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The Scientific World Journal
Volume 2014, Article ID 793236, 32 pages
Research Article

Multivariate Analysis, Mass Balance Techniques, and Statistical Tests as Tools in Igneous Petrology: Application to the Sierra de las Cruces Volcanic Range (Mexican Volcanic Belt)

Universidad Autónoma de Nuevo León, Facultad de Ciencias de la Tierra, Ex-Hacienda de Guadalupe, Carretera Linares-Cerro Prieto km 8, 67700 Linares, NL, Mexico

Received 26 August 2013; Accepted 25 November 2013; Published 5 March 2014

Academic Editors: J. Glodny, N. Hirao, and G.-L. Yuan

Copyright © 2014 Fernando Velasco-Tapia. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Magmatic processes have usually been identified and evaluated using qualitative or semiquantitative geochemical or isotopic tools based on a restricted number of variables. However, a more complete and quantitative view could be reached applying multivariate analysis, mass balance techniques, and statistical tests. As an example, in this work a statistical and quantitative scheme is applied to analyze the geochemical features for the Sierra de las Cruces (SC) volcanic range (Mexican Volcanic Belt). In this locality, the volcanic activity (3.7 to 0.5 Ma) was dominantly dacitic, but the presence of spheroidal andesitic enclaves and/or diverse disequilibrium features in majority of lavas confirms the operation of magma mixing/mingling. New discriminant-function-based multidimensional diagrams were used to discriminate tectonic setting. Statistical tests of discordancy and significance were applied to evaluate the influence of the subducting Cocos plate, which seems to be rather negligible for the SC magmas in relation to several major and trace elements. A cluster analysis following Ward’s linkage rule was carried out to classify the SC volcanic rocks geochemical groups. Finally, two mass-balance schemes were applied for the quantitative evaluation of the proportion of the end-member components (dacitic and andesitic magmas) in the comingled lavas (binary mixtures).