A Linear Programming and Least Squares Computer Method for Solving Petrologic Mixing Problems

Wright, Thomas L.; Doherty, Patrick C.

doi:10.1130/0016-7606(1970)81[1995:alpals]2.0.co;2

Cited by 464 publications

(104 citation statements)

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“…2). Least square linear approximation calculations (Wright and Doherty 1970) suggest that the least-magnesian melt inclusion compositions (MgO $8 wt%) can be produced from primitive melts (MgO $10.3 wt%) by 44.8 wt% crystallization of olivine, clinopyroxene, and plagioclase in proportions 3.9:21.8:18.4 (Table 4), which are consistent with Fig. 7 Compositions of melt inclusions in olivine from sample TRD-150 compared with those in olivines from UPL-I (shaded area, after Sobolev et al 1993).…”

Section: Discussionmentioning

confidence: 99%

Coexistence of two distinct mantle sources during formation of ophiolites: a case study of primitive pillow-lavas from the lowest part of the volcanic section of the Troodos Ophiolite, Cyprus

Portnyagin

Danyushevsky²,

Kamenetsky³

1997

Contributions to Mineralogy and Petrology

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We present a detailed mineralogical, petrological and melt inclusion study of unusually fresh, primitive olivine + clinopyroxene phyric Lower Pillow Lavas (LPL) found near Analiondas village in the northeastern part of the Troodos ophiolite (Cyprus). Olivine phenocrysts in these primitive LPL show a wide compositional range (Fo 82±92 ) and have higher CaO contents than those from the Upper Pillow Lavas (UPL). Cr-spinel inclusions in olivine are signi®cantly less Cr-rich (Cr/Cr + Al = 28±67 mol%) compared to those from the UPL (Cr# = 70±80). These features reect di erences in melt compositions between primitive LPL and the UPL, namely higher CaO and Al 2 O 3 and lower FeO* compared to the UPL at a given MgO. LPL parental melts (in equilibrium with Fo 92 ) had $10.5 wt% MgO and crystallization temperatures $1210°C, which are signi®cantly lower than those previously published for the UPL (14±15 wt% MgO and $1300°C for Fo 92 ). The fractionation path of LPL parental melts is also di erent from that of the UPL. It is characterized initially by olivine + clinopyroxene cotectic crystallization joined by plagioclase at $9 wt% MgO, whereas UPL parental melts experienced a substantial interval of olivine-only crystallization. Primitive LPL melts were formed from a mantle source which was more fertile than that of tholeiites from well-developed intra-oceanic arcs, but broadly similar in its fertility to that of MidOcean Ridge Basalt (MORB) and Back Arc Basin Basalts (BABB). The higher degrees of melting during formation of the LPL primary melts compared to average MORB were caused by the presence of subduction-related components (H 2 O). Our new data on the LPL coupled with existing data for the UPL support the existing idea that the LPL and UPL primary melts originated from distinct mantle sources, which cannot be related by progressive source depletion. Temperature di erences between these sources ($150°C), their position in the mantle ($10 kbar for the colder LPL source vs 15±18 kbar for the UPL source), and temporal succession of Troodos volcanism, all cannot be reconciled in the framework of existing models of mantle wedge processes, thermal structure and evolution, if a single mantle source is invoked. Possible tectonic settings for the origin of the Troodos ophiolite (forearc regions of intra-oceanic island arc, propagation of backarc spreading into arc lithosphere) are discussed.

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Section: Discussionmentioning

confidence: 99%

Coexistence of two distinct mantle sources during formation of ophiolites: a case study of primitive pillow-lavas from the lowest part of the volcanic section of the Troodos Ophiolite, Cyprus

Portnyagin

Danyushevsky²,

Kamenetsky³

1997

Contributions to Mineralogy and Petrology

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“…The percentage of residual minerals has been calculated by linear programming, minimizing the sum of squares of residuals as a constraint (SSR; e.g. Wright & Doherty, 1970) starting from the bulk partition coefficient modelled and using literature partition coefficients (Table 5; GERM data set, http://earthref.org/GERM/main.htm).…”

Section: B Gdsmentioning

confidence: 99%

“…Bulk partition coefficients used to model GDS rocks. Residuum assemblages calculated using linear programming (Wright & Doherty, 1970) minimizing the sum of squares of residuals as a constraint (SSR). Mineral abbreviations are after Kretz (1983).…”

Section: B Gdsmentioning

confidence: 99%

“…Fractionating assemblages have been calculated by linear programming, minimizing the sum of squares of residuals as a constraint (SSR; e.g. Wright & Doherty, 1970), starting from the bulk partition coefficient modelled and using literature partition coefficients (GERM dataset, http://earthref.org/GERM/main.htm). Calculated fractionating assemblages are similar for the two models AFC1 and AFC2, and are roughly dominated by quartz (∼ 40 %), plagioclase (∼ 35 %), Kfeldspar (∼ 8 %) and biotite (∼ 13 %).…”

Section: C Tmgmentioning

confidence: 99%

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Petrogenetic and tectonic inferences from the study of the Mt Cer pluton (West Serbia)

et al. 2010

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-The Mt Cer Pluton, Serbia, is a complex laccolith-like intrusion (∼ 60 km 2 ), situated along the junction between the southern Pannonian Basin and northern Dinarides. It intrudes Palaeozoic metamorphic rocks causing weak to strong thermal effects. Based on modal and chemical compositions, four rock-types can be distinguished: (1) metaluminous I-type quartz monzonite/quartz monzodiorite (QMZD); (2) peraluminous S-type two-mica granite (TMG), which intrudes QMZD; (3) Stražanica granodiorite/quartz monzonite (GDS); and (4) isolated mafic enclaves (ME), found only in QMZD. 40 K-39 Ar dating and geological constraints indicate that the main quartz monzonite/quartz monzodiorite body of Mt Cer was emplaced not later than 21 Ma, whereas the emplacement ages of the Stražanica granodiorite/quartz monzonite and two-mica granites are estimated at around 18 and 16 Ma, respectively. The Mt Cer pluton is similar to the Mt Bukulja pluton, some 80 km southwestwards. Genesis of QMZD cannot be interpreted by fractional crystallization coupled with mixing or assimilation. It is best explained by a convection-diffusion process between mantle-derived minette/leucominette magmas and GDS-like magmas followed by two end-member magma mixing. The composition of GDS rocks suggests that GDS-like magmas could have formed by melting of lower crustal lithologies similar to amphibolite/metabasalts. The geochemistry of TMG is reproduced by an Assimilation/Fractional Crystallization model with a ratio of rate of assimilation to rate of fractional crystallization of 0.4, using the compositions of the least evolved TMG of the Bukulja pluton and adjacent metamorphic rocks as proxies for the parental magma and contaminant, respectively. The origin and evolution of the Mt Cer and adjacent Mt Bukulja plutons provide new constraints on the Tertiary geodynamics of the northern Dinarides-southern Pannonian region. The quartz monzonite/quartz monzodiorite is interpreted as a result of the Oligocene post-collisional Dinaride orogen-collapse, which included a limited lithosphere delamination, small-scale mantle upwelling, and melting of the lower crust. By contrast, the two-mica granite magmas formed through melting in shallower crustal levels during the extensional collapse in the Pannonian area.

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“…Los más sencillos realizan el cálculo de balances de masas por mínimos cuadrados [p. ej., XLFRAC, Stormer y Nicholls (1978); GENMIX, Le Maitre (1981) y Wright y Doherty (1974)]. Otros programas como TRAZAS (Cebriá y López Ruiz, 1990y 1992 Y PEARCE.PLOT (Stanley y Russell, 1989) permiten la modelización directa de la cristalización en equilibrio y fraccionada simple y la elaboración de diagramas de Pearce, respectivamente.…”

Section: Recomendaciones Prácticasunclassified

Untitled

Cebriá¹,

Ruíz²

1994

Estud. geol.

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RESUMENDurante los procesos de diferenciación por cristalización los elementos mayores y traza y los isótopos estables sufren fraccionación, mientras que los isótopos radiogénicos no varían.Las ecuaciones propuestas parlO_ los diferentes procesos de diferenciación permiten establecer las pautas de variación de los elementos mayores y traza durante cada uno de estos procesos. En la cristalización fraccionada simple el líquido residual se empobrece rápidamente en elementos compatibles y se enriquece en elementos incompatibles, a medida que progresa la cristalizaciélll. En la cristalización in situ el líquido evoluciona de forma idéntica a la cristalización fraccionada simple por lo que respecta a los elementos altamente incompatibles, pero experimenta un menor incremento en lo que concierne a los elementos moderadamente incompatibles; en cuanto a los elementos compatibles, los líquidos residuales también se empobrecen, aunque mucho más suavemente que en los derivados por cristalización fraccionada simple, incluso para valores de faltos.Si tiene lugar el rellenado cíclico de la cámara y todo el líquido presente en la misma desaparece al final de cada ciclo, el magma sigue las mismas pautas que en la cristalización fraccionada simple. Por el cortrario, si la fracción de líquido que cristaliza en cada ciclo y la del líquido eruptado al final de cada ciclo son pequeñas, la composición del líquido residual se aproxima a la que se obtiene por cristalización en equilibrio.La modelización de los proceses de cristalización plantea menos dificultades que la de la fusión parcial. Si una serie d~rocas s~ha generado por cristalización fraccionada simple, su proyección en diagramas el -C-L si i es un elemento compatible y j un elemento altamente incompatible, permite una buena aproximación a la composición del magma inicial. Asimismo la proyección en diagramas log Cl-log Ci, en la que el elemento i es altamente incompatible, permite identificar las distintas etapas del proceso y calcular los coeficientes de distribución global de los elementos traza del sistema. Palabras clave: Cristalización en equilibrio, cristalización fraccionada simple, cristalización in situ, relleno cíclico, elementos mayores, elementos traza, isótopos radiogénicos, isótopos estables. ABSTRACTDuring crystallization processes, major and trace elements and stable isotopes fractionate, whereas radiogenic isotopes do not change.The different equations proposed allow us to reproduce the variation in major and trace elements during these differl~ntiation processes. In the case of simple fractional crystallization, the residualliquid i~impoverished in compatible elements faster than it is enriched in incompatible elements as crystallization proceeds. During in situ crystallization the highly incompatible elements evolve in a similar way to the case of simple fractional crystallization but the enrichment rate of the moderately incompatible elements is slower and the compatible element; do not suffer a depletion as strong as the one observed during simple fractio...

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A Linear Programming and Least Squares Computer Method for Solving Petrologic Mixing Problems

Cited by 464 publications

References 4 publications

Coexistence of two distinct mantle sources during formation of ophiolites: a case study of primitive pillow-lavas from the lowest part of the volcanic section of the Troodos Ophiolite, Cyprus

Coexistence of two distinct mantle sources during formation of ophiolites: a case study of primitive pillow-lavas from the lowest part of the volcanic section of the Troodos Ophiolite, Cyprus

Petrogenetic and tectonic inferences from the study of the Mt Cer pluton (West Serbia)

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