A network-based approach to model volcanic repose durations

The global distributions of volcanic eruption durations and of repose times between two eruptions have broad and heterogeneous shapes. Statistical analyses indicate that both distributions may exhibit a power-law tail for medium-to-long timescales. This scale-free behaviour could be symptomatic of volcanic systems that self-organize into a critical state. In this paper, we build on a former model for magma ascent through a pipe of stacked cells, which successfully reproduces the trend of the global distribution of volcanic eruption durations, but does not account for the inter-event times between eruptive episodes. By adapting and implementing this model within tree-like graphs instead of a linear structure, we are able to retain the behaviour of the eruption duration distribution, while obtaining a broad distribution for the repose times. In contrast with the pipe linear structure, the tree-like structure accounts for the fact that a large part of the magma that ascends through the crust does not reach the surface. This result highlights the importance of modelling volcanic plumbing systems as networks that reflect their complexity and variety.