We study the possibility of muon radiography as a tool to investigate space and time changes in the internal density distribution inside geological structures. Previous work has shown the practical applicability of this method. Nevertheless, quantitative information on factors which impose limitations on it are still sorely lacking in the literature. We discuss the main issues that can influence the final result of a geophysical imaging experiment. In particular, with the view of optimizing the signal-to-noise ratio, we address issues concerning (i) the energy spectrum for muons arriving at different zenith angles, (ii) the muon propagation model through matter and (iii) the characteristics of the muon detector (telescope) that we have designed to perform experiments of muon radiography against the harsh environment usually encountered in the active zone of a volcano. We thus identify factors that can induce either static or dynamic effects and that should be taken into account. We also define a feasibility eq. (32) relating the geometrical characteristics of the telescope and the duration of the experiment to the expected density resolution, in turn a function of the geometrical characteristics of the target structure. This relation is especially important to define the applicability domain of muon radiography and it is utilized to test the suitability of the method to investigate the density distribution inside some candidate target structures.