Top: Density profiles from the PV model (grey) and the density enhancement model (green) for SN 2012fr. Bottom: Relative fraction of silicon material in the singly ionised state for the PV model (grey) and the density enhancement model (green) across the first four epochs of SN 2012fr. The black vertical lines correspond to the measured HVF velocities from the synthesised spectra. The shaded region represents the velocity range centred at b with width 2c (i.e. from b − c to b + c), where b and c are the centroid and width of the Gaussian density enhancement, respectively, as given in Table 1.