An Approximate Approach to Nonisothermal Emplacement of Kilometer‐Sized Kilometer‐Deep Sills at Calderas

Caldera unrest is often caused by kilometer‐sized kilometer‐deep sills. Still unanswered questions include the following: How do sills spread? Why can magma propagate for kilometers without solidifying? Why do ground deformation data rarely, if ever, detect sill propagation? We show that kilometer‐sized kilometer‐deep magmatic sills spread like hydraulic fractures in an infinite medium. How magma propagates depends 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, 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. We also show that the ground deformation pattern does not change appreciably over time if the final sill radius is smaller than 2 to 3 km, explaining why deformation is usually attributed to the inflation of a stationary source.