  We present a self consistent method to perfom a joint analysis of
Sunyaev-Zel'dovich and weak gravitational lensing observation of galaxy
clusters. The spatial distribution of the cluster main constituents is
described by a perturbative approach. Assuming the hydrostatic equilibrium and
the equation of state, we are able to deduce, from observations, maps of
projected gas density and gas temperature. The method then naturally entails a
X-ray emissivity prediction which can be compared to observed X-ray emissivity
maps. When tested on simulated clusters (noise free), this prediction turns out
to be in very good agreement with the simulated surface brightness. The
simulated and predicted surface brightness images have a correlation
coefficient higher than 0.9 and the total flux differ by 0.9 % or 9 % in the
two simulated clusters we studied. The method should be easily used on real
data in order to provide a physical description of the cluster physics and of
its constituents. The tests performed show that we can recover the amount and
the spatial distributions of both the baryonic and non-baryonic material with
an accuracy better than 10 %. So, in principle, in it might indeed help to
alleviate some well known bias affecting, eg baryon fraction measurements.
