Non-isothermal Propagation of Km-sized Km-deep Sills at Calderas.

Caldera unrest is often attributed to the emplacement and inflation of a km-sized km-deep magmatic sill; if the sill is schematized as circular in shape, its depth-to-radius ratio is usually larger than one. Remarkable examples are: Fernandina and Sierra Negra (Galapagos), Kilauea south caldera (Hawaii), and perhaps Campi Flegrei (Italy), even though in this last case the unrest cause is somewhat still debated. Although the mechanism controlling sill formation is under investigation since at least half a century, a few key aspects still remain poorly understood. In particular: how sills spread, why magma can propagate for kilometers without solidifying, and why ground deformation data rarely, if ever, detect sill propagation, while they usually evidence inflation. We show that the free-surface effects on sill shape and propagation at calderas may often be neglected; thus, magmatic sills actually spread like hydraulic fractures in an infinite medium. Generally speaking, magma propagation depends on the overburden pressure, magma viscosity, and injection rate. In the case of non-isothermal propagation, we find that a key role is played by the small lag which exists between the propagating magma and fracture fronts and is filled with vapors from the fluid and/or the rock. If the lag did not exist, the sill would propagate more than few tens of meters only when the rock temperature and/or influx rate were very high. The lag defers magma solidification and allows km-sized sills even when the rock temperature is initially tens of degrees lower than that where magma solidifies, because heat exchange between the magma and the rock is effective only behind the thermal-insulating lag. As expected, the maximum achievable radius grows with the magma injection rate, but, somewhat unexpectedly, it also grows with viscosity, because the lag size increases with viscosity as well. Finally, we show that only the post-arrest sill inflation is usually detected, because ground deformation is below the threshold of current monitoring networks during sill spreading.