Journal of Volcanology and Geothermal Research
Deciphering magma mixing: The application of cluster analysis to the mineral chemistry of crystal populations
Introduction
Cluster analysis (Tryon, 1939) is one of the most powerful tools with which to classify and sort data and furthermore, to establish relationship (taxonomies) within such data (Sneath and Sokal, 1973). The method creates groupings of objects that share a “similarity”, which can be quantified in terms of any measurable parameter. In this regard, cluster analysis can be used as a tool for exploratory data analysis, aiming to sort different objects into groups in a way that objects in a given group or cluster have a high degree of similarity. Many different fields of study, such as engineering, zoology, medicine, linguistics, anthropology, psychology, marketing, and indeed geology have contributed to the development of clustering techniques and the application of such techniques (Sneath and Sokal, 1973, Gordon, 1980, Aldenderfer and Blashfield, 1984, Kaufman and Rousseeuw, 1990, Jongman et al., 1995, Corter, 1996, Legendre and Legendre, 1998, Pillar, 1999, Jerram and Cheadle, 2000, Everitt et al., 2001).
This work explores the use of cluster analysis in igneous petrology, in the particular context of the quantitative identification of the products of magma mixing. The proposed method is evaluated using a set of phenocryst composition data from lavas of the Vancori period (15–20 ky) of Stromboli volcano (Italy), studied previously in detail by Cortés et al. (2005), in which mixing between a basaltic andesite–latite hosted in a high-level magma chamber and a less evolved basaltic recharge magma was originally proposed by Francalanci et al. (1989). Cortés et al. (2005) studied the Vancori sequence from the point of view of the bulk-rock and the mineral chemistry of the main phases (olivine, clinopyroxene, plagioclase, spinel) in samples from the Lower, Middle and Upper Vancori sub-periods, using conventional bulk-rock analytical methods and detailed electron microprobe analyses of phenocryst and groundmass minerals. They found that the main stratigraphic changes during the Vancori period are recorded by changes in bulk-rock and mineral chemistry and evidence of textural and thermodynamic disequilibrium in the eruptive products. In particular, Cortés et al. (2005) postulated that the transition from the Middle Vancori to the Upper Vancori period reflects the mixing of olivine–phyric basalt with residual more silica-rich (trachyte) magma still residing in the chamber at the end of the Middle Vancori period, in agreement with the earlier work of Francalanci et al. (1989). This study explores whether these changes can be tracked using the cluster analysis technique to interpret the mineral chemistry of the main phenocrysts phases (olivine, clinopyroxene and plagioclase) and furthermore, whether the results of the proposed methodology can be used to reconstruct the composition of the mixing end-members. In order to proceed, the mineral chemistry of the phenocrysts of a particular phase is represented by a system of coordinates in which each coordinate represents the amount of a given component in cations per formula unit in the phase. The “distance” between the vectorial representation of phenocrysts, a measure of how similar the compositions of the phenocryst are, is used to determine whether such phenocrysts represent a compositional cluster or not. This is similar to the approach utilized to study physical clusters of phenocrysts of different sizes (cf. Jerram and Cheadle, 2000).
Section snippets
Magma mixing and magma recharging processes
In a simplistic way, magma mixing can be described as a process of total or partial blending of two or more magmas or magma batches to form a hybrid magma. Leaving aside the complexity of the physico-chemical processes involved in magma mixing (e.g. Spera and Bohrson, 2004), or its consequences for triggering eruptions (Sparks et al., 1977), it is intuitive that the resulting magma will inherit properties from the two mixing end-members. These will depend on the physical (temperature, density,
The cluster analysis technique
Cluster analysis is a classification technique, also called segmentation analysis or taxonomy analysis. For practical purposes the technique is briefly introduced here; a more extensive discussion can be found in many books devoted to the subject, such as Aldenderfer and Blashfield (1984) or Everitt et al. (2001). The overall idea is the development of an algorithm to define a group of objects in a set that are similar in some given sense; objects that are not in the set are different using the
Mineral chemistry data and its vectorial representation
Traditionally, linear algebra has been used in many fields of geology in which projections or 3-D representations of data are needed. For example, in metamorphic petrology, a projection in ternary diagrams from a ubiquitous mineral phase as projection apex is a standard technique (Thompson, 1957), whilst in structural geology, eigenvectors and eigenvalues are used to calculate the main components of the stress tensor (Twiss and Moore, 1992). In mineralogy, the approach has been used spatially
Application to the Vancori period, Stromboli volcano
Stromboli, known since Roman times as the “Lighthouse of the Mediterranean” is in a state of almost continuous volcanic activity (Rosi et al., 2000), reflecting frequent recharge of the high-level magma chamber system. The geological evolution of the volcano as recorded in its subaerial part represents a time span of about 100,000 years. Four major volcanic periods, Paleostromboli (100–35 ky), Vancori (26–13.8 ky), Neostromboli (13.8–5.6 ky) and Recent (5.6 ky–present), have been recognized and
Conclusions
Despite the “simplicity” of the Vancori example in which the effects of magma mixing on phenocryst chemistry can be studied adequately using simple parameters such as An# for plagioclase, Mg# or Fo mol% for olivine, the potential of the cluster analysis technique to discriminate subtle mixing scenarios has been clearly demonstrated. On the other hand, since the proposed method based on the interpretation of the dendrograms and their degree of inconsistency is still subjective, further
Acknowledgments
The authors acknowledge the careful reviews of Vera Pawlosky-Glahn and Dougal Jerram who improved the original manuscript with they suggestions. The original first approach in cluster analysis was supported by the ERUPT (European Research on Understanding Processes and Timescales in magma systems) project, funded by the European Commission (EVG1-CT2002-00058), when the main author was involved in his PhD research.
References (79)
- et al.
The evolution of the magmatic system of Stromboli Volcano during the Vancori period (26–13.8 ky)
Journal of Volcanology and Geothermal Research
(2005) - et al.
Magma recharge, contamination and residence times revealed by in situ laser ablation isotopic analysis of feldspar in volcanic rocks
Earth and Planetary Science Letters
(2001) - et al.
Sr-isotope evidence for short magma residence time for the 20 century activity at Stromboli volcano, Italy
Earth and Planetary Science Letters
(1999) - et al.
The volcanic activity of Stromboli in the 1906–1998 A.D. period: mineralogical, geochemical and isotope data relevant to the understanding of the plumbing system
Journal of Volcanology and Geothermal Research
(2004) The statistical analysis of compositional data
Journal of the Royal Statistical Society Series B
(1982)The Statistical Analysis of Compositional Data
Monographs on Statistics and Applied Probability
(1986)On criteria of measures of compositional difference
Mathematical Geology
(1992)- et al.
Compositional data analysis: where are we and where should we be heading?
Mathematical Geology
(2005) - et al.
Cluster Analysis
(1984) - et al.
Algorithmic modifications extending MELTS to calculate subsolidus phase relations
American Mineralogist
(1998)
Crystal-chemistry of Ba-rich trioctahedral micas-1M
European Journal of Mineralogy
Vector sets
Acta Crystallographica
Crystal size distribution (CSD) in rocks and the kinetics and dynamics of crystallization II. Makaopuhi lava lake
Contributions to Mineralogy and Petrology
A chlorite solid solution geothermometer. The Los Azufres (Mexico) geothermal system
Contribution Mineralogy and Petrology
On correlation between variables of constant sum
Journal of Geophysical Research
Numerical correlation and petrographic variation
The Journal of Geology
Ratio Correlation
Textural and Sr isotopical analysis of plagioclase phenocrysts from Stromboli volcano (Aeolian Islands): evidence for open-system magmatic processes in the evolution and eruption of the Vancori series
Compositional layering and Syn-eruptive mixing of a periodically refilled shallow magma chamber: the AD 79 plinian eruption of Vesuvius
Journal of Petrology
Magma mixing and convective compositional layering within the Vesuvius magma chamber
Bulletin of Volcanology
Reaction rim growth on olivine in silicic melts: implications for magma mixing
American Mineralogist
The occurrence of forsterite and highly oxidising conditions in basaltic lavas from Stromboli Volcano, Italy
Journal of Petrology
Recharge in volcanic systems: evidence from isotope profiles of phenocrysts
Science
Single-Chain Silicates
Magma storage region processes inferred from geochemistry of Fe–Ti oxides in Andesitic magma, Soufrière Hills Volcano, Montserrat, W.I.
Journal of Petrology
Isometric logratio transformations for compositional data analysis
Mathematical Geology
Cluster Analysis
On the cophenetic correlation coefficient
Systematic Zoology
Sur la liason et la division des points d'un ensemble fini
Colloquium Mathematicae
Sr-isotopic systematics in volcanic rocks from the island of Stromboli (Aeolian arc)
Chemical Geology
Volcanological and magmatological evolution of Stromboli volcano (Aeolian islands): the roles of fractional crystallisation, magma mixing, crustal contamination and source heterogeneity
Bulletin of Volcanology
Magmatological evolution of the Stromboli volcano (Aeolian Arc, Italy): inferences from major and trace element and Sr-isotopic composition of lavas and pyroclastic rocks
Acta Vulcanologica
Intra-grain Sr isotope evidence for crystal recycling and multiple magma reservoirs in the recent activity of Stromboli Volcano, Souther Italy
Journal of Petrology
Compositional data analysis and zeros in micro data
Applied Economics
Chemical mass transfer in magmatic processes. IV. A revised and internally consistent thermodynamic model for the interpolation and extrapolation of liquid–solid equilibria in systems at elevated temperatures and pressures
Contributions to Mineralogy and Petrology
The pMELTS; a revision of MELTS for improved calculation of phase relations and major element partitioning related to partial melting of the mantle to 3 GPa
Geochemistry, Geophysics, Geosystems-G
Classification
Metrics on surfaces
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