Progressive evolution of whole-rock composition during metamorphism revealed by multivariate statistical analyses

The geochemical evolution of metamorphic rocks during subduction‐related metamorphism is described on the basis of multivariate statistical analyses. The studied data set comprises a series of mapped metamorphic rocks collected from the Sanbagawa metamorphic belt in central Shikoku, Japan, where metamorphic conditions range from the pumpellyite–actinolite to epidote–amphibolite facies. Recent progress in computational and information science provides a number of algorithms capable of revealing structures in large data sets. This study applies k‐means cluster analysis (KCA) and non‐negative matrix factorization (NMF) to a series of metapelites, which is the main lithotype of the Sanbagawa metamorphic belt. KCA describes the structures of the high‐dimensional data, while NMF provides end‐member decomposition which can be useful for evaluating the spatial distribution of continuous compositional trends. The analysed data set, derived from previously published work, contains 296 samples for which 14 elements (Si, Ti, Al, Fe, Mn, Mg, Ca, Na, K, P, Rb, Sr, Zr and Ba) have been analysed. The KCA and NMF analyses indicate five clusters and four end‐members, respectively, successfully explaining compositional variations within the data set. KCA indicates that the chemical compositions of metapelite samples from the western (Besshi) part of the sampled area differ significantly from those in the east (Asemigawa). In the west, clusters show a good correlation with the metamorphic grade. With increasing metamorphic grade, there are decreases in SiO₂ and Na₂O and increases in other components. However, the compositional change with metamorphic grade is less obvious in the eastern area. End‐member decomposition using NMF revealed that the evolutional change of whole‐rock composition, as correlated with metamorphic grade, approximates a stoichiometric increase of a garnet‐like component in the whole‐rock composition, possibly due to the precipitation of garnet and effusion of othe