liquid core inside the cylinder tangent to the inner core, a structure insulated from the rest of the core during rotation. We investigate the possibility that anisotropy be present in that part of the liquid core, using PKPbc waves which have a long path inside the tangent cylinder, but which do not sample the inner core. We also investigate the possibility of heterogeneities which could have deposited beneath the polar caps, using differential travel times of S3KS-SKKS waves. The data do not reveal heterogeneity or anisotropy inside the tangent cylinder, nor the presence of anomalous polar caps.