Frequency differences between BiSON observations of low-degree solar oscillations and Model S before (grey points) and after (white points) the near-surface layers are replaced by the profile of the G2-type MURaM simulation averaged over time and surfaces of constant geometric depth. The solid line shows the difference between the frequencies before and after replacing the near-surface layers. In addition, the dotted and dashed lines show the frequency differences when the MURaM simulation is instead averaged over surfaces of constant pressure P or optical depth τ. With the averaged MURaM profile, the residual frequency difference is reduced to at most about 3 μHz. The frequency changes are sensitive to the averaging method at about the 1 μHz level, which is smaller than the surface effect itself.