Evaluation of magma mixing and fractional crystallization using whole‐rock chemical analyses: Polytopic vector analyses

Abstract

[1] Magma mixing and crystal fractionation are fundamental processes that lead to the diversity of magma compositions, but rarely are all of the major and trace element data on whole rocks used simultaneously in evaluating proposed models. Polytopic vector analysis (PVA) is an oblique factor analysis procedure designed specifically to evaluate mixing or unmixing (fractional crystallization) in geologic systems using all of the analytes (major and trace elements) simultaneously. It differs from other techniques in that it not only determines the number of end-members and their compositions, but also partitions the relative proportions of the end-members into each sample in the data array. These samples, expressed as proportions of end-members, can be used as input in other multivariate analyses. The purpose of this paper is to use PVA to evaluate some examples of magma mixing and fractional crystallization and use these examples as templates for more complicated systems in order to show both the strengths and the weaknesses of the approach. Five well-constrained examples illustrate how PVA can discriminate between these two processes and provide additional petrogenetic information. Using PVA, mixing between magma types can be easily distinguished from crystal fractionation. With fractional crystallization the endmembers, generated by PVA, are the initial and final liquids and the compositions where new phases join the crystallizing assemblage.

Evaluating Complex Magma Mixing via Polytopic Vector Analysis (PVA) in the Papagayo Tuff, Northern Costa Rica: Processes that Form Continental Crust

“…Like simple plots of any two elements, mixing between end members produces a linear trend. Other magmatic processes, such as fractional crystallization and partial melting, can also produce linear trends if the crystallizing/melting assemblage remains constant [19]. Figure 12 shows two trends.…”

“…However, Tefend et al [18] and Vogel et al [19] demonstrate that a multivariate technique, like PVA, has advantages over these tests alone, because it (1) assesses relationships among samples using all available data rather than select sets of variables, (2) places the same relative importance of each variable in the data set rather than artificially weighting more abundant components (e.g., SiO 2 ) and (3) requires a solution that "fits" every sample, rather than placing a disproportionate importance on just the samples used in modeling. For these reasons, Vogel et al [19] also note that PVA is not a stand-alone test, but only adds to the petrological toolbox for evaluating magmatic systems.…”

“…Although PVA has been used for several decades to evaluate source mixing in cases of environmental contamination [54][55][56], its application to igneous petrology is fairly new. An extensive discussion of PVA applied to relatively simple igneous systems can be found in Vogel et al [19]. Tefend et al [18] used PVA to evaluate a complex volcanic system involving multiple mixed magma batches; Deering et al [57] used PVA to document the evolution of rhyolites in the Taupo Volcanic Zone in New Zealand; Barclay et al [17] used PVA to evaluate recharge events in the erupting Soufrière Hills Volcano, Montserrat, as evidenced in chemically diverse mafic enclaves.…”

“…A more comprehensive discussion of the technique and its development can be found in [18,[52][53][54]. In brief, PVA is an oblique factor analysis procedure that uses all available geochemical analytes to simultaneously evaluate a group of samples that result from mixing (or "unmixing," such as the case of fractional crystallization [19]). PVA determines the number and composition of end members required to explain the variation within the sample population.…”

“…Microchemical and isotopic analyses of glass, crystalline phases and melt inclusions in volcanic rocks have emphasized the prevalence of recharge, mixing and mingling in arc magmas (e.g., [1,[13][14][15][16]). Compared to linear regression and simple bivariate plots of element ratios, application of multivariate statistical tests, such as polytopic vector analysis (PVA), can be used to extract more robust information about mixing from bulk rock chemical data [17][18][19].…”