Identifying relationships among silicic magma batches by polytopic vector analysis: A study of the Topopah Spring and Pah Canyon ash-flow sheets of the southwest Nevada volcanic field

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

“…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.…”

“…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].…”

“…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 also determines the unique composition of every sample by expressing the relative proportion of each end member in each sample. By definition, the proportions of each end member in every sample yield a constant sum of one (or 100%) [18]. Therefore, PVA should not be used as a "blind" probative technique to look for genetic or, even, descriptive statistical information about a sample suite.…”

“…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].…”