Model of Pattern Formation in Layered Igneous Intrusions

English Abstract:

Oscillations in composition and grain size can sometimes be generated in magmatic intrusions, giving rise to characteristic centimeter to meter-scale patterns called cyclic layering. Understanding the genesis of these patterns is essential to understand the geological context in which these bodies are formed. We hypothesize that these patterns result from a nonlinear self-organization process in which the interplay between crystallization dynamics and diffusion causes mineral and crystal size segregation. The mechanism is similar to the one behind the formation of Liesegang bands and leads to comparable features, such as a geometric progression of the band positions. With the goal of obtaining a more complete description of the pattern formation process in the context of a binary eutectic magmatic system in cooling contact with a host-rock, we present a one-dimensional numerical model of nucleation and growth that generalizes previously available versions. The model includes optionally Ostwald ripening, as well as tortuosity corrections for the porosity.  The emergence of cyclic layering is described in terms of key parameters that control the solidification. Moreover, by using a spherically symmetric geometry, the model can be applied to the formation or orbicular granites.