Nonisothermal Emplacement of Sills at Calderas: An Approximate Approach to Stopping by Magma Freezing

The emplacement and inflation of a kilometer-sized kilometer-deep magmatic sill is often invoked to explain caldera unrest, like Fernandina and Sierra Negra (Galapagos), Kilauea south caldera (Hawaii), and Campi Flegrei (Italy). Although the mechanism controlling sill formation is under investigation since decades, still unanswered questions include the following: How do sills spread? Why can magma propagate for kilometers without solidifying? We show that the free-surface effects may often be neglected and kilometer-sized kilometer-deep magmatic sills spread like hydraulic fractures in an infinite medium. Magma propagation details depend on overburden pressure, magma viscosity, injection rate, and difference between magma and rock temperatures. A small lag, filled with vapors from the fluid and/or the rock, exists between the propagating magma and fracture fronts. If the sill spreads along an interface or in a weak rock, the lag slightly affects isothermal sill spreading but takes a key role in the case of nonisothermal propagation: A sill would stop after few tens of meters without it, unless magma intrudes rocks that are as hot as the solidification temperature or has unrealistic overpressures, because spreading velocity decreases soon to the critical value at which the tip becomes blocked with solidified magma. The lag defers magma solidification as heat exchange between the magma and the rock is effective only behind the thermal-insulating lag, where magma has some finite thickness and sill opening grows with distance from the tip faster than thickness of solidified magma. Thus, the critical velocity decreases, allowing greater maximum sill sizes.