  We present first results of a novel technique that provides, for the first
time, constraints on the energy input flux at the coronal base
($r\sim\,1.025\,{\rm R}_\odot$) of the quiet-Sun at a global scale. By
combining differential emission measure tomography (DEMT) of EUV images, with
global models of the coronal magnetic field, we estimate the energy input flux
at the coronal base that is required to maintain thermodynamically stable
structures. The technique is described in detail and first applied to data
provided by the Extreme Ultraviolet Imager (EUVI) instrument, on board the
Solar TErrestrial RElations Observatory (STEREO) mission, and the Atmospheric
Imaging Assembly (AIA) instrument, on board the Solar Dynamics Observatory
(SDO) mission, for two solar rotations with different levels of activity. Our
analysis indicates that the typical energy input flux at the coronal base of
magnetic loops in the quiet-Sun is in the range $\sim\,0.5-2.0\times 10^5\,{\rm
(erg\,sec^{-1}\,{\rm cm}^{-2})}$, depending on the structure size and level of
activity. A large fraction of this energy input, or even its totality, could be
accounted for by Alfv\'en waves, as shown by recent independent observational
estimates derived from determinations of the non-thermal broadening of spectral
lines in the coronal base of quiet-Sun regions. This new tomography product
will be useful for validation of coronal heating models in magnetohydrodinamic
simulations of the global corona.
