  Muography or muon radiography is a non-invasive emerging image technology
relying on high energy atmospheric muons, which complements other standard
geophysical tools to understand the Earth's subsurface. This work discusses a
geophysical inversion methodology for volcanic muography, based on the
Simulated Annealing algorithm, using a semi-empirical model of the muon flux to
reach the volcano topography and a framework for the energy loss of muons in
rock. The Metropolis-Simulated-Annealing algorithm starts from an 'observed'
muon flux and obtains the best associated inner density distribution function
inside a synthetic model of the Cerro Machin Volcano (Tolima-Colombia). The
estimated initial density model was obtained with GEOMODELER, adapted to the
volcano topography. We improved this model by including rock densities from
samples taken from the crater, the dome and the areas associated with
fumaroles. In this paper, we determined the minimum muon energy (a function of
the arrival direction) needed to cross the volcanic building, the emerging
integrated flux of muons, and the density profile inside a model of Cerro
Machin. The present inversion correctly reconstructed the density differences
inside the Machin, within a 1 percent error concerning our initial simulation
model, giving a remarkable density contrast between the volcanic duct, the
encasing rock and the fumaroles area.
