Publication
Context. Asteroseismology experienced a breakthrough in the last two decades thanks to the so-called photometry revolution with space-based missions such as CoRoT, Kepler, and TESS. Because asteroseismic modelling will be part of the pipeline of the future PLATO mission, it is relevant to compare some of the current modelling strategies and discuss the limitations and remaining challenges for PLATO. In this first paper, we focused on modelling techniques treating directly the seismic information.Aims. We compared two modelling strategies by directly fitting the individual frequencies or by coupling a mean density inversion with a fit of the frequency separation ratios.Methods. We applied these two modelling approaches to six synthetic targets with a patched atmosphere, for which the observed frequencies were obtained with a non-adiabatic oscillation code. We then studied ten actual targets from the Kepler LEGACY sample.Results. As is well known, the fit of the individual frequencies is very sensitive to the surface effects and to the choice of the underlying prescription for semi-empirical surface effects. This significantly limits the accuracy and precision that can be achieved for the stellar parameters. The mass and radius tend to be overestimated, and the age therefore tends to be underestimated. In contrast, the second strategy, which is based on mean density inversions and on the ratios, efficiently damps the surface effects and allows us to obtain precise and accurate stellar parameters. The average statistical precision of our selection of targets from the LEGACY sample with this second strategy is 1.9% for the mass, 0.7% for the radius, and 4.1% for the age. This is well within the PLATO mission requirements. The addition of the inverted mean density to the constraints significantly improves the precision of the stellar parameters by 20%, 33%, and 16% on average for the stellar mass, radius, and age, respectively.Conclusions. The modelling strategy based on mean density inversions and frequencies separation ratios showed promising results for PLATO because it achieved a precision and accuracy on the stellar parameters that meet the PLATO mission requirements with ten Kepler LEGACY targets. The strategy also left some margin for other unaccounted systematics, such as the choice of the physical ingredients of the stellar models or the stellar activity.