Contribution of the Use of a Plate Model to Calculate the Stresses at Large Silicic Systems

Large silicic systems can produce devastating eruptions with emitted volumes greater than 100 km³ and worldwide impacts. Such eruptions suggest the presence of significant reservoirs of silicic magma at shallow depths. Understanding how these reservoirs form is crucial to understanding how they affect the surrounding rock. But the shape and the organization of magmatic storage are still debated, despite their crucial influence on the results of theoretical predictions. Based on physical considerations of silicic-magma properties and the continental-crust state of active systems; our hypothesis is that the rise of silicic magma is stopped by the Brittle Ductile Transition. As the relaxation time of the ductile part of the crust is very short compared to the lifetime of such systems, magma storage could be considered as a buoyant liquid stored beneath an elastic plate. We thus used a plate model to theoretically predict the stress above those large magma chambers. To test our hypothesis, we computed the general behaviours of large silicic systems and compared them to natural cases. We first calculated the stress field produced in the plate. Results show that stressed values can reach tens of MPa, which is enough to cause plate failure. Then, we compared reservoir dimensions and volumes predicted by our model when failure could occur with documented ones for past eruptions. We showed that the two are consistent with each other. In a broader perspective, we then showed that stresses produced in the plate by the magma chamber can produce circular faults above the storage zone. This result has direct implications for the understanding of caldera formation during large silicic eruptions.