Unraveling the presence of multiple plagioclase populations and identification of representative two-dimensional sections using a statistical and numerical approach

Many plagioclase phenocrysts from volcanic and plutonic rocks display quite complex chemical and textural zoning patterns. Understanding the zoning patterns and variety of crystal populations holds clues to the processes and timescales that lead to the formation of the igneous rocks. However, in addition to a "true" natural complexity of the crystal population, the large variety of plagioclase types can be partly artifacts of the use of two-dimensional (2D) petrographic thin sections and random cuts of three-dimensional (3D) plagioclase crystals. Thus, the identification of the true number of plagioclase populations, and the decision of which are "representative" crystal sections to be used for detailed trace element and isotope analysis is not obvious and tends to be subjective. Here we approach this problem with a series of numerical simulations and statistical analyses of a variety of plagioclase crystals zoned in 3D. We analyze the effect of increasing complexity of zoning based on 2D chemical maps (e.g., backscattered electron images, BSE). We first analyze the random sections of single crystals, and then study the effect of mixing of different crystal populations in the samples. By quantifying the similarity of the compositional histogram of about a hundred 2D plagioclase sections it is possible to identify the so-called reference and ideal sections that are representative of the real 3D crystal populations. These section types allow filtering out the random-cut effects and explain more than 90% of the plagioclase compositional data of a given sample. Our method allows the identification of the main crystal populations and representative crystals that can then be used for a more robust interpretation of magmatic processes and timescales.