  Since the CoRoT and Kepler missions, the availability of high quality seismic
spectra for red giants has made them the standard clocks and rulers for
Galactic Archeology. With the expected excellent data from the TESS and PLATO
missions, red giants will again play a key role in Galactic studies and stellar
physics, thanks to the precise masses and radii determined by asteroseismology.
The determination of these quantities is often based on so-called scaling laws,
which have been used extensively for main-sequence stars. We show how the SOLA
inversion technique can provide robust determinations of the mean density of
red giants within 1 per cent of the real value, using only radial oscillations.
Combined with radii determinations from Gaia of around 2 per cent precision,
this approach provides robust, less model-dependent masses with an error lower
than 10 per cent. It will improve age determinations, helping to accurately
dissect the Galactic structure and history. We present results on artificial
data of standard models, models including an extended atmosphere from averaged
3D simulations and non-adiabatic frequency calculations to test surface
effects, and on eclipsing binaries. We show that the inversions provide very
robust mean density estimates, using at best seismic information. However, we
also show that a distinction between red-giant branch and red-clump stars is
required to determine a reliable estimate of the mean density. The stability of
the inversion enables an implementation in automated pipelines, making it
suitable for large samples of stars.
