  Thanks to space-based photometry missions CoRoT and Kepler, we benefit from a
wealth of seismic data for stars other than the sun. In the future, K2, Tess,
and Plato will complement this data and provide observations in addition to
those already at hand. The availability of this data leads to questions on how
it is feasible to extend linear structural inversion techniques to stars other
than the sun. Linked to this problem is the question of the validity of the
linear assumption. In this study, we analyse its limitations with respect to
changes of structural variables.We wish to provide a more extended theoretical
background to structural linear inversions by doing a study of the validity of
the linear assumption for various structural variables. First, we recall the
origins of the linear assumption for structural stellar inversions and explain
its importance for asteroseismic studies. We recall the impact of unknown
structural quantities such as the mass and the radius of the star on structural
inversion results. We explain how kernels for new structural variables can be
derived using two methods, one suited to asteroseismic targets, the other to
helioseismic targets. For this second method, we present a new structural pair,
namely the (A, Y) structural kernels. The kernels are tested in various
numerical experiments that enable us to evaluate the weaknesses of different
pairs and the domains of validity of their respective linear regime. The
numerical tests we carry out allow us to disentangle the impact of various
uncertainties in stellar models on the verification of the linear integral
relations. We show the importance of metallicity, the equation of state,
extra-mixing, and inaccuracies in the microphysics. We discuss the limitations
of the method of conjugated functions due to the lack of extremely precise
determinations of masses or radii in the asteroseismology.
