Reaction-diffusion modelling of petrological mixing mechanisms in the evolution of continental crusts

Abstract

Petrological assimilation is a key process in the evolution of high-grade metamorphic terrains in the continental crusts. This study examines the mechanisms of such macroscopic assimilation between felsic (F) and mafic (M) constituents as two petrologically interacting continuum phases, as observed in the Chotanagpur Granite Gneissic Complex (CGGC), India, which underwent amphibolite to granulite facies metamorphism (∼775 to 900°C and 7 to 11 kb) between from the Paleoproterozoic to the late Mesoproterozoic. From field investigation we could recognized four interface patterns: planar, wavy, fingering and incoherent, which are generated at the interface between the F and M units. We have adopted the Turing type reaction-diffusion (RD) approach, which is a well established theoretical model to interpret any complex auto-regulatory pattern in natural and physical sciences, to understand the physics of the self-organizing interface geometries observed across the CGGC. The RD model findings suggest that these patterns are constrained by a combination of: diffusion coefficients (DF, DM) of F and M, a linear or non-linear reaction term (R) that describes phase interactions and a pinning field (W) that introduces microscale heterogeneity. For linear interactions, F − M undergo homogeneous mixing and show planar/wavy interfaces, when DF = DM and W = 0. The mixing turns heterogeneous as DF ≠ DM and W > 0, resulting in phase boundary migration with a fingering pattern. Non-linear reaction coupling enhances heterogeneous mixing and produces incoherent phase boundaries where F-phases host relics of M-phases, following a power-law size distribution. Striking similarities of interface patterns and fractal dimensions estimated from model and CGGC validate the proposed mechanism of macroscopic petrological assimilation. We argue that RD model provides a new insight into the genesis of hybrid rocks in metamorphic terrains.