Effect of a Temperature-Dependent Viscosity on the Spreading of Laccoliths.

Shallow magmatic intrusions make room for themselves by upward bending of the elastic overburden. Previous studies have shown that the dynamics of such intrusions is first controlled by the bending of the overlying layer and transitions to a gravity current regime when the radius reaches a few times the flexural wavelength of the overburden. Laccoliths have been shown to stop their spreading in the elastic regime; however, their radius are too small to be fracture-controlled. Hence their size and morphology are probably related to their cooling.

Here, we study the thermal evolution of a shallow magmatic intrusion and account for a temperature-dependent viscosity. We model the conductive cooling of an intrusion below an overlying elastic layer through two thermal boundary layers at the contact between the magma and the encasing rocks. The magma viscosity is inversely related to temperature and is bounded between two extreme values, a "hot" and a "cold" viscosity.

Our model shows that the hot core of the intrusion grows slower than the intrusion itself and becomes concentrated within a 'thermal radius' where heat advection compensates for diffusion within the country rocks. As predicted by our analytical scaling law, the thermal radius essentially depends upon the Peclet number as well as on the ratio between the cold and hot viscosities.

The effective viscosity of the flow increases with time and is much higher than the average flow viscosity. This effective viscosity depends on the temperature of the intrusion front. Indeed, with time, the intrusion radius leaves behind the thermal anomaly, the temperature of the front decreases and the effective viscosity increases. This acts to enhance the thickening over the spreading of the intrusion and would stop laccolith in the bending regime.