  In the present paper, we aim to constrain the properties of the ionisation
region in a star from the oscillation frequency variation (a so-called glitch)
caused by rapid structural variations in this very region. In particular, we
seek to avoid the use of calibration based on stellar models thus providing a
truly independent estimate of these properties. These include both the helium
abundance and other physical quantities that can have a significant impact on
the oscillation frequencies such as the electronic degeneracy parameter or the
extent of the ionisation region.
  Taking as a starting point our first paper, we applied structural
perturbations of the ionisation zone to the wave equation for radial
oscillations in an isentropic region. The resulting glitch model is thus able
to exploit the information contained in the fast frequency oscillation caused
by the helium ionisation but also in the slow trend accompanying that of
hydrogen. This information can directly be expressed in terms of parameters
related respectively to the helium abundance, electronic degeneracy and extent
of the ionisation region.
  Using a Bayesian inference, we show that a substantial recovery of the
properties at the origin of the glitch is possible. A degeneracy between the
helium abundance and the electronic degeneracy is found to exist, which
particularly affects the helium estimate. Extending the method to cases where
the glitch is subject to contamination (e.g. surface effects), we noted the
importance of the slow glitch trend associated with hydrogen ionisation. We
propose using a Gaussian process to disentangle the frequency glitch from
surface effects.
