Scale-invariance and self-organized criticality in migmatites of the southern Hualapai Mountains, Arizona

Whether or not melt-flow networks are scale-invariant may have broad implications for the understanding of the development of magmatic systems. Leucosome distributions in natural migmatite samples from the Hualapai Mountains, Arizona, are used to investigate the scaling characteristics of an inferred syndeformational melt-flow network. One-dimensional line and two-dimensional box-counting analyses yield distributions that are consistent with a scale-invariant relationship between the leucosome size and leucosome frequency. We infer from these results that the interactions of anatexis and deformation gave rise to a self-organized critical system in which melt distribution and melt movement were linked over a range of scales (at least millimeter- to meter-scale). We conclude that, even in metatexite migmatites volumetrically dominated by solid phases, melts can play an active role in determining the architecture of the melt-flow network. One implication of the envisioned self-organized critical system is the potential for rapid, large-scale melt coalescence and escape without long-term maintenance of a fully interconnected melt-flow network.