Unmixing mid-ocean ridge basalts with EXTENDED QMODEL

Horkowitz, Jack; Stakes, Debra S.; Ehrlich, Robert

doi:10.1016/0040-1951(89)90031-0

Cited by 7 publications

(3 citation statements)

References 21 publications

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“…PVA extracts end‐member compositions and the proportion of end‐members in each sample in the database. Although one of the original researchers that led to the development of PVA was a petrologist/geochemist [ Miesch , 1976b], there have been few investigations that have applied this technique (or its earlier versions) to mixing problems in petrology [ Horkowitz et al , 1989; Vogel et al , 1989]. However, recently Tefend et al [2007] used PVA to evaluate the complex mixing/fractionation processes in the Topopah Springs–Pah Canyon ash‐flow sheets in the Southwest Nevada Volcanic Field.…”

Section: Polytopic Vector Analysesmentioning

confidence: 99%

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

Vogel

Hidalgo

Patino

et al. 2008

Geochem Geophys Geosyst

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[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.

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Section: Polytopic Vector Analysesmentioning

confidence: 99%

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

Vogel

Hidalgo

Patino

et al. 2008

Geochem Geophys Geosyst

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“…Igneous rock researchers have also been an adapter of these unmixing algorithms. These include Horkowitz et al (1989), Stattegger and Morton (1992), Tefend et al (2007), Vogel et al (2008, Deering et al (2008), Barclay et al (2010), Szymanski et al (2013), Lisowiec et al (2015) and most recently by Blum-Oeste and Wörner (2016).…”

Section: Review Of the Applications Of Constant Sum Unmixingmentioning

confidence: 99%

Linear Unmixing in the Geologic Sciences: More Than A Half-Century of Progress

Full

2018

Handbook of Mathematical Geosciences

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For more than a half-century, scientists have been developing a tool for linear unmixing utilizing collections of algorithms and computer programs that is appropriate for many types of data commonly encountered in the geologic and other science disciplines. Applications include the analysis of particle size data, Fourier shape coefficients and related spectrum, biologic morphology and fossil assemblage information, environmental data, petrographic image analysis, unmixing igneous and metamorphic petrographic variable and the unmixing and determination of oil sources, to name a few. Each of these studies used algorithms that were designed to use data whose row sums are constant. Non-constant sum data comprise what is a larger set of data that permeates many of our sciences. Many times, these data can be modeled as mixtures even though the row sums do not sum to the same value for all samples in the data. This occurs when different quantities of one or more end-member are present in the data. Use of the constant sum approach for these data can produce confusing and inaccurate results especially when the end-members need to be defined away from the data cloud. The approach to deal with these non-constant sum data is defined and called Hyperplanar Vector Analysis (HVA). Without abandoning over 50 years of experience, HVA merges the concepts developed over this time and extends the linear unmixing approach to more types of data. The basis for this development involves a translation and rotation of the raw data that conserves information (variability). It will also be shown that HVA is a more appropriate name for both the previous constant sum algorithms and future programs algorithms as well.

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“…Therefore, PVA has criteria to determine a "best" or, in some sense, the smallest polytope for a given data set. The basic assumptions used in this procedure (the mixing model, linearity, and the sufficiency of the samples to position and orient the faces of the polytope) are satisfied in geochemical-thermodynamical contexts given proper sampling [Horkowitz et al, 1989]. PVA (in its so-called extended Q model form) has also been applied to the analysis of sediment shapes as natural tracers [Van Nieuwenhuise et al, 1978;Porter et al, 1979;Brown et al, 1980;Mazzullo et al, 1984].…”

Section: Polytopic Vector Analysismentioning

confidence: 99%

A comparison between polytopic vector analysis and empirical orthogonal function analysis for analyzing quasi‐geostrophic potential vorticity

Evans¹,

Ehrlich²,

Krantz³

et al. 1992

J. Geophys. Res.

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Output from highly resolved, long-duration ocean models, and measurements taken by satellites and other modern observational tools, present critical problems in storage and assessment. While empi. rical orthogonal function analysis (EOFA) can be used for data compression, the data are often difficult to assess in compressed form. A relatively new procedure, polytopic vector analysis, has compression capabilities equal to those of EOFA but improves assessment of the data in the compressed form. The two procedures are illustrated by analysis of upper layer quasi-geostrophic potential vorticity from a simple two-layer ocean circulation model.

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Unmixing mid-ocean ridge basalts with EXTENDED QMODEL

Cited by 7 publications

References 21 publications

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

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

Linear Unmixing in the Geologic Sciences: More Than A Half-Century of Progress

A comparison between polytopic vector analysis and empirical orthogonal function analysis for analyzing quasi‐geostrophic potential vorticity

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