A cellular automaton model for the rise of magma in closed-conduit volcanoes

We model the vertical section of a volcanic edifice by means of a two-dimensional grid and characterize the state of each cell of the grid by assigning the values of two dynamical variables: a time dependent variable e describing the status of the local stress and a time-dependent variable n describing the presence of magma. At first step of approximation, we treat the magma presence field n as a diffusing lattice gas, and, therefore, we assume its value to be either zero or one if the corresponding cell is empty or filled by magma, respectively. We study the probability distribution, P(V), of eruptions of volume V and the probability distribution, P(t), of inter-event time t and find that the model is able to reproduce, at least in a descriptive way, the essential statistical features of the activity of volcanoes.