Igneous rock associations 8. Arc magmatism II: geochemical and isotopic characteristics.
Geochemical and isotopic data provide insights into the origin and evolution of magmatism found at destructive plate margins. Tholeiitic magmas are dominant in the early stages of oceanic island-arc genesis and calc-alkalic magmas are most common in mature oceanic arcs and in continental arcs where they may range from basalt to rhyolite in composition, including voluminous intermediate (andesitic) rocks. Experiments suggest that calc-alkalic mafic magmas are formed by melting of a hydrated mantle wedge and undergo low pressure fractional crystallization under near-[H.sub.2]O saturated conditions. Intermediate to felsic magmas are derived in a wide variety of ways, including the fractionation of a more mafic parent, mixing between mafic and felsic magmas (a process supported, in many cases, by field and textural evidence), crustal contamination, or partial melting of the crust. All these processes appear to take place, to some degree, in arc systems, although in any given arc system, one mechanism may predominate.
Arc-related calc-alkalic and tholeiitic basalts typically show moderate degrees of light rare-earth-element (LREE) enrichment, and flat heavy rare-earth-element (HREE) profiles, indicating an origin in a shallow (spinel lherzolite) mantle. More evolved magmas exhibit Eu anomalies, consistent with low pressure plagioclase fractionation. Compared to within-plate settings, tholeiitic and calc-alkalic arc magmas have lower abundances in high-field-strength (HFS) elements, possibly because these elements are bound during the accessory phases in the mantle wedge, and are stable during partial melting. Compared to arc tholeiites, calc-alkalic magmas have higher abundances of incompatible large ion lithophile (LIL) elements reflecting enrichment in the mantle wedge source. This characteristic depletion in HFS, and enrichment in LIL, elements, in arc magmas is the basis for a variety of discrimination diagrams. These diagrams constrain processes operating in modern and ancient arc systems and include chondrite-normalized, MORB-normalized and mantle-normalized spidergrams, which are characterized by jagged patterns of trace-element abundances (in contrast to the relatively smooth patterns of within-plate suites).
Some arc suites have depleted initial [sup.143]Nd/[sup.144]Nd and lower initial [sup.87]Sr/[sup.86]Sr than the bulk earth, and are similar to MORB. Other suites have enriched isotopic patterns consistent with the influence of subducted oceanic sediments on the composition of the magma. Samarium-Nd and Rb-Sr isotopic studies can be used to distinguish between felsic magmas derived from fractional crystallization of a more mafic parent (which would have similar values) and those derived from the melting of ancient crust.
Les donnees geochimiques et isotopiques fournissent des indications quant a l'origine et a l'evolution du magmatisme des marges de subduction des plaques tectoniques. Les magmas sont principalement tholeiitiques darts les premieres phases de formation des arcs insulaires oceaniques, alors qu'ils sont principalement calco-alcalins pendant les phases terminales des arcs insulaires oceaniques ainsi que dans les arcs insulaires continentaux, off leur composition peut aller du basalte a la rhyolite, dont des volumes considerables de roches de composition intermediaire (andesitique). Des experiences permettent de penser que les magmas mafiques calco-alcalins sont formes par la fusion d'un biseau mantelique hydrate qui subit une cristallisation fractionnee a basse pression en des conditions de quasi-saturation en [H.sub.2]O. Les magmas de composition intermediaire a felsique resultent de mecanismes tres varies, dont le fractionnement d'une roche mere plus mafique, le melange de magmas felsiques et mafiques (mecanismes mis en evidence par des donnees de terrain et l'analyse texturale), la contamination crustale, ou la fusion partielle de la croute. Tous ces mecanismes semblent se produire, au moins partiellement, au sein d'arcs insulaires, mais l'un d'eux peut constituer le mecanisme predominant de quelque systeme d'arcs insulaires particulicr.
L'enrichissement modere typique des basaltes calco-alcalins et tholeiitiques d'arcs insulaires en elements legers des terres (LREE) rares ainsi que le profil plat de leur contenu en elements lourds desterres tares (HREE) sont des indicateurs d'une origine mantelique peu profonde (iherzolithe a spinelle). Les magmas plus evolues affichent des anomalies en Eu, ce qui concorde avec un fractionnement a basse temperature des plagioclases. Compares a ceux des contextes intra-plaques, les magmas tholeiitiques et calco-alcalins d'arcs insulaires affichent des contenus moindres en elements a grande intensite de champ, peut-etre parce que ces elements sont lies pendant les phases accessoires dans le biseau mantelique, et sont stables pendant la phase de fusion partielle. Compares aux tholeiites d'arcs insulaires, les magmas calco-alcalins ont des contenus plus eleves en elements lithophiles a grands champs ioniques incompatibles, ce qui est le reflet d'un enrichissement au sein du biseau mantelique source. Cet appauvrissement caracterisuque en elements a grande intensite de champ (HFS) et cet enrichissement en elements lithophiles a grands champs ioniques (LIL) des magmas d'arcs insulaires forment la base d'une variete de diagrammes de discrimination. Ces diagrammes permettent de preciser les processus en jeu des systemes d'arcs insulaires modernes et anciens et incluent des diagrammes radiaux normalises pour les chondrites, pour les basaltes de dorsales oceaniques (MORB) et pour le manteau, lesquels son caracterises par des profils anguleux irreguliers des courbes de contenus en elements traces (en contraste avec les profils relativement reguliers des suites intra-cratoniques).
Certaines suites d'arcs insulaires montrent des ratios initiaux [sup.143]Nd/[sup.144]Nd appauvris et [sup87]Sr/[sup.86]Sr inferieurs a celui de la valeur planetaire actuelle, et qui sont semblables a celui des basaltes de dorsales oceaniques. D'autres suites ont des profils isotopiques enrichis, ce qui correspond a une influence de sediments oceaniques subductes sur la composition du magma. Les etudes samarium-neodymium et rubidium-strontium peuvent etre utilisees pour differencier entre les magmas felsiques issus d'une cristallisation fractionnee d'une roche mere plus mafique (qui montrerait des valeurs similaires) et ceux provenant de la fusion d'une croute ancienne.
This is the second of two articles on arc magmatism intended for geoscientists who do not specialize in petrology or geochemistry. The first article (Murphy 2006) explored the broad relationship between the tectonic evolution of arcs and magma genesis, composition and evolution. This article focuses on the geochemical, isotopic and petrological evolution of arc magmas. For a more detailed analysis, the reader is referred to comprehensive reviews of the geochemical and petrological aspects of arc magmatism in papers (e.g. Arculus and Curran 1972; Ringwood 1977; Pearce and Norry 1979; Gill 1981; Pearce 1982; Tatsumi and Eggins 1995; Morris and Ryan 2004; Keleman 2004) and in recent textbooks (e.g. Winter 2001; Blatt et al. 2005).
Arc magmatism is the end result of subduction of oceanic lithosphere caused by the sinking of a dense oceanic plate beneath an adjacent, less dense overriding plate (Fig. 1). This descent is characterized by a long, narrow, curvilinear trench in the ocean floor. With rare exceptions, magmas form in the mantle wedge above the subduction zone (i.e. in the overriding plate), and/or the crust. These magmas ascend to form arcs, either continental arcs (e.g. the Andes) or island arcs (e.g. the western Pacific Ocean). Island arcs capped by oceanic crust are dominated by mafic magmatism, and those capped by continental crust by felsic magmatism. Magmatism is also important in the "backarc" region behind these arcs, especially during episodes of extension.
[FIGURE 1 OMITTED]
This article begins with an overview of the major-, trace- and rare-earth chemistry of arc magmas to provide constraints on the source of the magmas and their subsequent evolution. This is followed by a review of the principles behind tectonic and magmatic discrimination diagrams including the so-called "spider diagrams" and the information they provide about petrogenesis. A review of petrogenetic-indicating isotopes is presented, which helps constrain the source regions of magmas and the relationships among coeval mafic, intermediate and felsic magmas. Some of the less common igneous rocks that can occur in arc settings (e.g. adakites, shoshonites, and boninites) are reviewed and the paper concludes with a brief overview of arc rocks in ancient settings.
In contrast to most other tectonic regimes, arc plutonic and volcanic rocks are characterized by chemical diversity as shown by their wide distribution on standard classification schemes (e.g. Streckeisen 1976, 1979; LeMaitre et al. 1989), and range from mafic to felsic in composition. There are, however, some useful generalities. Mafic rocks, such as gabbros and basalts, tend to be most abundant in primitive oceanic arcs. With increasing arc maturity, and/or crustal thickness, intermediate to felsic magmas (diorites to granites, andesites to rhyolites) predominate (e.g. Miyashiro 1974). Except for some special cases, even the most mafic arc rocks are quartz-normative. Alkali-rich rocks and feldspathoidal rocks are tare (feldspathoids and quartz are mutually exclusive) and plagioclase typically dominates over alkalifeldspar.
In recent years, chemical studies of arc magmas have integrated data from major elements (those that typically comprise 0.1 wt % or higher), trace elements (less than 0.1 wt %), rare-earth elements (generally the "lanthanides") and isotopes (typically RbSr, Sm-Nd and U-Pb systems). Important goals of these studies are to determine i) the nature of the source region of arc magmas, ii) how the magma chemistry evolves as it rises toward the surface and interacts with its surroundings, and iii) the cooling history as the magma is transformed into igneous rock.
Phase equilibria predict that intermediate and felsic rocks can originate by fractional crystallization of a more basic parent because the early fractionation of olivine, clinopyroxene and plagioclase drives the liquid toward more silicic compositions (Fig. 2). Experimental and theoretical studies (e.g. Grove and Baker 1984; Ghiorso and Sack 1995) show that this fractionation scheme yields a tholeiitic trend (i.e. significant enrichment in Fe[O.sup.*]/MgO) because the fractionating phases contain lower Fe[O.sup.*]/MgO than the melt (note that Fe[O.sup.*] is the symbol for total iron oxide, in which FeO and [Fe.sub.2][O.sub.3] are combined). However, in the simplest sense, this process should produce volumetrically less andesite than basalt, and still less rhyolite. So, many authors consider it unlikely that such a process could, by itself, yield the vast volumes of andesitic and rhyolitic magmas that occur in matute arcs, even if magnetite were to appear on the liquidus to subdue iron enrichment trends.
[FIGURE 2 OMITTED]
Alternatively, ongoing underplating by mantle-derived magma delivers a significant amount of heat to the base of the crust, eventually sufficient to induce partial melting of crust, which typically produces felsic magmas (see Murphy 2006, fig. 16). Many arc systems, especially those capped by thick continental crust, have mafic magmas derived from the mantle, intermediate to felsic magmas formed by fractionation of a more mafic parent, and felsic magmas that are derived by partial melting of the crust. Magmas with intermediate compositions can also be produced by mixing at depth of mafic and felsic end-member compositions (e.g. Eichelberger 1975; Gill 1981; Carmichael 2002). There is a general consensus that all these processes occur to some degree in arc systems, and in any locality, it can be challenging to distinguish among them.
[FIGURE 16 OMITTED]
Major Element Chemistry
Major element abundances profoundly influence physical properties such as magma viscosity and density, which in turn affect the rate at which magmas rise in the crust. The major element chemistry of parental magmas formed by partial melting is primarily controlled by phase equilibria. This principle is shown schematically in Figure 2 in which a magma of composition M, representing the minimum temperature in the system, is produced by melting of host rocks (e.g. X) with a wide range of bulk compositions. Once magma is produced, its major-element composition mostly controls what silicate minerals eventually grow from the magma, and so the chemical evolution of the cooling magma is constrained by phase equilibria. Experimental and observational evidence suggest that olivine, followed by clinopyroxene and plagioclase, are the earliest crystallizing phases from mafic magma. Fractional crystallization of ferromagnesian phases such as olivine and clinopyroxene leads to systematic depletion in Fe[O.sup.*], MgO, and enrichment in elements such as Si[O.sub.2], [Na.sub.2]O and [K.sub.2]O. When plagioclase appears on the liquidus, the remaining liquid becomes depleted in CaO and [Al.sub.2][O.sub.3]. Figure 2 shows the evolution of a typical basaltic liquid in a shallow magma chamber (i.e. low pressures). As long as the system remains closed, cooling of a basaltic liquid of composition X will initially produce forsterite (olivine), and then enstatite. Equilibrium crystallization or fractionation of these minerals drives the residual liquid composition away initially from olivine (X to T) until it reaches and then descends the olivine-enstatite curve (T to P). Along pathway X to P, the magma becomes enriched in other components, including those of plagioclase (represented by anorthite). As path T to P is alonga reaction curve, olivine reacts with the liquid and enstatite is precipitated. Once plagioclase begins to crystallize, the residual magma also becomes depleted in CaO and [Al.sub.2][O.sub.3]. The overall result is that mafic liquids evolve towards more intermediate and felsic compositions.
The composition of the minerals also reflects fractionation. The Fe[O.sup.*]/MgO ratio found in the olivines and pyroxenes increases with fractionation, as shown, for example, in the simple phase relationships in Figure 3. Olivine and clinopyroxene phenocrysts in arc basalts are more iron-rich than those that are in equilibrium with mantle rocks, suggesting that even the most primitive arc magmas are fractionated to some degree and that true primary magmas (i.e. melts directly derived from the mantle) are rare.
[FIGURE 3 OMITTED]
Mineral compositions are also susceptible to the tectonic environment in which they are formed. For example, Leterrier et al. (1982) showed that for clinopyroxenes of similar Ca content, those in arc-related mafic rocks have lower Ti + Cr than those in non-orogenic settings (Fig. 4).
[FIGURE 4 OMITTED]
As most volcanic rocks are dominated by a glassy or fine grained matrix, their minerals are poorly developed and so they are more effectively classified by their chemistry rather than their mineral content. The most familiar classification of lavas is based on silica content (Fig. 5). However, arc magmas are so chemically diverse, that to be able to understand the petrologic processes responsible, additional elements must be use& Magmas with similar silica content can be distinguished from one another by examining the concentration of other elements. For example, many basalts in subduction zone environments are characterized by high [Al.sub.2][O.sub.3] (17.0-21.0 wt %) and low MgO (< 6 wt %), compared with basalts in other tectonic settings, and are known as high-alumina basalt. Although their origin is unclear, their low MgO content suggests that they are fractionated (by removal of olivine and augite) from a more mafic parent. The high [Al.sub.2][O.sub.3] implies that plagioclase was not a liquidus phase.
Two suites, or collections of magmas, known as alkalic and subalkalic, can be distinguished on the basis of their alkali content ([Na.sub.2]O + [K.sub.2]0; MacDonald 1968; Cox et al. 1979; Wilson 1989; Rollinson 1993). For the same silica content, alkalic basalts have higher [Na.sub.2]O + [K.sub.2]O than subalkalic basalts, and alkalic rhyolites have higher [Na.sub.2]O + [K.sub.2]O than subalkalic rhyolites (Fig. 5). Subalkalic suites are further divided into tholeiitic or calc-alkalic suites on the basis of their Fe[O.sup.*] and MgO contents. In both suites, Fe[O.sup.*] and MgO decreases with fractionation, which suggests the importance of ferromagnesian minerals, such as olivine and pyroxene in the evolution of both types of magma. However, for rocks of the same silica content, tholeiitic rocks have higher Fe[O.sup.*]/MgO ratios than calc-alkalic rocks (Miyashiro 1974; Fig. 6).
[FIGURES 5-6 OMITTED]
Even within an individual suite, there are further distinctions that can be made. For example, tholeiitic rocks that occur in arc environments can be distinguished from tholeiitic rocks in other settings by the concentrations of other elements, including their [K.sub.2]O content, which tends to be lower than in rift-related tholeiites (e.g. Gill 1981). These island-arc tholeiites (IAT) are also known as "low-K tholeiites" and typically have [K.sub.2]O < 0.8 wt%.
Although the generation of each suite of rocks is controversial, there are some general over-arching principles. Using the Japanese arc as an example, Kuno (1966) drew attention to the increasing [K.sub.2]O content in rocks that have similar Si[O.sub.2], with increasing distance from the trench (and hence greater height above the subduction zone), the so-called K-h relationship (Dickinson 1975). Thus tholeiitic basalts, which typically occur nearer to the trench, have lower [K.sub.2]O contents than calc-alkalic basalts, whose [K.sub.2]O content increases farther away from the trench. Gill (1981) recognized volumetrically small, but petrologically significant, potassic-rich basaltic to intermediate lavas, known as shoshonites that occur far from the trench in continental arcs.
Some experimental data suggest that high [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] in the mantle may yield silica-undersaturated (i.e. olivine-nepheline normative) aikalic basalts whereas high [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] produces silica-saturated basalts (e.g. Mysen and Boettcher 1975, Boettcher 1977; Eggler 1978; Mysen 1988). As alkalies readily partition into melt, alkalic basalts are thought to represent small degrees of partial melting, possibly from a source mantle previously enriched in alkalies. However, the ascent of such small volumes of melt is mechanically problematic (see Murphy 2006) and so alkalic magmas in arc settings tend to be restricted to specialized settings, such as local rift zones within the arc or backarc region.
The major element composition of calc-aikalic and tholeiitic lavas is reflected in their mineral contents. Arc lavas, especially calc-alkalic lavas, contain abundant phenocrysts and microphenocrysts (up to 20%). A summary of the range of phenocryst content with magma type and composition is shown in (Table 1; after Wilson 1989). Plagioclase is the most abundant phenocryst, and occurs in both calc-alkalic and tholeiitic suites in lavas that range from basaltic to rhyolitic in composition. Plagioclase is characterized by complex zoning patterns that reflect disequilibrium conditions (Shelley 1993; Stewart and Fowler 2001; Murphy 2006) For both tholeiitic and calcalkalic suites, clinopyroxene phenocrysts occur in mafic to intermediate lavas, olivine phenocrysts are typically restricted to the more mafic lavas and orthopyroxene, amphibole and quartz phenocrysts are more common in intermediate to felsic lavas. Many phenocrysts, like plagioclase, exhibit textural and chemical evidence of disequilibrium. Although magnetite is a common phenocryst in intermediate to felsic lavas of both magma series, it also occurs as a phenocryst in mafic lavas in calc-alkalic suites.
As the calc-alkalic suite is the most dominant suite in arc environments, especially so in mature arcs, the processes responsible for their limited increase in Fe[O.sup.*]/MgO have received considerable attention. Phase-equilibria studies show that, like tholeiites, fractionation of olivine and pyroxene are important in the earliest stages of fractionation of calc-alkalic magmas. Miyashiro (1974) proposed that water derived from the subduction zone leads to oxidized melts, and the early precipitation of oxide minerals such as magnetite ([Fe.sub.3][O.sub.4]). This interpretation is consistent with petrographic observations that magnetite is a common phenocryst in basaltic calc-alkalic basalts bur is rare in tholeiitic basalts. Precipitation of magnetite would inhib it enrichment in Fe[O.sup.*]/MgO with fractionation, leading to a calc-alkalic trend. Experimental evidence, however, yields conflicting results. Lee et al. (2005) found that the oxidation state of the magma in arc environments is similar to that of the mid-ocean ridge basalts (MORB), and that the degree of oxidation might be buffered by mantle mineral assemblages. Sisson and Grove (1993) show that low pressure (2 kb) fractionation of a [H.sub.2]O-rich (4-6 wt %) basalt can reproduce calc-alkalic trends by crystallization of olivine, Ca-rich plagioclase (An > 90) and either magnetite or spinel. Ringwood (1977) and Boettcher (1977) point out that [H.sub.2]O-rich magmas would increase the stability of hornblende, which would have a similar Fe[O.sup.*]/MgO to the melt. Fractionation of hornblende would also inhibit the increase of Fe[O.sup.*]/MgO during fractionation and so produce a calc-alkalic trend. The importance of amphibole as a phenocryst in intermediate rocks suggests it may play a role at this stage in the cooling of the magma.
Although there are some controversies, it is generally accepted that water plays a major role in producing calc-alkalic magmas, and so it is not surprising that these magmas are the dominant suite in many arcs. Several experimental studies (e.g. Sisson and Grove 1993; Grove et al. 2003) suggest that calc-alkalic magmas form by hydrous melting of the mantle, and then rise to the shallow crust where they undergo fractional crystallization under near-[H.sub.2]O saturated conditions. Sisson et al. (2005) point out that a significant quantity of rhyolitic liquid can be derived by differentiation or by low-degree partial re-melting of mantle-derived basalt.
Another alternative is that calc-alkaline trends and high volume of intermediate magmas are generated by mixing of mafic and felsic end-member magmas. This is supported by widespread petrographic evidence of textural disequilibrium in andesites (e.g. Eichelberger 1975; Eichelberger et al. 2000, 2006), and by geochemical and isotopic patterns consistent with mixing (Grove et al. 2005; see also the discussion below) and field observations (e.g. Wiebe et al. 2002).
Although several exceptions have been documented, arc magmas exhibit broad chemical trends in space and time during arc evolution. Tholeiitic magmas are common in the early stages of oceanic island-arc genesis and are closer to the trench. The calc-alkalic suite of magmas is the most common in mature oceanic arcs and generally occurs farther from the trench than arc tholeiites; this suite is especially common in continental arcs. There is also a tendency in both suites toward more silicic compositions with increasing arc maturity and crustal thickness, and many calc-alkalic suites range from basaltic to rhyolitic composition, and are typified by an abundance of intermediate (andesitic) rocks.
Trace Element and REE Geochemistry
Trace element, rare-earth-element (REE) and isotopic abundances reflect a variety of factors including the source of the magma, the percentage of the source rock that undergoes melting, the extent of crystal fractionation, and the contamination of either magma from adjacent rocks or from other magmas of other arc systems. In each case, trace element abundances can be modelled (see Appendix 1).
Trace element and REE abundances are sensitive to the appearance of minerals as liquidus phases. For example, Ni and Cr are heavily concentrated into early-crystallizing minerals such as olivine and pyroxene, and Y, Yb and Eu are concentrated in garnet. The fractionation of olivine and pyroxene depletes the remaining liquid in Ni and Cr, providing a sensitive indicator on the extent of their fractionation. Such elements are also known as compatible trace elements because they fit into the structure of early crystallizing minerals and so have a low concentration in the melt. Alternatively, trace elements such as Zr, Hf, Nb, Ta, Ti, and Th are known as incompatible trace elements. They strongly partition into magma, and so their abundances should increase systematically during crystal fractionation. Note that some elements behave incompatibly in some magmas but compatibly in others. For example, Ti is concentrated in hornblende and both V and Ti are concentrated in magnetite. Nevertheless, these minerals can crystallize early or late in the evolution of magmas depending on PH20 and f[O.sub.2] (e.g. Miyashiro 1974; Ringwood 1977). Most calc-alkalic suites record a decrease in Ni, Cr, Ti and V from basalt to andesite, consistent with experimental evidence for the fractionation of olivine and magnetite.
Generally, early crystallizing minerals such as olivine, clinopyroxene, plagioclase and orthopyroxene contain very low REE abundances (Table 2). Therefore, the REE are incompatible elements and partition into the melt causing the total REE to increase during fractionation from mafic to intermediate magmas. As the magma cools, REE elements eventually become concentrated in accessory phases such as zircon, rutile, ilmenite, titanite and monazite. In some highly siliceous magma, precipitation of accessory minerals is common (Miller and Mittlefehldt 1982) so that REE abundances can decrease during the later stages of magma evolution. Rare-earth-element abundances are most commonly displayed on diagrams in which the lanthanide elements are arranged from left to right with increasing atomic number (57-71, La to Lu on the periodic table). The lanthanides have similar chemical and physical properties (all but Eu are trivalent) and their ionic radius decreases with increasing atomic number (the so-called "lanthanide contraction"); Europium can be divalent or trivalent depending on the degree of oxidation of the magma. According to Goldschmidt's rules, if ions have the same charge, the smaller ions are preferentially incorporated into growing crystals.
The concentration of each REE is divided by the concentration of that element in chondrite, which is thought to reflect the composition of the early Earth. This results in smooth patterns that facilitate comparisons among samples and between two suites. The resultant chondrite-normalized rare-earth-element plot (note that the y axis is dimensionless) allows an analysis of the enrichment (or depletion) in each lanthanide element relative to the same standard reference, in this case, that of the early Earth (Fig. 7). Analysis of these plots focuses on two different aspects. First, as REE elements are equally incompatible during fractionation of the early crystallizing phases, the slope on the REE diagram (as represented by normalized La/Lu) is virtually unaffected by fractionation and so represents their relative abundances in the source rock. An overall envelope around the REE data from a given suite may therefore yield valuable information of the chemistry of that source. Second, total REE ([SIGMA]REE) should increase until the latest stages of fractionation (Fig. 7a), and suites, derived from the same source and related by fractionation, should yield parallel profiles. For crystal fractionation to be a viable model, samples that have higher [SIGMA]REE should have higher abundances of incompatible elements and so the REE profiles are generally checked against abundances of elements such as Zr and Nb.
[FIGURE 7 OMITTED]
Island arc tholeiites exhibit relatively flat REE profiles, with minor depletion in light rare-earth-elements LREE). These profiles are broadly similar to MORB (although MORB has more pronounced LREE depletion) suggesting derivation from a similar source, i.e. the depleted mantle. In contrast, calc-alkalic basalts show moderate degrees of light rare-earth enrichment, although they are not as enriched as alkalic or plume-related basalts, suggesting derivation from a mantle source enriched in these elements relative to the source for MORB or IAT.
Tholeiitic and calc-alkalic lavas are both characterized by flat heavy REE (HREE) profiles. These profiles imply a source in the shallow (spinel lherzolite) mantle (i.e. < 50 km depth) rather than a deeper (garnet lherzolite) mantle. Garnet preferentially incorporates HREE over LREE, so that a steepened REE slope (i.e. higher La/Lu) will result if either fractional crystallization of garnet occurs during cooling, or if garnet remains in the residuum during partial melting (Fig. 7b). The effect of garnet on REE profiles contrasts with other silacates, the fractionation of which increases [SIGMA]REE but does not change the slope of REE profiles. In addition, the flat HREE patterns are also a strong argument that the magmas are not directly derived from melting of the subducted slab, because oceanic lithosphere subducted to 110 km depth would be metamorphosed to eclogite (a garnetomphacite bearing metamorphic rock).
Plagioclase incorporates more Eu than the other REE because, unlike other lanthanides, which are predominantly trivalent, Eu is predominantly divalent ([Eu.sup.2+]/[Eu.sup.3+] depends on f[O.sub.2]) and so can be incorporated into the [Ca.sup.2+] site in the plagioclase structure. If fractionation of plagioclase occurs during cooling, the increase in Eu concentration lags behind the increases in other REE, resulting in a negative "kink" in chondrite-normalized REE patterns (Fig. 7b), known as a "negative europium anomaly". The extent of the anomaly increases with fractionation, and so is very pronounced in felsic rocks as can be seen by comparing normalized Eu abundance with a hypothetical Eu value obtained by extrapolating a hypothetical line from neighbouring elements (dashed line, Fig. 7b). The presence of a negative Eu anomaly in many tholeiitic and calc-alkalic volcanic arc suites is consistent with plagioclase fractionation, which is typical of processes in crustal magma chambers and matches field and petrographic evidence of the abundance of plagioclase phenocrysts.
When trace elements and REE elements are considered together, it is evident that arc systems are complex and magma compositions represent interplay of a large number of factors, including magma mixing, crustal contamination, crustal assimilation, and fluid transport. These complexities are revealed if ratios between incompatible trace elements in basaltic rocks are studied. If arc liquids evolve by simple fractionation, ratios such as La/Nb and Zr/Nb remain constant because La, Zr and Nb are (approximately) equally incompatible elements. Geochemical studies from most arc magmas show that this is rarely the case, and while they do not negate the possibility that fractional crystallization played an important role, they also indicate that other processes are responsible for these variations, such as source heterogeneities, magma mixing or crustal assimilation.
Arc Magmas on Discrimination Diagrams
Since the early 1970s, a plethora of geochemical discrimination diagrams have been published utilizing the varying behaviours of compatible and incompatible trace elements to distinguish magmas by type (alkalic, tholeiitic, calc-alkalic) and by tectonic setting (arc, within plate, etc), and also to constrain the chemistry of the magma source. In this approach, incompatible elements are subdivided on the basis of their ionic potential (charge/ionic radius) into high-field-strength elements and large ion lithophile (LIL) elements. High-field-strength elements are relatively small incompatible elements that have a high charge density (e.g. [Ti.sup.4+], [Zr.sup.5+]) and high ionic potential; other HFS elements include Th, U, Hf, Nb, Y, Ta and REE. They are typically insoluble in [H.sub.2]O-rich solutions. Large ion lithophile elements, however, have low charge and low ionic potential and are soluble in water-rich solutions (e.g. K, Rb, Cs, Ba, Sr). As [H.sub.2]O plays a key role in the genesis of arc magmas, the contrasting behaviour of LIL and HFS is crucial to understanding their petrogenesis and many arc magmas have high LIL/HFS elemental ratios (Pearce 1996).
Although the foundation for many discrimination diagrams (e.g. Figs 8-10) is basically empirical (they are based on data from volcanic rocks in known tectonic settings), and the reasons for these variations are not fully understood, they do provide some general constraints for the origin of arc basalts.
[FIGURES 8-10 OMITTED]
The first type of discrimination diagram relies on HFS elements. For example, on the Zr/Ti vs Nb/Y plot (Fig. 8a; Winchester and Floyd 1977; modified by Pearce 1996), fractionation of early crystallizing phases such as olivine, augite and plagioclase does not significantly affect either the Zr/Ti or Nb/Y ratio because all four elements are incompatible in these phases. However, fractionation of amphibole or magnetite will drive liquids toward intermediate and felsic compositions. As noted by Pearce (1996), this diagram is a proxy for the total alkalies vs silica classification diagram, where Nb/Y measures the degree of alkalinity and Zr/Ti is an index of fractionation. However, the HFS trace-element diagram has the considerable advantage in that the elements selected are relatively immobile during secondary processes (e.g. weathering, low-grade metamorphism), in contrast to the alkalies and silica.
The high Nb/Y of alkalic suites can be attributed to the presence of residual garnet which retains Y in the source rock. Thus, the relatively low Nb/Y in calc-alkalic and tholeiitic arc basalts is consistent with REE evidence suggesting derivation from a shallower (spinel lherzolite) mantle than alkalic basalts. Similar principles can be seen in other discrimination plots (Figs. 8b, c) which emphasize the low Ti, Zr and Zr/Y in arc magmas compared to within-plate magmas, as is apparent on the Ti[O.sub.2] vs Zr and the Zr/Y vs Zr diagrams (Pearce and Norry 1979; Pearce et al. 1981).
As HFS elemental ratios (e.g. Zr/Y, Fig. 8c), Ti/Y and Nb/Y (Fig. 8d) are insensitive to fractionation in the shallow mantle, variations in these ratios may reflect heterogeneities in the mantle source. The behaviour of Y and Yb, however, changes depending on depth in the mantle. The elements are incompatible in the shallow (spinel lherzolite) mantle, but are compatible in the deep (garnet lherzolite) mantle, where they are retained in garnet during partial melting. Therefore, the lower Ti/Y for arc basalts compared to within-plate basalts (WPB) suggests an origin in the shallow spinel lherzolite mantle.
Fractionation and Partial Melting
A second type of discrimination diagram focuses on elements that have contrasting behaviours during igneous processes. The Cr-Y discrimination diagram (Pearce 1982; Fig. 9) is an example of a compatible element (Cr) plotted against an incompatible HFS element (Y) and can monitor the extent of fractionation and partial melting. According to Wood (1979), Cr and Y exhibit limited variability in the mantle, so that variations in basalts can be attributed to differences in degrees of partial melting and fractional crystallization. Because Cr is a highly compatible element but Y is incompatible, the fractionation trend on this graph is nearly parallel to the Cr axis. The diagram successfully discriminates between tholeiites formed in arc environments (IAT) and MORB. Island arc tholeiites have lower Y than MORB for a given Cr concentration. Petrogenetic modelling using these elements shows that variations in IAT can be explained by between 15-40% partial melting followed by fractionation of mafic phases. Clearly MORB rocks are, on average, less fractionated than IAT.
Mantle Heterogenelty anal Source
A third type of discrimination diagram is based on the geochemical differences between LIL and HFS incompatible elements and the high LIL/HFS ratio of arc magmas. The concentrations of HFS elements are not appreciably affected by processes that cause mantle heterogeneity. The LIL incompatible elements (e.g. Th and LREE) are soluble in fluids derived from the subduction zone; therefore, they are enriched in the mantle wedge and the melts derived from this mantle inherit that enrichment. Although there is a consensus that arc magmas are LIL-enriched, there is some debate as to the extent of depletion in HFS elements. At one extreme, McCullough and Gamble (1991) and McCullough (1993) argue that HFS element concentrations of the arc magmas are similar to MORB and so are not significantly depleted. In contrast, others (e.g. Saunders and Tarney 1984; Saunders et al. 1991) point out that the oxidizing environment (caused by the addition of water to the mantle wedge) stabilizes minerals such as titanite, rutile, ilmenite and hornblende, which contain high abundances of HFS elements (Zr, Ti, Nb, Hf, Ta). These minerals remain in the residue during partial melting, so the HFS elements are depleted in arc magmas. Another possibility is that low HFS elemental abundances reflect contamination with continental crust that was previously depleted in HFS elements, and so magmas contaminated by it would inherit this depletion. Although such contamination has been documented in several localities, this model does not address how the crust originally became depleted in HFS elements.
On elemental ratio plots such as Th/Yb or Ce/Yb vs Ta/Yb (Figs. 10 a, b; Pearce 1982), the vertical axis detects subduction components so that arc-related rocks plot above the typical mantle values. Calc-alkalic basalts (CAB) have higher Ce/Yb and Th/Yb than arc tholeiitic basalts. These traits are further evidence of the chemical effects of fluids derived from the subduction zone carrying Ce and Th to the mantle wedge source region of arc basalts (Pearce 1996). Whereas MORB and WPB plot near the mantle array, arc basalts (both CAB and IAT) have lower Ti/Y and Ta/Yb than rift-related basalts and typically plot above the mantle array.
The Hf-Th-Ta diagram (Fig. 10c; Wood et al. 1979) also identifies the influence of subduction components in the trace-element chemistry. As arc magmas are enriched in Th, and are especially depleted in Ta (Pearce 1996), they plot nearer the Hf-Th join than MORB or within-plate basalts. Calc-alkalic basalts have higher Th than IATs and so plot closer to the Th apex of the discrimination diagram (compare D1 and D2). As arc systems mature, they also become more enriched in LREE relative to HREE. This tendency is identified on the La/Yb vs Th/Yb diagram (Fig. 10d, after Condie 1989) where primitive island arcs have lower ratios than continental (Andean) arcs.
Other discrimination diagrams are used to elucidate the tectonic setting. The Ti-Zr plot (Fig. 11) is sensitive to crystal fractionation in arc and within-plate suites (Pearce and Norry 1979). Fractionation of most early-crystallizing phases (such as olivine, cpx, opx, plag) results in an increase in these two elements. However, fractionation of magnetite causes depletion in Ti, and fractionation of amphibole or biotite may cause depletion in Ti and Zr (see partition coefficients in Table 2). Fractionation vectors (Fig. 11) show that differentiated arc lavas (both tholeiitic and calc-alkalic) have lower Ti and Zr than differentiated within-plate lavas.
[FIGURE 11 OMITTED]
Pearce et al. (1984) showed that arc-related felsic magmas have lower Rb, Y, Nb, Ta and Y than within-plate or ocean-ridge granites (Figs. 12 a, b). Petrogenetic models of compositional trends of arc granites on the Rb-(Y+Nb) plot indicate that source rocks are enriched in Rb (presumably from fluids derived from the subduction zone). The authors note that fractionation vectors for amphibole in intermediate and felsic rocks enhance the vertical trend, facilitating distinction between arc and within-plate granites.
[FIGURE 12 OMITTED]
Some Limitations to the use of Discrimination Diagrams
While these diagrams have been a valuable tool in fingerprinting magma type and tectonic settings, there are some limitations and inconsistencies in their application. First, these diagrams assume that the abundances of these elements in a given rock sample are essentially unchanged since the time of crystallization. This assumption generally holds because HFS elements are typically insoluble in water-rich solutions and are most concentrated in stable accessory phases such as zircon, ilmenite and titanite. However, dissolution of these phases can occur under certain conditions (e.g. rocks subjected to hydrothermal alteration or carbonatization (Hynes 1980)) and samples from rocks so affected yield spurious results.
Second, there are some inconsistencies among the diagrams themselves. For example, on the Zr/Y vs Zr plot, within plate basalts (e.g. continental rift-related basalts) are classified by Zr/Y > 4. If one plots this line on the Zr-Ti-Y discrimination diagram, it is evident that some rocks with Zr/Y > 4 plot in the IAT, CAB or MORB fields (Fig. 8b, c). It is important to remember that these diagrams are projections that look at a very restricted compositional plane and so a variety of diagrams must be employed to be sure of consistency in interpretation.
Perhaps the most important, but under-appreciated, limitation to the use of discrimination diagrams is that trace elements are highly sensitive to a variety of petrological processes, whereas major element variations are primarily controlled by phase equilibria. The net result is that major and trace elemental behaviour may "decouple", leading to conflicting results for tectonic settings for volcanic rocks (see Spandler et al. 2003; Leibscher 2004).
Consider, for example, a typical are plumbing system that has magma chambers of the same starting composition, but of varying size connected by a set of conduits (Fig. 13). There is abundant field and petrological evidence to show that magma chambers are open, rather than closed systems and that magma is pumped along conduits between magma chambers in response to pressure variations in the system, much as water is pumped through a municipal water system. If relatively small increments of magma from a large, more mafic chamber (Y) are repeatedly pumped into a smaller, more silicic chamber (M), then major and trace elements will behave differently. A standard phase diagram of a basaltic magma (X) undergoing olivine-enstatite fractionation shows that the magma composition in each chamber will be driven down the olivine-enstatitc reaction curve (Fig. 13), where olivine reacts with the liquid, as enstatite precipitates. Although there is a tendency for the bulk composition of magma chamber M to migrate incrementally toward the composition of invading magma Y, this is immediately counterbalanced as magma M enters the pyroxene stability field, thereby resulting in rapid crystallization of pyroxene that drives the liquid away from the enstatite composition back toward the pyroxene-plagioclase cotectic (Boudreau and McBirney 1997). Major element chemistry, therefore, is only moderately affected by the invading magma. Trace elements, on the other hand, are not controlled by this process, and so would plot on mixing curves between the two end member compositions Y and M.
[FIGURE 13 OMITTED]
Geochemical data are also presented on normalized multi-element diagrams, in which the abundances of a range of elements are compared with a reference source, known as spider diagrams (Figs. 14 a, b). Many spidergrams compare the trace element content of samples with those of a number of diverse reservoirs that could represent potential sources, such as MORB, depleted mantle (DM, the mantle from which basalt has been extracted), and enriched mantle (EM, mantle that has been extensively metasomatized). The elements are ordered with increasing compatibility from left to right. Spider diagrams are analyzed in a similar fashion to chondrite-normalized diagrams. The data are normalized relative to a candidate reservoir. If basaltic suites are being studied, typically they are either compared with MORB or with a mantle reservoir (e.g. DM or EM). An envelope around the data is compared with that of the candidate mantle reservoir and yields valuable evidence about the source of the magma. Variations within the data ser provide information about the extent of fractionation. Fractionated magmas derived from the mantle reservoir, for example, ideally should yield a set of parallel profiles within the envelope.
[FIGURE 14 OMITTED]
Mafic to intermediate arc rocks typically exhibit jagged MORB-normalized patterns, and most notably, a negative Nb anomaly relative to Th or La (Fig. 14a, e.g. see Sun and McDonough 1989). In contrast, mafic rocks from non-arc settings are characterized by relatively smooth MORB-normalized patterns (especially ocean-island basalts) and some have positive Nb anomalies. Jagged patterns are also evident in mantle normalized plots for mafic and felsic rocks generated in arc environments (Fig. 14b). In essence, the jagged patterns show the same LIL element enrichment relative to HFS elements (see Nb, Ti, Zr, and Ta), which is evident in several discrimination diagrams. Although these same traits can be recognized on standard discrimination diagrams, the advantage of these plots is that trends can be shown and compared for many elements on the same diagram. Although mafic magmas in both arc and non-arc settings are derived from the mantle, these diagrams also identify the distinctive high LIL/HFS ratio of arc magmas. When the metasomatized mantle wedge melts, LIL elements strongly partition into the melt, whereas HFS elements preferentially remain in stable accessory minerals. Melts derived from this metasomatized mantle wedge are therefore enriched in LIL relative to HFS elements (e.g. Miskovic and Francis 2006). Tatsumi and Kogiso (2003) have used this approach to propose that the dehydration of subducted sediments and oceanic crust released water and LIL elements into the mantle wedge. This hypothesis is supported by boron and beryllium studies. Boron and [sup.10]Be are enriched in sediments, but escape very easily upon entering the subduction zone. Many modern arc volcanic rocks have elevated concentrations in these elements, which can only be derived from subduction of recent sediments (e.g. Morris et al. 1990; Morris and Ryan 2004).
The origin of the jagged mantle-normalized patterns in felsic magmas could arise in several ways. As fractionation generates a series of parallel trends, these patterns could be derived from fractionation of a more mafic parent. Alternatively, these features can be inherited from mafic magma derived from metasomatized mantle, and the differentiated products from such magma reproduce the jagged pattern. Supporting evidence for this hypothesis is gained from the analyses of xenoliths (retrieved from kimberlite bodies) that are derived from the mantle beneath some continental arcs. These data indicate that the mantle source may have suffered extensive and long-term metasomatism. Alternatively, as continental crust is primarily formed by earlier arc magmatism, they may reflect partial melting of continental crust that was mostly generated by earlier arc activity. In this case, the jagged pattern is inherited from the crustal source, rather than a reflection of coeval subduction.
Intermediate to felsic magmas in arc settings are also depleted in HFS elements relative to felsic magmas from within-plate settings. However, there is considerable debate about the origin of intermediate to felsic magmas in arc settings, and their origin may vary from one arc to another (Gill 1981; Carmichael 2002). As these magmas tend to be most dominant in mature arcs with thick continental crust, such as the Andes, much discussion focuses on whether the thickened crust allows more scope for fractionation, or whether the crust supplies a direct chemical contribution (see Carmichael 2002, and references therein). In some instances it is argued that this signature is inherited from basalts by fractional crystallization. In others, the felsic composition is attributed to partial melting of the crust or contamination of mafic to intermediate lavas by the crust. Since this crust is depleted in HFS elements, it is difficult to distinguish between these hypotheses using trace-element geochemistry alone. Given that the average continental crust is very similar in composition to calc-alkaline andesites (e.g. Taylor 1995), resolution of the problem has fundamental implications for understanding the evolution of the crust. The following section discusses how radiogenic isotopes, particularly Sm-Nd isotopic studies, can help distinguish among these various possibilities.
In addition to their use in dating rocks and minerals, certain types of isotopes can be used as tracers to yield information about the original source material from which a volcanic rock was derived. Several isotopic methods are used, including Rb-Sr, and Sm-Nd and U-Pb. Rubidium-Sr and Sm-Nd are commonly considered together.
Rb-Sr and Sm-Nd Isotopes
Rubidium has an ionic radius of 1.48 [Angstrom], which is similar to K (1.33 [Angstrom]). As a result, Rb is common in K-bearing minerals, including micas and K-feldspars. As an alkali element, Rb strongly partitions into crustal rocks, so that Rb/Sr is higher in crustal rocks than in the bulk Earth and higher in the bulk Earth than in the depleted mantle source. Therefore, [sup.87]Sr/[sup.86]Sr increases more rapidly in the crust than it does in the bulk Earth, and more rapidly in the bulk Earth than it does in the depleted mantle.
Variations in Sm/Nd ratios in crustal rocks are mostly inherited from their mantle sources (see DePaolo 1988). When the mantle melts, all LREEs tend to concentrate in the magma rather than in the remaining, now depleted mantle. Although Sm and Nd are both lanthanides and have the same valency (+3), Nd has a lower atomic number (60), and is slightly larger than Sm. Thus, it is slightly more concentrated than Sm in magmas leaving the depleted mantle (in accordance with Goldschmidt's rules). The larger Sm ions are slightly more concentrated than Nd in mantle minerals. Thus, the average Sm/Nd is lower in the crust than it is in the depleted mantle (0.2 and 0.5 respectively, Fig. 15a). Therefore, the decay of [sup.147]Sm to [sup.143]Nd results in a more rapid increase in [sup.143]Nd/[sup.144]Nd in the depleted mantle than in the bulk Earth, and a more rapid increase in the bulk Earth (average Sm/Nd = 0.32) than in the crust (Fig. 15a). Consequently, the Sm-Nd isotopic characteristics of magmas generated in the crust and the depleted mantle are very different. However, in the case of the RbSr system, the crust is enriched in the radioactive component, whereas in the case of the Sm-Nd system, the crust is depleted in the radioactive component. Upon melting, magmas acquire the [sup.87]Sr/[sup.86]Sr and [sup.143]Nd/[sup.144]Nd ratio of their source, and so this negative relationship also exists in magmas. Magmas formed by melting the depleted mantle will have lower initial [sup.87]Sr/[sup.86]Sr and higher initial [sup.143]Nd/[sup.144]Nd ratios than those produced by melting the crust.
[FIGURE 15 OMITTED]
On a plot showing typical Nd-Sr isotopic variations in modern arc volcanics the negative relationship between [sup.87]Sr/[sup.86]Sr and [sup.143]Nd/[sup.144]Nd initial ratios is apparent (Fig. 16). Some arc suites, such as the Aleutians, New Britain, South Sandwich and the Marianas have values that are more depleted than the bulk earth (i.e. higher initial [sup.143]Nd/[sup.144]Nd and lower initial [sup.87]Sr/[sup.86]Sr) and are almost as depleted as MORB. Other arcs, however, are enriched in these isotopes (i.e. lower initial [sup.143]Nd/[sup.144]Nd and higher initial [sup.87]Sr/[sup.86]Sr than the bulk earth), suggesting that subducted oceanic sediments may have influenced the composition of the magma. As the data lie close to a mixing line between depleted mantle and sediments, a permissible interpretation is that arc magmas are sourced in a depleted mantle (similar to MORB) that has been variably influenced by fluids derived from subducted sediments or crust (about 5% contamination, Fig. 16).
These isotopic data can also be used to determine if the magmas were recently derived from the mantle or from recycling of ancient crust. Changes in the isotopic signature of the depleted mantle and the average or "bulk Earth" with time are well constrained (Fig. 15). The isotopic signature of the crust, however, depends on how long ago it separated from the mantle, i.e. the greater the time interval, the bigger the differences in Rb/Sr and Sm/Nd ratios. Compared to newly formed crust, older crust has a much greater difference between its isotopic signature and that of the depleted mantle from which it originated.
One of the most challenging tasks of arc magmatism is to evaluate how intermediate to felsic magmas are derived, i.e. by fractionation of a more mafic parent, by crustal melting or by some combination of these two processes. Samarium-Nd isotopic studies can help reveal the relationship between coeval basalts and rhyolites in arc magmas. Fractionation of the basaltic magma does not change its isotopic characteristics, and rhyolite derived from it inherits these same characteristics. In contrast, intermediate to felsic magmas derived by melting old crust will have Sm and Nd isotopic characteristics of the crust and will be very different from coeval, mantle-derived basaltic magma and its differentiates. In northeastern Japan, the basaltic and rhyolitic rocks generally have different Sm-Nd isotopic compositions, suggesting they are not co-magmatic, and the rhyotites reflect partial melting of the crust (e.g. Tatsumi 2005).
These isotopic methods for deducing the nature of the source rock assume that: 1) the isotopic evolution of the depleted mantle is known, 2) the samples' Rb/Sr or Sm/Nd ratios have not been modified by coeval or subsequent intra-crustal processes (e.g. assimilation of host rock, fractionation of REE-bearing phases, hydrothermal activity), 3) a crustal Rb/Sr or Sm/Nd ratio was acquired during, or very soon after, the sample was emplaced in the crust, and 4) all the material in the sample was derived from a single event in the mantle (e.g. Arndt and Goldstein 1987)
In many cases, these assumptions break down in the Rb-Sr system. Because Rb is an alkali metal, and Sr an alkali earth metal, they behave very differently in the crust, and the Rb/Sr can be affected by a wide variety of crustal processes including weathering, diagenesis and metamorphism. In contrast, the decay of samarium (Sm), to neodymium (Nd), provides one of the best tracers for tectonic processes (e.g. DePaolo 1981a, b; 1988). Samarium and neodymium are both light "rare earth" elements with similar ionic radii and valencies (+3), so they have similar chemical properties and thus Sm/Nd is rarely affected by crustal processes.
The differences in the [sup.143]Nd/[sup.144]Nd ratios of crustal and mantle rocks are relatively small. For convenience, a parameter, [[epsilon].sub.Nd], is defined which reflects the difference between the [([sup.143]Nd/[sup.144]Nd).sub.o] in the sample and that of "bulk Earth" at the time the rock crystallized (DePaolo 1988). In this scheme, [[epsilon].sub.Nd] for the bulk Earth at any time is set at zero. As [sup.143]Nd/[sup.144]Nd increases more rapidly in the depleted mantle and less rapidly in the crust compared to the bulk Earth, over time the depleted mantle has evolved toward more positive [[epsilon].sub.Nd] values, while the crust has evolved toward more negative values. The evolution of the crust produces a growth line with a predictable slope because the Sm/Nd ratio of crustal rocks is typically about 0.2 (Fig. 15b).
Because of their contrasting growth tines, [[epsilon].sub.Nd] values can be used to distinguish between magmas derived from a depleted mantle source and those derived from the melting of an ancient crustal one (Fig. 15b). This is particularly important in the understanding of the genesis of intermediate and felsic rocks in arc systems. In contrast to magmas formed by partial melting of the crust, andesites and rhyolites derived from fractional crystallization of a basaltic magma will each have the same [[epsilon].sub.Nd] value as the coeval basalt because these isotopic ratios are not affected by fractional crystaltization. Samarium-Nd isotopic studies can also identify intermediate magmas formed by mixing of mafic and felsic "end-members", which should have [[epsilon].sub.Nd] values that lie between those of the mafic and felsic parents. The degree of crustal inheritance in the genesis of magma can also be assessed because most crustal processes do not change the Sm/Nd ratio (e.g. Murphy et al. 1996).
In practical terms, these principles are used in reverse. The isotopic analysis of a rock sample reveals the present-day value of [[epsilon].sub.Nd] The growth line, representing the rate of change in this value with time, can be determined, so that the time when [[epsilon].sub.Nd] would have had the same value as that of the depleted mantle can be deduced from the intersection of the growth line with the depleted mantle curve. This date is referred to as the depleted-mantle model age (or [T.sub.DM]). If the four assumptions listed by Arndt and Goldstein (1987) are satisfied, this is the time when the sample had the same isotopic signature as its depleted mantle source. For arc magmas, the [T.sub.DM] age represents the time when the source rock for the magmas was itself extracted from the mantle (Fig. 15).
Most crust is derived, either directly or indirectly, from the depleted mantle reservoir. As a result, the value of [[epsilon].sub.Nd] for a sample compared to that of the depleted mantle at the time of the rock's crystaltization, i.e. its initial [[epsilon].sub.Nd] value, is crucial to tectonic interpretations. Volcanic rocks with initial [[epsilon].sub.Nd] values similar to those of the depleted mantle must have been derived from the depleted mantle reservoir at, or about, the time of their formation, and are therefore considered "juvenile". For a juvenile rock, its [T.sub.DM] age will be similar to its crystallization age. Conversely, volcanic rocks with [[epsilon].sub.Nd] values well below those of the depleted mantle at the time of their crystallization are generally interpreted to have been derived from the melting of ancient crust. The time at which this ancient crust was itself separated from the mantle can be determined from the intersection of its growth line with that of the depleted mantle (Fig. 15). For magma derived from ancient crust, its [T.sub.DM] age will be significantly older than its crystallization age.
A hypothetical example of three volcanic rocks, all with the same crystallization age ([T.sub.3]), is shown in Fig. 15b. The basalt plots on the depleted mantle curve and would be interpreted as a juvenile melt derived directly from the depleted mantle. The rhyolite is highly negative, and following its growth line back to the depleted mantle curve yields a model age of [T.sub.1]. The rhyolite would be interpreted as being derived from the melting of a continental crustal source that has an average extraction age from the depleted mantle of [T.sub.1]. The andesite has [[epsilon].sub.Nd] values between those of the basalt and the rhyolite, and so cannot be related by fractionation to either. In this case, a possible interpretation is that the andesite was derived by mixing of basalt and rhyolite. If so, the [T.sub.DM] age of the andesite is merely a happenstance of the mixing process and is therefore geologically meaningless (see Arndt and Goldstein 1987).
As many authors have pointed out, [T.sub.DM] ages can only be used with extreme caution. As magmas ascend to the surface, they may mix or mingle with other melts from different sources, as may be the case in some magma with intermediate compositions. These rocks are actually mixtures of ancient recycled crust and juvenile material extracted from the mantle. Although the range in [[epsilon].sub.Nd] values may help deduce the origin of such magmas, the [T.sub.DM] ages have no specific geological meaning (Fig. 15b). However, the tell-tale signs of mixing can generally be detected using field evidence (e.g. presence of xenoliths, evidence of mixing or mingling), microscopic evidence such as textures (e.g. mantled phenocrysts) that indicate disequilibrium, or chemical indicators. Samples contaminated by mixing must be excluded when determining the crustal formation age of the source rocks.
Textural evidence for mixing is commonly found in andesites, including multi-stage growth and oscillatory zoning of plagioclase and pyroxene phenocrysts, the coexistence of olivine and quartz, and the presence of rounded olivine rimmed by pyroxene (e.g. Eichelberger 1975; Eichelberger et al. 2000, 2006; Clynne 1999; see also Murphy 2006).
The influence of source regions on isotopic signatures is classically demonstrated in the Mesozoic--Cenozoic magmatism in western North America. Since the break-up of Pangaea, North America has been moving westward in response to the opening of the Atlantic Ocean. The western margin of North America is on the leading edge of the plate and so it's Mesozoic--Cenozoic history is dominated by subduction-related tectonics and collisions of oceanic terranes. Recent studies of terrane accretion in the Canadian Cordillera suggest that some accretionary processes can be "thick-skinned", i.e. up to 100-150 km of lithosphere (MacKenzie et al. 2005). After terrane accretion, subduction zones commonly step outboard, and become re-established along the continental margin (Burchfiel et al. 1992); then, recycling of the mantle roots of the accreted terranes begins (Fig. 17; e.g. Selby et al. 2003).
[FIGURE 17 OMITTED]
Armstrong et al. (1977), Kistler and Peterman (1978) and DePaolo (198 la) showed how isotopic signatures of Mesozoic--Cenozoic igneous rocks can constrain the boundary between ancestral North America and the accreted terranes. Magmatism in the accreted terranes has lower (<0.706) [sup.87]Sr/[sup.86]Sr initial ratios than that derived from ancestral North America (Armstrong et al. 1977; Kistler and Peterman 1978). In a study of the large batholiths in California and the Sierra Nevada, DePaolo (1981a) showed that [sup.87]Sr/[sup.86]Sr initial ratios increase from west to east from 0.703 to 0.708, and together with Sm-Nd isotopes define a west-to-east mixing curve between juvenile magmas with +ve [[epsilon].sub.Nd] and crustal magmas with -ve [[epsilon].sub.Nd] in the east. These differences are attributed to the more juvenile mantle source for magmas in the accreted terranes, compared with the ancient source for magmas in ancestral North America.
Uranium-Pb isotopic analyses of minerals such as zircon, monazite and titanite are commonly viewed to be the most reliable method available to date igneous and metamorphic events (e.g. Krogh 1973). However, these isotopic systems, in conjunction with Th-Pb systems can also be useful tracers of igneous suites. Uranium, Th and Pb are LIL elements and so are preferentially incorporated in the crustal melts or fluids relative to the mantle during tectonothermal events.
Although the Earth's crust is ultimately derived from the mantle, the chemical exchange is not a one-way street. During subduction, some of the chemical residue from the subducted slab is recycled back into the mantle. Lead ratios indicate that the mantle source of basalts is commonly contaminated by the residue from subducted slabs. Assuming subduction has been active since the Archean, the cumulative effects of this recycling can account for about 10% of the lower mantle composition (Tatsumi 2005). The overall result of this exchange is that the mantle is chemically heterogeneous, and several idealized reservoirs of varying mantle composition have been identified that reflect crust-mantle interactions (Figs. 18, 19). As mantle-derived basalts inherit the isotopic compositions of their source, heterogeneity of the mantle is evident in the subtle, but systematic, variations in the chemical and isotopic composition of basalts from a variety of tectonic settings (Zindler and Hart 1986). The principle source of mantle heterogeneity appears to be related to the descent of subducting slabs into the mantle. Although the exact mechanism is disputed, tomographic imaging of seismic data and geodynamic modelling (Zhong and Guris 1997) indicate that subduction zones extend to the core-mantle boundary and contribute to convection systems in the mantle. The isotopic data suggest that these subduction zones deliver refractory components to the mantle which are derived from oceanic sediments and lithosphere that were not extracted and incorporated into the overlying mantle wedge. This interaction happens continuously as subduction proceeds, bur it can also occur when the slab breaks and founders into the mantle during collisional orogenesis (Whalen et al. 1996; Hildebrand and Bowring 1999), or potentially during slab avalanche events (Tan et al. 2002).
[FIGURES 18-19 OMITTED]
From studying the Pb isotopic characteristics of terrestrial basalts, there is a consensus among petrologists that at least five isotopically distinct reservoirs exist in the mantle. For example, the ocean island basalts of St. Helena are highly enriched in [sup.206]Pb/[sup.204]Pb and [sup.207]Pb/[sup.204]Pb relative to DM, and characterize an isotopic reservoir known as HIMU (high [mu]). The isotopic characteristics of these reservoirs are shown in Table 3 (after Rollinson 1993).
The [sup.207]Pb/[sup.204]Pb vs [sup.206]Pb/[sup.204]Pb plot (Fig. 19) is particularly instructive. The data from a given suite are compared to the known values of potential mantle reservoir and crustal rocks, and to the "geochron", which is a line where all data from modern suites plot if their Pb isotopic compositions are unaffected by secondary processes. A hypothetical un-depleted mantle (known as BSE, Bulk Silicate Earth), also plots on this line because such a mantle, by definition, is not affected by events that would have fractionated U, Pb or Th into the crust.
Despite a broad consensus on their existence, the origin of some of the reservoirs in Table 3 is controversial. The reservoir that is most commonly represented at the surface is the depleted mantle (DM), the mantle from which basalt has been extracted during seafloor spreading. Mid-ocean ridge basalts lie close to DM but clearly contain another isotopic component. As subduction zones recycle MORB and the underlying DM, it is not surprising that many arc basalts have a similar Pb isotopic signature to MORB. Like MORB, Pb isotopes indicate that arc magmas have an important (but not exclusive) DM component, an interpretation consistent with trace element and Sm-Nd isotopic data discussed above.
Many petrologists, including Greenough et al. (2005), have drawn attention to the fact that data from arc magmas are either spread along or above the join between DM and HIMU (Fig. 19). Those that plot along the DM-HIMU join (e.g. Aleutians) can be explained by contributions from both reservoirs, and the data that plot above the line (e.g. South Sandwich, Sunda, Lesser Antilles) require the additional influence of a third reservoir, possibly EM-II, which is thought to reflect contamination of the mantle by dehydrated subducted sediments (e.g. Johnson and Plank 1999).
The origin of HIMU is controversial. Its strong radiogenic lead enrichment suggests a source that is enriched in U relative to Pb (Chauvel et al. 1992). Tatsumi and Kogiso (2003) point out that the residue of dehydrated MORB would be relatively enriched in U, and would, over time yield high [sup.206]Pb/[sup.204]Pb and [sup.207]Pb/[sup.204]Pb values, because MORB loses Pb as it dehydrates in a subduction zone. If so, the Pb-isotopic signal of arc basalts could be derived from a mantle source that has previously assimilated ancient oceanic crust, presumably the residue of ancient subducted slabs.
In summary, U-Pb isotopes from basaltic rocks indicate that the mantle source for modern arc magmas reflects contamination by hundreds of millions, if not billions, of years of subduction. It is clear that arc magmas are influenced by several isotopic reservoirs. These reservoirs share a fundamental property: their Pb-isotopic compositions are too enriched in Pb to be explained by internal mantle processes. The cumulative effects of contamination from the residues of ancient subduction zones are required to explain them.
OTHER ARC ROCKS
Not all magmas generated in arc environments fit neatly into calc-alkalic, tholeiitic or alkalic classifications. Shoshonites, boninites and adakites are volumetrically small, but are nonetheless petrologically significant igneous rocks that form in specialized arc environments. Their occurrence reveals much about the thermal structure of the arc and the potential effects of some complications induced by local tectonic activity.
Shoshonite is an alkali-rich ([Na.sub.2]O + [K.sub.2]O > 6.5 wt %) trachyandesite that occurs in continental rift, collisional and arc settings (Rogers and Setterfield 1994). Shoshonite occurs in association with calc--alkaline volcanism in intra-arc rift settings, in intra-oceanic island arcs and backarc basins, (Sun and Stern 2001; Adams et al. 2005) and continental arcs (Conrey et al. 1997). In oceanic arcs, shoshonite magma development is related to a change in subduction processes or arc-rifting (Rogers and Setterfield 1994). In continental arcs, shoshonite generally occurs a significant distance from the trench where the subducted slab is at a great depth and is commonly associated with rifting of the arc or backarc (Gill 1981; Baluyev et al. 1988). Shoshonites in all environments are markedly enriched in LIL (100-1000x chondrite), including LREE. The high Ce/Yb is attributed to LREE enrichment, and the role of residual garnet in the source. The subduction component in shoshonites is also indicated by pronounced negative Nb, Ti and Ta anomalies (e.g. Turner et al. 1996).
Boninites (named after the Bonin Islands, south of Japan, where they are most abundant, Cameron et al. 1979, 1983) are high MgO (> 6 wt% MgO) andesites that predominantly occur in the early stages of oceanic arc development in fore-arc regions, an unusual locality for magma generation. Compared to typical andesites, they have higher Cr, Ni and LIL elements but lower Ti and Nb (Arndt 2003). They are generally thought to represent melting of a hydrated and refractory Mg-rich mantle wedge that was contaminated with LIL elements transported from the subduction zone. It is clear that to generate boninitic magma, a steep geothermal gradient is needed to melt depleted peridotite. Such environments can occur in some extensional environments within the arc, either at shallow levels in the fore-arc, or where a backarc spreading centre propagates into an active arc. Published models for the origin of boninites include 1) the initiation of subduction (Stern and Bloomer 1992), 2) intra-arc rifting (Crawford et al. 1981; 3) ridge subduction (Cameron 1989), 4) the effect of seafloor spreading in a forearc basin (Bedard et al. 1998) or 5) where an active arc undergoes backarc spreading (e.g. Falloon and Crawford 1991; Monzier et al. 1993).
Adakites (Kay 1978; Defant and Drummond 1990; Defant and Kepezhinskas 2001; Grove et al. 2005), named after Adak Island in the Aleutians, are also high-Mg andesites, but unlike boninites, they are very LREE enriched (normalized La/Yb > 40), contain high Sr (> 400 ppm), high Sr/Y values, low initial [sup.87]Sr/[sup.86]Sr and low ratios of radiogenic to non-radiogenic Pb. Kay (1978) attributed adakites to the interaction of a LIL element-rich hydrous melt from the subducted oceanic crust with overlying mantle, and then eruption without interaction with the island arc crust. The question then becomes: under what conditions does the slab become hot enough to melt? Models favouring the subduction of young crust (e.g. Green and Harry 1999) are supported by experiments where adakites are produced by reaction of slab melts with peridotite in the mantle wedge (e.g. Rapp et al. 1999). The thermal structure of subduction zones (e.g. Peacock et al. 1994) predicts that only very young oceanic crust (<5 Ma) can melt. This prediction is at odds with geologic data (e.g. Defant and Drummond 1990) which indicate that slab melting occurs in crust as old as 20 Ma. This discrepancy is attributed to a higher contribution from shear heating in subduction zones than is accounted for in the Peacock et al. model (Green and Harry 1999). Dickinson and Snyder (1979) and Thorkelson (1996) show that in a ridge-trench collisional environment, a "window" in the slab forms between the downgoing plates that is filled with upwelling asthenosphere. Such an environment can induce slab melting along the thinned margins of the window (Johnston and Thorkelson 1997; Thorkelson and Breitsprecher 2005). Defant and Kepezhinskas (2001) propose that slab melting and adakite production can also occur near tears in the subducted slab, which also facilitates asthenospheric upwelling. It is clear that slab melting may occur in several environments, but the common denominator appears to be anomalous local supply of heat.
Adakites have recently been recognized in many other localities in the modern and ancient record. Indeed, some authors use them as an analogy for generating Archean magmas, in which it is viewed that the more elevated geothermal gradient might result in more common melting of the slab (Martin et al. 2005). Archean complexes are dominated by trondhjemite, tonalite and granodiorite (the so called TTG suite, Martin 1987). During the Archean, it is generally believed that the geothermal gradient was higher implying a hotter upper mantle than today (e.g. de Wit and Hynes 1995) which could promote slab melting (e.g. Martin 1987; Defant and Drummond 1990). Experiments suggest that slabs under these conditions can melt, and if that melt interacts with the mantle, it can produce intermediate compositions similar to those of Archean complexes (Rapp et al. 1999; Tatsumi 2000).
There are several possible sources for arc magmas in the vicinity of the subduction zone, including the subducted oceanic crust and sediments, as well as the mantle wedge and crust above the subduction zone.
To a greater or lesser extent, a chemical signal from all these sources can be found in arc magmas. However, when the thermal conditions in the vicinity of the subduction zone are considered in conjunction with phase equilibria, it is clear that arc magmas are most commonly generated in the mantle wedge and crust above the subduction zone. The thermal regime at subduction zones is profoundly influenced by the rate of descent of cold oceanic lithosphere, which is generally too fast to allow significant transfer of heat from the surrounding mantle. As a result, the isotherms are deflected downwards, and this cooling leads to a low geothermal gradient (10-15[degrees]C per km) and low heat flow in the fore-arc region above the subducted slab. As it descends, the slab is slowly warmed up, so that sediments, oceanic crust and lithosphere undergo prograde blueschist-eclogite facies metamorphism resulting in dehydration of the slab.
Although magma is not produced, the subducted oceanic lithosphere does play a vital role in the origin of arc magmas because the metamorphic fluids are released and migrate upward to invade and chemically modify the overlying mantle wedge. Of all the magmas1 formed in a subduction zone environment, IATs show the least contamination from subduction zone processes, an interpretation consistent with their occurrence in immature arcs. In more mature arcs, the effect of the fluids is more profound. The hydrated mantle melts at a significantly lower temperature than dry mantle and the magmas produced are oxidized and hydrated, inducing early crystallization of minerals such as magnetite and hornblende, which inhibit the rise in Fe/Mg ratio and so produce a calc-alkalic trend.
These oxidizing fluids tend to be enriched in water-soluble LIL elements. They also may stabilize HFS-bearing accessory minerals so that magmas derived from the mantle wedge tend to be enriched in LIL but depleted in HFS elements, patterns that are clearly evident in MORB-normalized or mantle-normalized spidergram plots in which HFS depletion is identified by negative Nb and Ti anomalies.
Except in rare cases, the subducted oceanic lithosphere does not attain temperatures that are sufficient for it to melt, so that the slab itself cannot be the main source of arc magmas. Relatively flat HREE profiles for most arc magmas are consistent with a derivation from the spinel lherzolite portion (< 50 km depth) of the mantle. For similar reasons, the asthenospheric mantle below the slab does not warm up appreciably and so cannot be an important source of magma. Adakites, however, which do show significant HREE depletion, may well be representative of slab melts, but they are rare, and their formation requires anomalous local supplies of heat within the subduction regime.
The Sr, Nd and Pb isotopic signatures of continental arc magmas commonly have a crustal component. In some arcs, these signatures are imposed by crustal contamination as the magma rises toward the surface. However, other arcs have this signature, even if they are capped by oceanic, rather than continental crust. The only plausible sedimentary source is from the subduction zone itself, supporting the notion that sediments are dragged down the subduction zone, and LIL elements derived from them are introduced into the mantle wedge. This hypothesis is supported by elevated concentrations of boron and beryllium in arc volcanic rocks, which can only be derived from subduction of recent sediments (e.g. Morris et al. 1990).
In mature subduction zones, original chemistry of the mantle wedge is progressively blurred by metasomatic fluids from the subducting slab. Depending on previous history, the mantle wedge may have a quite variable initial chemistry, which can influence the compositions of early arc magmas.
As arc magmas rise toward the surface, their compositions are strongly modified by interaction with their surroundings, especially during final cooling. Intermediate to silicic arc magmas can form in a variety of ways, including fractional crystallization of a more mafic parent, mixing between mafic and felsic magmas, partial melting of the crust, and assimilation and digestion of the crust by more mafic magma. Where felsic magmas are voluminous relative to intermediate or mafic melts, they are unlikely to be generated by fractional crystallization because there is not enough parent mafic magma to produce the felsic differentiates. Andesites formed either by mixing of basaltic and rhyolitic magmas, or by contamination of a more mafic parent by the continental crust commonly display textural evidence of disequilibrium (Eichelberger 1975) or field evidence of magma mixing or host rock assimilation (Wiebe et al. 2002). All these processes seem to occur in arc magmas to some extent although their relative importance may vary from one suite to another, or even within a given suite.
The extent of crustal involvement in the composition of intermediate to felsic magmas can be assessed using isotopes. Samarium-Nd isotopes are particularly robust because they are normally not affected by secondary processes. Magmas related by fractional crystallization should yield similar Sm-Nd isotopic signatures. Those formed by anatexis of older crust should have depleted mantle model ages that are significantly older than their crystallization age and those that reflect contamination or assimilation should plot on calculated mixing curves and should have a range in TDM ages between the end member components (DePaolo 1981a, b; Arndt and Goldstein 1987).
Given that 1) intermediate rocks are the dominant product of arc magmatism, and 2) they approximate the average composition of the continental crust, identifying the dominant process that forms intermediate magmas is fundamental to the understanding of crustal evolution.
Although hotly debated (e.g. Hamilton 1998; Stern 2005), many geologists contend that arcs have existed at least since the end of the Archean. Much of the petrological evidence is derived from geochemical and isotopic studies, which indicate that Late Archean volcanic and plutonic rocks share many similar geochemical traits with their modern counterparts (see Dostal and Mueller 1997; Corcoran and Dostal 2001; Canil 2004; Cousens et al. 2004; Dostal et al., 2004). If so, then processes like those occurring in modern arcs may well have had an influence on the evolution of continental crust for at least the last 2.5 billion years.
APPENDIX 1: Trace Element Modelling in Igneous Rocks
For any element, the relative distribution, or partitioning (D) between mineral and magma, given by;
D = [C.sub..S]/[C.sub.L]
where [C.sub.S] and [C.sub.L] are the concentration of the element in the solid and liquid phases, respectively. Typical values for D (known as the distribution coefficient or partition coefficient) are shown in Table 1, (see Pearce and Norry 1979; Rollinson 1993).
As a liquid cools, more than one mineral crystallizes, and in this instance the bulk distribution coefficient, [D.bar], is used, which is the weighted average of the distribution coefficients for an element in each of the crystallizing minerals. Compatible elements have [D.bar] [much greater than] 1, whereas incompatible elements [D.bar] [much less than] 1.
Arc magmas commonly undergo a range of processes as they cool, and three simple examples are considered here; equilibrium crystallization, fractional crystallization and magma mixing. Equilibrium crystallization (i.e. crystals remain in contact with the melt) and fractional crystallization (i.e. crystals are separated and chemically isolated from the melt) are examples of the effect of [D.bar] on the trace element abundance of a cooling magma. Under equilibrium crystallization conditions, mass is conserved so that
[C.sub.O] = [C.sub.S](1-F) + [C.sub.L] (F)
where [C.sub.O] is the starting concentration of a given element in a source, [C.sub.S] is the concentration of that element in the solid and F is the fraction of magma remaining. Substituting [C.sub.S] = [D.bar].[C.sub.L] and simplifying, we get
[C.sub.L]/[C.sub.O] = 1 / [D (1-F) + (F)] (after Shaw 1970)
Curves describing the increase or decrease in elemental concentrations with the fraction of melt can be readily calculated for any element if its [D.bar] is known. For example, if an element has a [D.bar] = 0.1, then for F = 0.5, [C.sub.L]/[C.sub.O] = 1.9 and as F approaches 0, [C.sub.L]/[C.sub.O] approaches 10 (Fig. A1-a). The abundances of incompatible elements, therefore, increase exponentially with decreasing F (and so their abundances are often represented on log-log plots, where they commonly exhibit linear relationships, e.g. Pearce and Norry 1979). Such low percentages of melt occur in either the early stages of melting or the late stages of crystallization. The abundances of compatible elements systematically decrease with decreasing F. For example, an element with [D.bar] = 10, approaches [C.sub.L]/[C.sub.O] = 0.1 as F approaches 0.
[FIGURE 1A OMITTED]
For perfect fractional crystallization of a cooling magma in a closed system (also known as Raleigh fractionation):
[C.sub.L]/[C.sub.O] = [F.sup.([D.bar] - 1)]
(Allegre et al. 1977)
For [D.bar] = 1, [C.sub.L] = [C.sub.O] = 1. For very low [D.bar], [C.sub.L]/[C.sub.O] = 1 / F, and for very high [D.bar], [C.sub.L] becomes very small as F decreases.
Although they are described by different equations, equilibrium and fractional crystallization produce similar enrichment and depletion trends described by exponential curves. Simple mixing between two arc magmas (e.g. Langmuir et al. 1978), on the other hand, produces linear trends on X-Y plots (Fig. A1-b). If we mix two magmas A and B of different composition, the mixing parameter f is given by;
f = A/A + B
the concentration of elements X and Y in the mixture (M) are given by:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
These equations are both in the linear form of y = mx + b. The mixing parameter, f, is the same in both equations;
f = ([X.sub.M] - [X.sub.B])/([X.sub.A] - [X.sub.B]) = ([Y.sub.M] - [Y.sub.B])/([Y.sub.A] - [Y.sub.B])
Substituting for f in (2) and simplifying gives:
[Y.sub.M] = [X.sub.M] ([Y.sub.A] - [Y.sub.B])/[X.sub.A] - [X.sub.B]) + ([Y.sub.B] [X.sub.A] - [Y.sub.A] [X.sub.B])/([X.sub.A] - [X.sub.B]).
This equation is also in a linear form (Fig. A1-b).
Magma mixing equations for elemental ratio plots have the form
[X.sub.M]/[Y.sub.M] = a/[Y.sub.M] + b
where a and b are constants. This is the equation of a hyperbola (see derivations in Langmuir et al., 1978; Faure and Mensing, 2005). Using this equation plots such as X/Y vs 1/Y or Z/Y are linear with a slope of "a" (Fig. A1-c). However, plots such as X/Y vs Y or X/Y vs W/Z have a hyperbolic form (Fig. A1-d). The curvature of the mixing line in the latter case depends on the ratio r, where
r = [Y.sub.A][Z.sub.B]/[Y.sub.B] [Z.sub.A]
Note that for r [??] 1, the hyperbola approximates a straight line.
The hyperbolic curves for mixing of two magmas can be readily extended to three sources by calculating the three hyperbolae that represent the combination of any two sources and interpolating between these curves (Fig. A1-e).
The above examples grossly oversimplify the range of processes that can affect trace element abundances in arc systems, but they do provide general insights into trace element behaviour during magma evolution. For further details see Allegre et al. (1978), Hanson (1978), and Langmuir et al. (1978).
Much of what I have learned about arc magmatism has been through collaboration and conversations with colleagues including Alan Anderson, Randy Cormier, Richard D'Lemos, Jarda Dostal, Javier Fernandez-Suarez, Gabi Gutierrez-Alonso, Andrew Hynes, Duncan Keppie, Damian Nance, Georgia Pe-Piper, Cecilio Quesada, Rob Strachan and participants in various UNESCO-IGCP projects. I am grateful to NSERC Canada for research funding, for which arc systems are a major part, to Derek Thorkelson, and Stephen Johnston for thorough, constructive reviews, Sowa Dehler, Steve McCutcheon and Georgia Pe-Piper for editorial advice, and Matt Middleton for cheerful technical assistance.
Accepted as revised, 27 February 2007
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J. Brendan Murphy
Dept of Earth Sciences, St. Francis Xavier University, Antigonish, NS, B2G 2W5, Canada
Table 1. Typical phenocryst content of Island arc tholeiitic and calc-alkalic basalt (B), basaltic andesite (BA), andesite (A), dacite (D) and rhyolite (R) (after Wilson 1989). Solid lines, common; dashed lines, rare. low-K tholeiite olivine clinopyroxene plgeonlte orthopyroxene amphibole biotite magnetite plagioclase alkali feldspar quartz medium-K calc alkaline olivine clinopyroxene plgeonlte orthopyroxene amphibole biotite magnetite plagioclase alkali feldspar quartz high-K calc alkaline olivine clinopyroxene pigeonite orthopyroxene amphibole biotite magnetite plagioclase alkali feldspar quartz Table 2. Partition coefficients for various trace elements in rock-forming minerals (see Winter 2001, p. 157; Pearce and Norry 1979). cpx opx plag olivine gamet Ni 7.0 5.0 0.01 14.0 0.955 Cr 34.0 10.0 0.01 0.70 1.345 Rb 0.004 0.005 0.08 0.00001 0.00001 Ba 0.002 0.0006 0.16 0.00001 0.00001 Nb 0.006 0.004 0.0236 0.00353 0.01 La 0.05 0.016 0.042 0.000007 0.001 Ce 0.08 0.04 0.036 0.00001 0.005 Sr 0.079 0.062 1.97 0.00012 0.0005 Nd 0.18 0.037 0.029 0.00007 0.04 Zr 0.13 0.03 0.09 0.003 0.9 Sm 0.29 0.054 0.022 0.0007 0.21 Eu 0.33 0.063 0.22 0.00095 1 Ti 0.36 0.08 0.045 0.017 0.28 Y 0.41 0.3 0.01 0.0074 3.1 Dy 0.46 0.1621 0.013 0.004 3.8 Er 0.38 0.1816 0.013 0.009 4.5 Yb 0.42 0.2605 0.012 0.023 5.5 Lu 0.45 0.318 0.012 0.03 7.1 spinel ilmenite magnetite apatite amph Ni 29 6.8 Cr 7.4 2.00 Rb 0.32 0.001 0.32 0.29 Ba 0.001 0.01 0.001 0.42 Nb 0.08 2.3 0.1 0.8 La 0.0006 0.0072 0.029 3.4 0.544 Ce 0.0006 0.00783 0.0217 4.5 0.843 Sr 0.4 0.7 0.4 3.7 0.46 Nd 0.0006 0.00847 0.0145 6.7 1.804 Zr 0.04 0.33 0.1 0.9 0.5 Sm 0.0006 0.0091 0.0072 6.7 1.340 Eu 0.0006 0.0084 0.00635 6.7 1.557 Ti 0.07 16 7.5 1.5 Y 0.0039 0.0045 0.0039 1.0 Dy 0.0015 0.0106 0.0071 5.1 Er 0.003 0.01625 0.0117 4.0 1.740 Yb 0.0045 0.02475 0.01923 2.9 1.642 Lu 0.0045 0.029 0.023 2.3 1.563 Table 3. Isotopic characteristics of various mantle reservoirs (after Zindler and Hart 1986; Rollinson 1993; Winter 2001). DM = depleted mantle, PREMA = prevalent mantle, HIMU = high [mu] mantle. DM is the probable source of mid-ocean ridge basalt. PREMA is a dominant reservoir of oceanic island rocks (see Greenough et al. 2005). HIMU is highly radiogenic mantle, its high [sup.206]Pb/[sup.204]Pb indicating a source rich in U. EM-I and EM-II are two types of enriched mantle. EM-I may represent a mantle contaminated with recycled oceanic or lower continental crust. EM-II may represent a mantle contaminated with upper continental crust (or sediments derived from upper continental crust). [sup.87]Sr/[sup.86]Sr [sup.143]Nd/[sup.144]Nd Bulk Earth 0.7052 0.51264 DM 0.7015-0.7025 0.5133-0.5136 PREMA 0.7033 <0.5128 HIMU 0.7025-0.7035 0.511-0.5121 EM-I c. 0.705 <0.5112 EM-II >0.722 0.511-0.512 Upper Crust 0.72-0.74 0.507-0.513 [sup.206]Pb/[sup.204]Pb [sup.207]Pb/[sup.204]Pb Bulk Earth 18.4 15.58 DM 15.5-17.7 <15.45 PREMA 18.2-18.5 15.4-15.5 HIMU 21.2-21.7 15.8-15.9 EM-I 17.6-17.7 15.46-15.49 EM-II 16.3-17.3 15.4-15.5 Upper Crust up to 28 up to 20
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