  Localised modelling error in the near-surface layers of evolutionary stellar
models causes the frequencies of their normal modes of oscillation to differ
from those of actual stars with matching interior structures. These frequency
differences are referred to as the asteroseismic surface term. Global stellar
properties estimated via detailed constraints on individual mode frequencies
have previously been shown to be robust with respect to different
parameterisations of this surface term. It has also been suggested that this
may be true of a broader class of nonparametric treatments. We examine
systematic differences in inferred stellar properties with respect to different
surface-term treatments, both for a statistically large sample of main-sequence
stars, as well as for a sample of red giants, for which no such
characterisation has previously been done. For main-sequence stars, we
demonstrate that while masses and radii, and hence ages, are indeed robust to
the choice of surface term, the inferred initial helium abundance $Y_0$ is
sensitive to the choice of surface correction. This implies that
helium-abundance estimates returned from detailed asteroseismology are
methodology-dependent. On the other hand, for our red giant sample,
nonparametric surface corrections return dramatically different inferred
stellar properties than parametric ones. The nature of these differences
suggests that such nonparametric methods should be preferred for evolved stars;
this should be verified on a larger sample.
