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)

Abstract

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).

Present state of knowledge and new geochemical constraints on the central part of the Mexican Volcanic Belt and comparison with the Central American Volcanic Arc in terms of near and far trench magmas

“…The presence of disequilibrium phenocryst assemblages is a common characteristic in several volcanoes of the C-MVB, which has been interpreted as mixing or mingling of magmas in crustal reservoirs (Nixon, 1988a(Nixon, , 1988bAguirre-Díaz, 2001;Márquez and De Ignacio, 2002;Witter et al, 2005;Velasco-Tapia, 2014). It is, therefore, indispensable to take into account shallowlevel processes before inferring about the deeper mantle and subduction processes.…”

“…The new discriminant function-based tectonic discrimination diagrams Agrawal et al, 2008;Verma and Agrawal, 2011) (Hofmann and Feigenson, 1983;Hofmann et al, 1984;McKenzie and O'Nions, 1991;Ormerod et al, 1991;Feigenson and Carr, 1993;Maaløe, 1994;Velasco-Tapia andVerma, 2001a, 2013;Feigenson et al, 2003;Verma, 2004Verma, , 2006. Basic magmas with characteristics of primitive, little-differentiated magmas are present throughout the MVB (e.g., Luhr et al, 1989;Luhr, 1997;Wallace and Carmichael, 1999;Verma, 2000aVerma, , 2002Verma, , 2004, as well as in the LTVF (Verma et al, 1993a;Nelson et al, 1995;Verma, 2006).…”

“…Sr, Nd, Pb, Os, Be, and Hf isotopes Isotopic compositions have proved to be extremely useful in petrogenetic studies of volcanic provinces (e.g., Best and Christiansen, 2001;Faure, 2001;McBirney, 2007), and the MVB has been no exception. Numerous studies have been published on the Sr, Nd, and Pb isotopes from the MVB (Verma, 1983(Verma, , 1999(Verma, , 2000a(Verma, , 2000b(Verma, , 2001a(Verma, , 2001b(Verma, , 2001c(Verma, , 2002(Verma, , 2003(Verma, , 2015aBoudal, 1985;Verma and Nelson, 1989;Verma et al, 1991;Nakagawa et al, 1998;Siebe et al, 1999Siebe et al, , 2004Blatter et al, 2001Blatter et al, , 2007Velasco-Tapia andVerma, 2001a, 2013;Aguirre-Díaz et al, 2002;Verma and Carrasco-Núñez, 2003;Martínez-Serrano et al, 2004;Verma and Hasenaka, 2004;Schaaf et al, 2005;Verma et al, 2005;Gómez-Tuena et al, 2007b;Mukasa et al, 2007;Meriggi et al, 2008;García Tovar, 2009;Agustín-Flores et al, 2011;Torres-Alvarado et al, 2011;Arce et al, 2013;Koloskov and Khubunaya, 2013;Cai et al, 2014), including the present work. The shift to the right of the mantl...…”

“…The shift to the right of the mantle array (Verma, 2006), towards and beyond the mean composition of subducted slab (Verma, 2000a(Verma, , 2002, commonly observed in all arcs around the world, has not been documented in the MVB, which makes this volcanic province atypical for it to be an arc. An important point to mention here is that the Sr and Nd isotopic data should be adjusted to given reference values for the standards used for estimating mass spectrometric bias, as has been done in all studies on the MVB published by our group (Verma and Nelson, 1989;Verma et al, 1991;Verma, , 1999Verma, , 2000aVerma, , 2000bVerma, , 2001aVerma, , 2001bVerma, , 2001cVerma, , 2002Verma, , 2003Verma, , 2015aVelasco-Tapia andVerma, 2001a, 2013;Verma and Carrasco-Núñez, 2003;Verma and Hasenaka, 2004;Verma et al, 2005;Torres-Alvarado et al, 2011;Velasco-Tapia and Verma, 2013). Most other scholars studying the MVB have unfortunately not followed this convention (e.g., Boudal, 1985;Nakagawa et al, 1998;Siebe et al, 1999Siebe et al, , 2004Blatter et al, 2001Blatter et al, , 2007Aguirre-Díaz et al, 2002;Martínez-Serrano et al, 2004;Schaaf et al, 2005;Mukasa et al, 2007;García-Tovar, 2009;Agustín-Flores et al, 2011;Arce et al, 2013;Koloskov and Khubunaya, 2013;Cai et al, 2014)<...>…”

“…The continental rift setting was represented by welldeveloped rifts as well as extensional areas and postcollision extension zones as follows: 1) San Luis Potosí, MexicoNeogene rocks (Aguillón-Robles et al, 2012, 2014; 2) Baja California, Mexico -Pliocene-Pleistocene as well as late Miocene (Calmus et al, 2003); 3) Mogollon-Datil volcanic field, New Mexico, USA (Davis and Hawkesworth, 1995); 4) NW Cerro del Rio, New Mexico, USA (Duncker et al, 1991); 5) Basin and Range, Nevada-Arizona, USA Feuerbach et al, 1993); 6) Rio Grande rift, New Mexico, USA (Gibson et al, 1992;McMillan et al, 2000); 7) San Juan volcanic field, Colorado, USA (Parat et al, 2005); 8) Hurricane volcanic field, Utah, USA (Smith et al, 1999); 9) Santa Rosa Calico volcanic field, Nevada, USA (Brueseke and Hart, 2009); 10) Western USA (Leat et al, 1989;Kempton et al, 1991); 11) Northwest Iran (Kheirkhah et al, 2009); 12) Eastern Iran (Pang et al, 2012); 13) Postcollision extensional Miocene-Holocene rocks from Western and Northwestern Anatolia, Turkey (Aldanmaz et al, 2000;Akal, 2003;Agostini et al, 2007Agostini et al, , 2010; 14) Postcollision extensional Miocene-Holocene rocks from Eastern Anatolia, Turkey (Karsli et al, 2008;Varol and Alpaslan, 2012); 15) North and Northeast China (Zhang et al, 1995;Han et al, 1999); 16) Postcollision extensional Miocene rocks from the Lhasa terrane, Tibet (Chen et al, 2010); 17) Postcollision extensional MiocenePleistocene rocks from Central and Southern Tibet (Turner et al, 1993;Zhidan et al, 2001;Hou et al, 2004;Zhao et al, 2009); 18) Morocco and Mali, NW Africa (Bertrand, 1991); 19) Djibouti, Afr...…”