Effects of surface layers on helioseismic inversion

In helioseismic inversions it is traditionally assumed that uncertainties in the treatment of surface layers of the Sun introduce frequency shifts which, after suitable scaling, can be expressed as a function of frequency alone. By considering explicit examples it is demonstrated that, although this assumption is correct to first order, the actual frequency changes are not a function of frequency alone to the accuracy of measured frequencies. This is true even for intermediate degree modes which are most useful for inversion. The errors introduced in inversion as a result of such simplifying assumptions are studied