Journal of Petrology | Volume 43 | Number 10 | Pages 1857-1883 | 2002
© Oxford University Press 2002
Plume-Associated Ultramafic Magmas of Phanerozoic Age
C. HERZBERG1,* and
M. J. O’HARA2
1DEPARTMENT OF GEOLOGICAL SCIENCES, RUTGERS UNIVERSITY, NEW BRUNSWICK, NJ 08903, USA
2DEPARTMENT OF EARTH SCIENCES, CARDIFF UNIVERSITY, PO BOX 914, CARDIFF CF10 3YE, UK
Received
February 23, 2001;
Revised typescript accepted
April 1, 2002
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ABSTRACT
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A parameterization of experimental data in the 0·2–7·0
GPa pressure range constrains both forward models of potential
primary magma compositions that exit the melting regime in the
mantle and inverse models for computing the effects of olivine
fractionation for any olivine-phyric lava suite. This is used
to infer the MgO contents of primary magmas from Gorgona, Hawaii,
Baffin Island and West Greenland. They typically contain 18–20%
MgO for wide variations in assumed peridotite source compositions,
but MgO can drop to 14–17% for Fe-enriched sources, and
increase to 24–26% for fractional melts from Gorgona.
Primary magmas with 18–20% MgO have potential temperatures
of 1520–1570°C. For Gorgona picrites with 24% MgO,
the potential temperature and initial melting pressure were
about 1700°C and 8·0 GPa, respectively; melting was
hot and deep, consistent with the plume model. There are important
restrictions to magma mixing in mantle plumes. Primary magmas
that exit the melting regime are both well-mixed aggregate fractional
melts and isolated fractional melts. The latter can originate
from a hot plume axis and be in equilibrium with olivines having
mg-numbers of 93·0–93·6, but they have MgO
contents and thermal characteristics that are difficult to constrain.
KEY WORDS: komatiite; picrite; basalt; MORB; olivine; mantle plumes; primary magmas; equilibrium melting; accumulated fractional melting
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INTRODUCTION
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Mantle plumes are localized regions of hot mantle that are thought
to offer ideal opportunities for ultramafic magmatism during
the Archaean (
Cawthorn, 1975;
Fyfe, 1978;
Jarvis & Campbell, 1983;
Arndt, 1986). However, the importance of ultramafic magmatism
is often diminished in models of Phanerozoic hotspot volcanism
because basalt eruptives are more common, and the plume model
is subject to debate (
Anderson, 2000). Even where ultramafic
lavas occur, they often have a large olivine phenocryst content
and this complicates interpretations of the MgO content of the
primary magma. Indeed, the interpretation that picrites can
only form by the accumulation of olivine in basaltic liquids
(
Bowen, 1928) went unchallenged until petrographic evidence
demonstrated that skeletal olivine can grow
in situ in ultrabasic
liquids (
Drever, 1956;
Drever & Johnston, 1957).
Discussions on primary magma compositions are often reduced to the following shortlist of frequently asked questions: How can the composition of a lava flow be used to derive the composition of its primary magma extracted from the melting regime in the mantle? How can an evaluation be made of the effects of olivine fractionation in crust and mantle lithosphere, and the possible sampling of wall-rock olivines from the melting regime? How can we best describe potentially complex fractional melting products of the mantle with equilibrium experimental data? Can the physics of the melt collection process be understood by identifying geochemical differences in the magmatic products of fractional and equilibrium melting? Can inferences be made concerning the extent of melting and crustal thickness from the major element geochemistry of ultramafic lavas? What is the role of heterogeneous mantle? How hot and deep must the melting regime be to produce an ultramafic magma, and can this be used to test the plume model?
Previous discussions of ultramafic rocks have been aggravated by taxonomical confusion over the distinction between picrites and komatiites. For example, we show in this paper that Cretaceous ‘komatiite’ lava flows from Gorgona Island and Tertiary ‘picrites’ from West Greenland crystallized from primary magmas with nearly identical major element compositions and T–P conditions of melting. The difference, therefore, is purely textural in that the ‘komatiite’ flows are spinifex-textured whereas the picrites are generally not. The qualification that komatiites be spinifex-textured (Arndt & Nisbet, 1982) has been dropped with the new IUGS chemical classification (Le Bas, 2000). Nevertheless, discussion continues over the merits of the new classification (Kerr & Arndt, 2001; Le Bas, 2001). As we are concerned mostly with the origin of primary magmas that fit the definitions of both picrite and komatiite, we will use the term ‘ultramafic’ magma to refer to all magmas with more than 18 wt % MgO.
In previous papers it was shown that Gorgona primary magmas are similar in composition to experimentally constrained anhydrous liquids in equilibrium with harzburgite [L + Ol + Opx] at 3–4 GPa (Herzberg & O’Hara, 1998; Herzberg & Zhang, 1998). Experimental liquid compositions and natural lavas were examined in simplified four-component CMAS space and projected into coordinates defined by olivine, pyroxenes, plagioclase, spinel or garnet. This method of data representation, developed by O’Hara (1968a), has the advantage of permitting a simple visual inspection to be made of the full range of analogue magma compositions that can be extracted from the mantle. However, all FeO is combined with MgO in projections, and information is lost in this procedure. Furthermore, the representation of lava compositions in projection is inadequate for distinguishing equilibrium melting from fractional melting processes.
We attempt to provide answers to the above shortlist of frequently asked questions by reporting a new method for constraining the composition of a primary magma for an olivine-phyric lava series. The method involves interfacing projections with diagrams that show absolute weight percentages of FeO and MgO for both equilibrium and fractional melting of various assumed peridotite sources. It differs from the computation of a parental magma using olivine compositions and FeO–MgO exchange coefficients (e.g. Albarède, 1992; Langmuir et al., 1992; Nisbet et al., 1993; Hauri, 1996; Larsen & Pedersen, 2000; Thompson & Gibson, 2000). Parental magmas may not be the same as primary magmas that exit the melting regime owing to modification by olivine crystallization in crustal magma chambers or mantle conduit walls (Larsen & Pedersen, 2000). Our method sees through olivine fractionation effects, and it anticipates potential problems that can arise from the use of olivine phenocrysts or wall-rock xenocrysts with complex fractional melting histories. Indeed, we demonstrate that olivine compositions can provide poor constraints on primary magma MgO content. Model primary magma compositions are used to evaluate the temperatures, pressures and petrological structures of the melting regimes for picrites and komatiites of Phanerozoic age. We show that melting is characteristically hot and deep, consistent with the plume model.
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A HYBRID FORWARD AND INVERSE MODEL FOR CALCULATING PRIMARY MAGMA COMPOSITION
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The forward component identifies potential primary magma compositions
as functions of melt fraction for an assumed peridotite source
and melting mechanism. This is done by a parameterization of
a large experimental database over a wide pressure range using
diagrams of CMAS projections and FeO–MgO. Peridotite compositions
that we examine are listed in Table
1. The melting mechanisms
that we explore are equilibrium, perfect fractional, and accumulated
perfect fractional melting. The inverse component selects a
derivative liquid in an erupted lava suite for which olivine
fractionation is computed, and this provides an array of possible
primary magma compositions. We compare the arrays of potential
primary magmas in both forward and inverse models, and make
use of model melt fractions in the forward component to seek
a unique primary magma solution. Model solutions provide primary
magma composition, melt fraction, residuum mineralogy, and temperature
of eruption and melt collection in the melting regime. Computed
primary magma compositions depend on assumptions concerning
peridotite source composition and melting mechanism, and we
evaluate these effects in the forward model component.
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MAGMAS IN PROJECTION
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The compositions of magmas formed by equilibrium melting of
mantle peridotite are shown in projection in Fig.
1a and b.
These projections are based on experiments in the system CaO–MgO–Al
2O
3–SiO
2 summarized by
Herzberg & O’Hara (1998). Other components
such as TiO
2, Cr
2O
3, FeO, MnO, Na
2O, K
2O and NiO can expand
and contract liquidus crystallization fields to varying degrees.
The replacement of MgO by FeO does little to change the projected
locations of the cotectics and invariant points, but the effects
of TiO
2, Na
2O and K
2O are more substantial. Cotectic shifts
have been evaluated in the projection code by optimizing the
match to the phase equilibria in the system CaO–MgO–Al
2O
3–SiO
2 (
Herzberg & O’Hara, 1998). A description of the projection
code is given in Electronic Appendix 1, which may be downloaded
from the
Journal of Petrology Web site at
http://www.petrology.oupjournals.org.
A CMAS description of mantle melting reduces the system SiO
2–TiO
2–Al
2O
3–Cr
2O
3–FeO–MnO–MgO–CaO–Na
2O–K
2O–NiO
to four ‘equivalent’ components in CaO–MgO–Al
2O
3–SiO
2.
The experimental database used in the construction of these
projections was listed by
Herzberg & O’Hara (1998),
and is here upgraded with new data at pressures from 1 to 2·7
GPa (
Falloon et al., 1999a,
1999b;
Gudfinnsson & Presnall, 2000),
previously published data that we had overlooked (
Kushiro, 1996)
and the experimental results of
Walter (1998). A preliminary
draft of Walter’s initial results was made available to
the first author, and these were encorporated into the projections
of
Herzberg & O’Hara (1998). The final set of experimental
results that were published by
Walter (1998) differed somewhat
in that only superior data were included, those being data for
which an optimum mass balance was demonstrated. Data of
Kinzler (1997) have not been used because totals in many reported liquid
compositions are low (i.e. 97–99%), and high pressures
arise as an artefact of low SiO
2.
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Fig. 1. (a) Projection of compositions (mole percent) of liquids in equilibrium with mantle peridotite from Diopside (CMS2) and Na2O·Si3O6 and K2O·Si3O6 into the plane Olivine (M2S)–Anorthite (CAS2)–Silica (S), modified from Herzberg & O’Hara (1998). F, Fertile mantle peridotite (KR-4003; Table 1); D, depleted mantle peridotite (abyssal; Table 1). Phase assemblages are indicated by labels. L, Liquid; Ol, Olivine; Opx, Orthopyroxene; Cpx, Clinopyroxene; Gt, Garnet; Sp, Spinel; Cr, Chromite (see text). Fine continuous lines with arrows indicate cotectic equilibria at the pressures shown (GPa); arrows point up-temperature in the sense of advanced partial melting. Bold continuous lines with large arrows indicate cotectics at 1 atm; arrows point down-temperature in the sense of progressive partial crystallization. Inset shows the effect of adding 1 wt % of CaO, MgO, Al2O3 and SiO2 to the compositions of liquids at the invariant points at the pressures indicated. Projection code for combining all oxide components to CMAS equivalents has been given by Herzberg & O’Hara (1998) and in Electronic Appendix 1. (b) Projection of compositions (mole percent) of liquids in equilibrium with mantle peridotite from Diopside (CMS2) and Na2O·Si3O6 and K2O·Si3O6 into the plane Olivine (M2S)–MgTschermak’s (MAS)–Enstatite (M2S2), modified from Herzberg & O’Hara (1998). Symbols as for (a).
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The new projections in Fig. 1 are very similar to those reported by Herzberg & O’Hara (1998), differing mainly in a more precise location of the harzburgite cotectics [L + Ol + Opx] at 3 and 4 GPa. In most cases the revised harzburgite cotectics at 2–6 GPa describe the experimental data to within ±0·5 GPa (Herzberg & O’Hara, 1998). Experimental picritic liquid compositions reported by Longhi (1995) exhibit model pressures in projection that are typically 0·5 GPa higher than his experimental nominal pressures, a difference that points to uncertainties associated with pressure calibrations (Herzberg et al., 2000; Hirschmann, 2000). The 1 GPa cotectics for lherzolite [L + Ol + Opx + Cpx ± Spinel ± Chromite) and harzburgite [L + Ol + Opx ± Chromite) shown in Fig. 1a describe data for a wide range of compositions to within ±0·2 GPa (Hirose & Kushiro, 1993; Baker & Stolper, 1994; Baker et al., 1995; Kushiro, 1996; Hirschmann et al., 1998; Falloon et al., 1999a).
The phase relations shown in Fig. 1a and b apply to equilibrium melting of a fertile and a depleted mantle peridotite (Table 1). The fertile peridotite is a xenolith from Kettle River, British Columbia (KR-4003; Xue et al., 1990; Walter, 1998), and the depleted composition is a sample of abyssal peridotite (Baker & Beckett, 1999). Oxides in KR-4003 sum to 99·18 (Xue et al., 1990), and we suspect that this arises from low MgO (Table 1); liquids analysed by Walter (1998) in experiments on this sample containing only liquid + olivine are better described with a bulk composition having 38·12% MgO rather than 37·3% MgO (Table 1). Liquids in low-variance assemblages such as spinel-lherzolite [L + Ol + Opx + Cpx + Sp] project along common cotectics. Differences can arise, however, for liquids in equilibrium with olivine [L + Ol] and harzburgite [L + Ol + Opx] near the melting out of Opx owing to the differences in bulk composition (Fig. 1).
The experimental data of O’Hara et al. (1971) and Walter (1998) are consistent with a 2·7 GPa pressure for the transformation of spinel to garnet peridotite (Herzberg et al., 2000). This pressure defines an important break in the pressure-induced track of liquids formed by initial melting of mantle peridotite (Fig. 1a). At higher pressures, liquids in equilibrium with garnet peridotite become substantially enriched in MgO and depleted in Al2O3 (see also Herzberg, 1992). At pressures between 3·0 and 4·0 GPa, initial melts of fertile peridotite KR-4003 are in equilibrium with Opx (L + Ol + Opx + Cpx + Gt; Walter, 1998). At pressures between 4·0 and 4·5 GPa, initial melts of KR-4003 are produced from the Opx-free assemblage [L + Ol + Cpx + Gt] owing to the stabilization of subcalcic clinopyroxene (Walter, 1998). When Opx becomes unstable, liquids on the solidus must have lower SiO2 than those in equilibrium with Opx because of the reaction Ol + Cpx + Gt = L + Opx (e.g. Herzberg & Zhang, 1998; Walter, 1998).
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CALCULATED MAGMA COMPOSITIONS: BALANCE OF MgO AND FeO IN MAGMAS, SOURCES AND RESIDUES
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Partition and exchange coefficients
The procedure of
Beattie et al. (1991) and
Jones (1995) has
been adopted for computing the compositions of olivine and orthopyroxene
in equilibrium with a liquid of a known composition. The liquid
composition in weight percent oxides is first recalculated to
mole percent oxides, and the compositions of olivine and orthopyroxene
are computed using the molecular percent partition coefficients:
and
where
Xi refers to
the mole fraction of oxide component
i in the phases liquid
(L), olivine (Ol) and orthopyroxene (Opx).
Beattie et al. (1991) and
Jones (1995) showed that
Di values for some components are
often dependent on the partitioning of MgO between mineral and
liquid, so that
and
where
and
Ai and
Bi are constants for each oxide component
i.
We have added to and re-evaluated the constants Ai and Bi of Beattie et al. (1991) and Jones (1995) for TiO2, Al2O3, Cr2O3, Fe2O3, MnO, CaO, Na2O and K2O, using experimental data described in Electronic Appendix 2 (available from the Journal of Petrology Web site at http://www.petrology.oupjournals.org). Results are listed in Tables 2 and 3. For the partitioning of Fe2O3, DFe2O3Ol/L = 0, and DFe2O3Opx/L = 0·3; this partition coefficient for Opx/Liquid yields Fe3+/
Fe = 0·06 as observed in orthopyroxenes from a wide range of peridotites (Canil et al., 1994). For the partitioning of FeO, AFeOOl/L and AFeOOpx/L are equivalent to the exchange coefficients
and
Roeder & Emslie (1970) determined the exchange coefficient for olivine to be 0·30 ± 0·03 for basaltic liquids with about 8% MgO at 1 atm, a value that is commonly used in petrological modelling. This is observed again in Fig. 2 with our database, but it can also be seen that KDOl/LFeO/MgO increases to 0·35–0·36 for liquids with MgO > 20%. Clearly, the values of AFeO in equations (3) and (4) are not constant. Experimental data shown in Fig. 2 have been regressed with the equations
where
MgO is the weight percent concentration in the liquid and
where
DMgOOl/L is the distribution of MgO between
olivine and liquid, on a molecular basis. A regression of experimental
data for orthopyroxene–liquid yields
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Fig. 2. (a, b) Exchange coefficient KD for FeO and MgO between olivine and liquid as a function of composition of the liquid and the partition coefficient for MgO between olivine and liquid. Data sources are cited in Electronic Appendix 2.
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The uncertainty in calculating KDOl/LFeO/MgO from equations (8) and (9) is ±0·019 at the 1
level, compared with an uncertainty of ±0·011 (1) that arises strictly from errors in the analysis of olivine and glass using the electron microprobe. Uncertainties arising from Fe2O3 should be small because experimental samples were encapsulated in either carbon or metallic iron, as discussed in Electronic Appendix 2. The difference between ±0·019 and ±0·011 is fairly small, and most of it is likely to arise from temperature and pressure effects (Takahashi & Kushiro, 1983; Ulmer, 1989; Sobolev & Danyushevsky, 1994). Indeed, we observe positive correlations of KDOl/L with temperature and pressure. However, regressions of KDOl/L vs pressure and temperature yield 1 uncertainties of ±0·024 (correlation coefficient R = 0·46) and ±0·021 (R = 0·60), respectively, larger than standard deviations for KDOl/L vs liquid MgO content (±0·019; R = 0·69). Values of KDOl/L estimated from equations (8) and (9) are significantly lower than those of Ulmer (1989). For example, both experiments reported by Walter (1998) and our regression in Fig. 2 yield KDOl/L = 0·34–0·36 for liquids equilibrated at 3·0–7·0 GPa, whereas Ulmer (1989) predicted 0·38–0·51. We have not attempted to resolve the independent effects of temperature, pressure and composition on KDOl/L for several reasons. First, it is difficult to do so with confidence because the MgO content of the liquid is highest in experiments conducted at elevated temperatures and pressures. Second, our method of calculating KDOl/L from liquid composition has the advantage of considerable simplicity because it does not require an independent way of evaluating pressure.
The fraction of sites available for Fe2+ and Mg is 0·667 and 0·5 for olivine and orthopyroxene, respectively. These are filled with Mn, Ca, Na, K and Ni; Ti is partitioned exclusively into the tetrahedral sites; Al and Cr are distributed equally between tetrahedral and octrahedral sites to maintain charge balance. The remaining octahedral sites are filled with Fe2+ and Mg, calculated by rearranging equations (6) and (7) to
and
with
solutions from equations (9) and (10). Olivine and orthopyroxene
compositions are then converted from mole percent to weight
percent. A computer program is provided in Electronic Appendix
2 for computing the weight percent composition of olivine and
orthopyroxene in equilibrium with a liquid of a known composition.
Effect of H2O on exchange coefficients
Ulmer’s (1989) FeO–MgO exchange coefficients for experimentally equilibrated olivine–liquid pairs were for starting material compositions that contained 1·98–3·28 wt % H2O. These hydrous data can be reproduced to within ±0·023 (1) using equations (8) and (9) for anhydrous data, indicating that H2O has little effect on KDOl/LFeO/MgO.
Liquids in equilibrium with olivine and harzburgite
The compositions of liquids in equilibrium with olivine [L + Ol] and harzburgite [L + Ol + Opx] were computed by mass balance solutions to the equilibrium melting equation
where
CL is the weight percent of an oxide component
in the liquid phase,
Co is the initial oxide concentration in
the peridotite source composition of interest (Table
1),
F is
the melt fraction, and
D is the bulk distribution coefficient
applicable at any chosen value of
F.
The bulk distribution coefficient is the concentration of the oxide component in the multiphase residue divided by the concentration in the liquid, and takes the form
D is determined from
where
XOl and
XOpx are the weight proportions of olivine and orthopyroxene
in the residue, and
DiOl and
DiOpx are the weight percent olivine–liquid
and orthopyroxene–liquid partition coefficients, respectively.
We distinguish weight percent partition coefficients from molecular
percent partition coefficients with
DiOl and
DiOl, respectively.
The weight percent partition coefficients have been calculated
by computing the weight percent composition of olivine and orthoproxene
in equilibrium with the melt, as discussed above, weighted with
equation (15) according to the proportions of olivine and orthopyroxene
in the residue.
Coexisting liquid and crystalline compositions were solved with equation (13) using an iterative procedure that incrementally varies F from 1·0 to a value that is regulated by the stability of clinopyroxene. Liquid compositions in equilibrium with olivine (L + Ol) are solved for XOpx = 0, and liquid compositions in equilibrium with harzburgite (L + Ol + Opx) are solved for XOpx = 0 to a value that is also regulated by the stability of clinopyroxene (L + Ol + Opx + Cpx). Clinopyroxene stability is constrained experimentally in Fig. 1, into which computed liquid compositions are projected. Harzburgite cotectics in Fig. 1 at 1–6 GPa constrain the pressure for projected liquid compositions. For example, in the case of equilibrium melting of fertile mantle peridotite KR-4003 (Table 1), Cpx melts out when F reaches 0·23 at 1·0 GPa, similar to that for other fertile compositions (Langmuir et al., 1992; Baker & Stolper, 1994). The effect of pressure is to increase F at which Cpx remains stable, and this is shown in more detail below.
The contents of FeO and MgO in liquids equilibrated with olivine and harzburgite residua at 1 GPa have been calculated for peridotite compositions PHN1611 (Kushiro, 1996) and MM3 (Hirschmann et al., 1998; Falloon et al., 1999a), and the results are shown in Fig. 3. The calculated compositions agree well with the experimentally observed liquids, and are consistently within the uncertainties associated with both the location of the harzburgite cotectic (Fig. 1a; ±0·2 GPa) and KDOl/L (Fig. 2; ±0·019 at the 1 level). Peridotite 1611 is considerably more FeO-rich than MM3 (Table 1), and this propagates to the partial melt products in a predictable way. Indeed, it is possible to independently compute the liquid compositions of PHN1611 from those for MM3. This can be done by the approximations
and
The approximations arise because D values for PHN1611 are not the same as D values for MM3 at a given melt fraction F. Nevertheless, the compositions of liquids formed by equilibrium melting of PHN1611 calculated by these different methods agree very well with the experimentally observed compositions (Fig. 3). We therefore have independent ways of evaluating the FeO and MgO contents of liquids formed by partial melting of a peridotite composition for which no experimental data are available.
Liquids on the solidus
We can constrain the compositions of liquids that form immediately on the solidus where F 
0 by combining equations (8) and (11):
where MgO and FeO for olivine and liquid are weight
percent oxides. This is done by solving for FeO
L for an array
of possible values for MgO
L on the solidus, given that (FeO/MgO)
Ol is known for the unmelted peridotite (
Smith & Boyd, 1987;
Baker & Stolper, 1994). Results are shown in Fig.
3.
A forward model for equilibrium melting of a fertile peridotite source (FeO 
8·0%)
A computation has been made of contents of SiO2, TiO2, Al2O3, Cr2O3, FeO, MnO, MgO, CaO, Na2O, K2O and NiO for magmas produced by equilibrium melting of a fertile peridotite source with 8·0% FeO (Table 1; KR-4003) at pressures that range from 1 to 6 GPa. Results for FeO and MgO are shown in Fig. 4a and representative model liquid compositions are listed in Table A1 of Electronic Appendix 3 on the Journal of Petrology Web site at http://www.petrology.oupjournals.org. Liquids were computed for olivine [L + Ol] and harzburgite [L + Ol + Opx] assemblages by the method discussed above, and for liquids immediately on the solidus. Uncertainties arising from 1 in KDOl/LFeO/MgO are typically ±1·4% MgO and ±0·52% FeO, and propagate to an uncertainty of ±1·5 GPa where isobaric cotectics are compressed in FeO–MgO space (Fig. 4a).
Liquids immediately on the anhydrous solidus were computed from equation (18) and the composition of subsolidus olivine, which has an mg-number of 89·5 (Walter, 1998; olivine analysis 60·02). The array of permissible solutions for FeO and MgO in liquids in equilibrium with this composition of olivine at the solidus is accurately defined (Fig. 4a), but difficulties arise in calibrating this array for pressure. For example, in the absence of any experimental data, the FeO and MgO contents of the first drop of liquid on the solidus at 4 GPa could be located anywhere on the solidus array.
Ironically, liquids on the solidus at 4–7 GPa may be better known than those at 1–3 GPa. The data of Walter (1998) show that FeO and MgO are negatively correlated and linear for [L + Ol + Cpx + Gt] at 6 and 7 GPa and for F ranging from 0·11 to 0·41. These isobaric FeO–MgO arrays are nearly orthogonal to the solidus array, which is intersected at well-defined points (Fig. 4a). Liquids on the solidus at 1 and 3 GPa were constrained by factoring liquid compositions for MM3 and PHN1611 according to bulk composition, as discussed above (Fig. 3). At 1 GPa the FeO and MgO contents of liquids at F in the 0–0·20 range nearly parallel those on the solidus FeO–MgO array (Figs 3 and 4a). For a basalt with 12% MgO, a ±1 uncertainty in KDOl/LFeO/MgO propagates to FeO contents at 1 GPa that cannot be statistically distinguished from those at 2 GPa. It is therefore understandable that disagreement exists over the FeO and MgO contents of the near-solidus liquid at 1 GPa for peridotite MM3 (Baker & Stolper, 1994; Baker et al., 1995; Hirschmann et al., 1998; Falloon et al., 1999a). The positions of the model isobaric cotectics between the solidus and harzburgite saturation shown in Fig. 4a usually differ from experimental determinations by no more than ±0·5 GPa. However, this uncertainty can increase to ±1·5 GPa where the isobaric cotectics are compressed in FeO and MgO space, similar to those for [L + Ol + Opx]. In most cases, the model FeO–MgO isobaric cotectics agree with experimental cotectics to within ±1 GPa in the 1–7 GPa range and therefore pressure information cannot be accurately obtained for natural lava compositions. We believe that a ±1 GPa uncertainty is a problem that is common to all petrological models that operate within the ±0·019 bound of uncertainty in KDOl/LFeO/MgO.
A forward model for equilibrium melting of an Fe-rich fertile peridotite source (FeO 9·0%)
We now examine the consequences of partial melting of a peridotite source that is enriched in FeO. The average of 590 samples of peridotite from off-craton occurrences contains 8·14% and this varies by ±0·90% FeO at the 1 level (Herzberg, 1993). Most peridotites from ocean basins and xenoliths display wide variations in MgO content at 8·0% FeO, and they display no relationship between FeO and indicators of fertility or depletion (e.g. TiO2, Al2O3, Na2O; Herzberg, 1993; Baker & Beckett, 1999; Griffin et al., 1999; excluding cratonic mantle). Calculations have been performed on a synthetic composition formed from Kettle River peridotite KR-4003 by a simple replacement of MgO with FeO. This Fe-rich source contains 9·04% FeO (Table 1), which is higher than the average FeO content by 1 (i.e. 8·14 + 0·90), and it is identically located in projection with its precursor, KR-4003.
Shown in Fig. 4b are the compositions of liquids formed by equilibrium melting of this Fe-rich fertile source with residual harzburgite and olivine. These liquids are elevated in FeO compared with normal fertile peridotite with about 8% FeO, a result that is intuitively obvious. Indeed, liquids are elevated in FeO by about 0·9% at most pressures, an amount that corresponds to enrichment of normal mantle with 0·9% FeO. We do not provide pressure information for compositions on the solidus or between the solidus and harzburgite-saturated assemblages because we have no experimental data for pressures in the 2–6 GPa range.
A forward model for equilibrium melting of a depleted peridotite source (FeO 8·0%)
The depleted peridotite sample chosen for this forward model is an abyssal peridotite from Baker & Beckett (1999). Inspection of Table 1 shows that it has nearly the same composition as the average of 590 mantle peridotite samples from off-craton occurrences (Herzberg, 1993). This depleted source contains about 42% MgO and 8% FeO, similar to FeO in fertile peridotite.
Shown in Fig. 5a are the compositions of liquids formed by equilibrium melting of this depleted source with residual harzburgite and olivine. Again, we do not provide pressure information owing to a lack of experimental data. The compositions shown for olivine- and harzburgite-saturated assemblages are compared with those for equilibrium melting of fertile peridotite in Fig. 5b. In the 1 atm to 2 GPa pressure range, there is a similarity in FeO and MgO contents of harzburgite-equilibrated liquids for fertile and depleted sources having 8·0% FeO. However, at 3–5 GPa, harzburgite-equilibrated liquids of a depleted source with 8·0% FeO are similar in FeO and MgO to those for Fe-rich fertile peridotite with 9·0% FeO. These observations illustrate the harzards that can result from using the composition of an erupted magma to infer the FeO content of a peridotite source.
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Fig. 5. (a) FeO and MgO contents of liquids formed by equilibrium melting of depleted mantle peridotite (Table 1). FeO–MgO–F systematics are computed from equations (21)–(23) given in the text. Liquids in equilibrium with olivine [L + Ol] and harzburgite [L + Ol + Opx] are computed from equations (13)–(15) and Fig. 1 (see text). Crosses indicate uncertainties in calculated FeO and MgO contents arising from ±1 KDOl/LFeO/MgO. (b) A comparison of FeO and MgO contents of liquids formed by equilibrium melting of various peridotite source compositions.
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FeO–MgO–F systematics for all forward models of equilibrium melting
It is sometimes convenient to consider a residue–liquid equilibrium rather than an olivine–liquid equilibrium, although both are obviously identical when olivine is the only residuum phase. If the mg-number of a residue is nearly identical to that of olivine in that residue, then equation (18) can be modified so that (FeO/MgO)Ol is replaced by (FeO/MgO)o, the initial source rock composition. Indeed, the arrays of FeO and MgO we compute for liquids on the solidus using source rock composition are nearly identical to those computed using olivine in equation (18), the difference being <0·1% FeO. The equation for the exchange coefficient can therefore be generalized as
where S refers to the solid residue.
For fertile peridotite KR-4003 shown in Fig.
4a, we have obtained
FeO and MgO contents for the residue compositions from the mass
balance equation
where
CS refers
to the residue composition. A regression yields
where MgO
L refers to the weight percent MgO in the
liquid. Solutions to equations (8) and (21) yield olivine–liquid
and residue–liquid exchange coefficients that are almost
identical. The batch melting equation (13) can be solved for
any melt fraction
F:
by combining
it with the equation for mass balance to yield
where FeO
o and MgO
o are the weight percent FeO and
MgO in the peridotite source. Equations (21), (22) and (23)
yield general solutions to the iron content of a liquid (FeO
L)
for any assumed MgO content of the liquid (MgO
L) and melt fraction
F, given FeO
o and MgO
o for any peridotite source composition.
For melting on the solidus where
F 0, FeO–MgO solutions
to these equations are essentially identical to those derived
from equation (18) for the olivine–liquid equilibrium
for peridotite compositions KR-4003, MM3 and PHN1611. For olivine–liquid
and harzburgite–liquid equilibria, solutions to equations
(21), (22) and (23) at elevated melt fractions yield FeO–MgO–F
systematics that are identical to those that have been independently
calculated from mass balance solutions to the batch melting
equation for all oxide components. However, solutions to equations
(21)–(23) are applicable to all phase assemblages and
at all melt fractions. These equations have therefore been applied
to FeO–MgO–F systematics for phase assemblages ranging
from the solidus to [L + Ol + Opx] in Figs
4b and
5a for Fe-rich
fertile peridotite and depleted peridotite.
A forward model for FeO–MgO–F systematics specific to isobaric accumulated perfect fractional melting (APFM) of a fertile peridotite source (FeO 8·0%)
Liquids formed by isobaric accumulated fractional melting were determined by first computing equilibrium liquid and residue compositions using equation (13) for equilibrium melting as discussed above. This provides a set of D and F values that were then used in Shaw’s (1970) equation for accumulated fractional melting:
The computational procedure is discussed in more detail in Electronic Appendix 4 on the Journal of Petrology Web site at http://www.petrology.oupjournals.org. Results are shown in Fig. 6a.
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Fig. 6. (a) FeO and MgO contents of liquids formed by accumulated perfect fractional melting of fertile peridotite KR-4003, from solutions to Shaw’s (1970) equation, (24), given in the text. (b) FeO and MgO contents of liquids formed by isobaric accumulated perfect fractional melting of fertile peridotite KR-4003, from solutions to the incremental batch melting equation for a continuously depleted residue. At the point of Opx exhaustion, olivine is the sole residuum phase (see text). It should be noted that FeO–MgO–F systematics are the same as in (a).
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An apparent paradox of Shaw’s (1970) equations for fractional and accumulated fractional melting is that the MgO content of the residue becomes greater than the MgO content of olivine when olivine is the sole residue phase, a problem that is also discussed in Electronic Appendix 4. We therefore examine accumulated perfect fractional melting using the following incremental batch melting approach. We compute liquid compositions with 0·01 mass fractions of melting of the residue, the liquid is completely removed from its residue, the residue is melted again at successive 0·01 mass fractions, and each new melt is perfectly extracted and mixed with the previously formed melt. The process is repeated many times until the residue is completely melted, and each instantaneous melt is formed by equilibrium melting of an instantaneous residue whose composition is continuously changing owing to melt extraction. Each 0·01 mass fraction of melt extracted from the residue is called an ‘instantaneous’ drop of melt. This analysis is restricted to fertile peridotite KR-4003 for which we have pressure information. We consider first the case of isobaric melting at 1–6 GPa, and this is followed by consideration of polybaric melting situations.
The MgO content of the instantaneous liquid is computed from
where
CMgO,Lin is the weight percent MgO content
of the instantaneous drop of liquid, C
MgO,Sin is the MgO content
of the instantaneous solid residue,
DMgO,in is the weight percent
partition coefficient of MgO between the residue and liquid,
and
FS = 0·01, a constant mass fraction of melting of
the residue S; it is worth noting that we could have chosen
lower values for
FS but this has little effect on the computed
liquid compositions. At each pressure, we parameterize
DMgO,in as a function of
CMgO,Sin, and these are obtained from liquid
compositions for isobaric equilibrium melting (Fig.
4a). For
phase assemblages between the solidus and the onset of harzburgite
melting,
DMgO,in is a nonlinear function of
CMgO,Sin at 1–3
GPa, but the function becomes linear at 4–6 GPa. For the
harzburgite phase assemblage [L + Ol + Opx] we obtain
DMgO,in and
CMgO,Sin from solutions to equations (13) and (20), and
these are modestly nonlinear. When olivine is the only residuum
phase [L + Ol], it melts incongruently to a liquid on the forsterite–fayalite
join where
KDOl/LFeO/MgO = 0·36 (Fig.
2a). The situation
for FeO is similar:
but
D for FeO
is obtained from
by solutions to
equations (13) and (20). We can obtain the exchange coefficient
KDS/LFeO/MgO by dividing
DFeO,in by
DMgO,in, and this becomes
equation (21).
The amount of liquid produced at the first increment of melting is 0·01, and this becomes progressively lower than 0·01 with each subsequent increment of melting because the mass of residue is progressively being reduced from 1·0 to zero. We keep track of the melt fraction of each increment with respect to the initial source mass, and call this Fin. Therefore, at the first increment of melting Fin = FS, but during subsequent increments Fin < FS. For the total melt fraction
for
N increments of melting. The average composition
of the aggregate melt
CL is simply the compositions of the instantaneous
melts (i.e.
CLin) weighted according to the mass of each increment
with respect to the initial source mass (i.e.
Fin). For MgO
and FeO this becomes
For constant D, this incremental solution to the batch melting equation for perfect melt extraction yields results that are identical to those calculated using the equations of Shaw (1970). That is, the instantaneous batch liquid composition is identical to Shaw’s (1970) perfect fractional melt composition, and the aggregated melt compositions in both cases are also the same.
Results for fractional melting of fertile peridotite with variable D are shown in Fig. 6a and b. Liquids formed by accumulated fractional melting have higher FeO contents than those for liquids that form by equilibrium melting (Fig. 4a) at any specific melt fraction, a conclusion reached previously by Langmuir et al. (1992). The most important observation is that identical FeO–MgO–F systematics are obtained for accumulated fractional melts calculated with Shaw’s (1970) equation and incremental solutions to the batch melting equation. The utility of the incremental batch approach is that it can be easily applied to polybaric melting, as discussed below, and it can be modified to include imperfect melt extraction, a problem we will not consider further. However, a close examination of Fig. 6a and b reveals several minor but important differences. The incremental batch melting approach (Fig. 6b) provides pressure information whereas Shaw’s (1970) equation does not. Additionally, there are minor differences in the compositions of aggregate liquids that form when olivine is the sole residue phase, an issue that is discussed further in Electronic Appendix 4.
Residue compositions of equilibrium and fractional melting are important for a complete mass balance analysis of peridotite melting, and bear on many problems of geological interest. Although a comprehensive discussion of residues is beyond the scope of this paper, there are several important aspects of this problem that require discussion. We consider only the mg-numbers of olivines in the residues. For the case of equilibrium melting of fertile peridotite, the mg-number of olivine increases from 89·5 to 95·9 from the solidus to the liquidus (Fig. 7a). For equilibrium melting of depleted peridotite, the mg-number of olivine increases from 90·2 to 96·2 from the solidus to the liquidus (Fig. 7a). The effect of perfect fractional melting is to produce residual olivines with mg-numbers that increase to 100 at the liquidus (Fig. 7b) for both depleted and fertile peridotite compositions. We consider now olivine phenocrysts with mg-numbers of 92·0 precipitated from an aggregate magma formed by accumulated perfect fractional melting of a fertile or depleted source. Olivines in the residue of the pooled liquid are in equilibrium with the last drop of perfect fractional melt, and these have mg-numbers of about 94·0 (Fig. 7b). A primary accumulated magma has a unique residue, but the accumulated liquid is not in equilibrium with that residue; only the final drop of liquid extracted is in equilibrium with the residue. This is the process treated by Gast (1968) and Shaw (1970) and specifies that the liquids that are integrated are produced from a progressively depleting residue and are then added in aliquots to the final accumulation.
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Fig. 7. (a) Olivine mg-number as a function of melt fraction for equilibrium melting of fertile peridotite KR-4003 and depleted peridotite. (b) Olivine mg-number in phenocrysts of primary magmas produced by accumulated perfect fractional melting (APFM) compared with mg-numbers of olivines in the residues and olivines that precipitate from perfect fractional melts. It should be noted that residues of fractional melts and accumulated perfect fractional melts are the same. Mg-numbers = 100 when F = 1.
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A forward model for FeO–MgO–F systematics specific to polybaric accumulated perfect fractional melting (APFM) of a fertile peridotite source (FeO 8·0%)
An examination is now made of perfect polybaric accumulated fractional melting of fertile peridotite KR-4003. Before proceeding with the FeO and MgO characteristics of such melts, we consider the range of temperatures and pressures under which decompression melting can occur, and we do this with aid of the phase diagram for Kettle River peridotite KR-4003 shown in Fig. 8a. The anhydrous solidus for mantle peridotite is from Herzberg et al. (2000), which is almost identical to that offered by Hirschmann (2000) except that it is higher by about 30°C at 3–4 GPa. Temperatures for olivine-in and orthopyroxene-in were computed using the method of Beattie (1993) for liquid in equilibrium with olivine ± orthopyroxene at 1 atm, and extended to high pressures by a recalibration with experimental data summarized above for KD. Using 322 data points from 0·2 to 7·0 GPa and 1100 to 1950°C, we have obtained minimum residuals between observed and calculated temperatures with
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where
T (°C) is the temperature of interest
at pressure
P (GPa), and
T1 atm (°C) is obtained from
Beattie (1993) at 1 atm. Using equation (30) the difference between
calculated and observed temperatures is ±31°C at
the 1
level for pressures up to 7 GPa; this is only marginally
higher than that obtained by
Beattie (1993) for a much smaller
dataset to 4 GPa. Temperatures for Cpx- and Gt-in were calculated
for harzburgite-saturated liquids at the point of saturation
in Cpx and Gt as defined by Fig.
1. The difference between calculated
temperatures and those in all experiments conducted by
Walter (1998) at 3–7 GPa on this same peridotite composition
averages 16°C.
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Fig. 8. (a) A temperature–pressure phase diagram for fertile peridotite KR-4003. Numbers in boxes are weight percent MgO contents of liquids (Electronic Appendix, Table A1). Anhydrous solidus for mantle peridotite is from Herzberg et al. (2000), and is almost identical to that offered by Hirschmann (2000) except that it is higher by about 30°C at 3–4 GPa. The difference between calculated temperatures and those in all experiments conducted by Walter (1998) averages 16°C at 3–7 GPa, but our preferred solidus is higher than Walter’s by 50°C at 5 GPa. Adiabatic gradients indicated by small circles are from Asimow et al. (2001). Adiabatic gradients indicated by arrows are revised from Iwamori et al. (1995). Arrow indicated by 5'' is a hypothetical isothermal polybaric path initiated at 5 GPa; arrow indicated by 5' is a more realistic polybaric path, modified from Iwamori et al. (1995; see text). It should be noted that most adiabatic gradients are approximately parallel to isopleths of MgO in equilibrium liquids. (b) Calculated FeO and MgO contents of accumulated fractional melts that are produced along the adiabatic gradients indicated by arrows in (a). Pressures of initial melting are 3, 5, 7 and 10 GPa. Solidus composition at 10 GPa is from Herzberg & Zhang (1996). Circles represent a 1 GPa drop in the pressure of final melting along each adiabatic gradient. Each decompression melting path exhibits a strong reduction in FeO at nearly constant MgO.
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We examine the FeO and MgO contents of liquids that are formed along the five T–P paths shown in Fig. 8a, where melting initiates at 3, 5, 7 and 10 GPa. In one case the melting path is isothermal, and the other four approximate adiabatic gradients from Iwamori et al. (1995) but modified to remove ‘bumps’ that arose from strong T–P curvature to their solidus for spinel-lherzolite (Herzberg et al., 2000). The other adiabatic T–P paths shown in Fig. 8a are from Asimow et al. (2001). Although we consider only linear paths in T–P space, the conclusions that follow are applicable to more realistic decompression melting paths. Fractional melt compositions were computed using equations for isobaric incremental batch melting, except that DMgO,in was parameterized as a polybaric function of CMgO,Sin; values of DMgO,in and CMgO,Sin at each pressure along the polybaric path were parameterized from solutions to isobaric equilibrium melting (Fig. 4a). Instantaneous residue compositions vary continuously along each melting path owing to perfect melt extraction. Compositions of the accumulated melts were calculated from perfect fractional melts along each path between the solidus and the final melting pressure. Final melting pressures vary at 1 GPa increments below the initial melting pressure. Results are shown in Fig. 8b.
In most cases there is a substantial drop in the FeO content of liquids with decompression, but MgO varies by no more than 2% despite considerable differences in the melting paths (Fig. 8b). The reason why there is little change in MgO is because all T–P melting paths are approximately coincident with T–P isopleths of MgO in liquids defined by olivine saturation surfaces (Fig. 8a). Dissolution of ‘wall-rock’ olivine into ascending magmas should not be significant, and olivine–liquid equilibrium temperatures must closely reflect actual eruption temperatures. An important corollary is that the MgO content of a primary magma is similar to the MgO content of the initial melt on the solidus, and it reflects the pressure of initial melting.
There is also an important relationship between aggregate polybaric and isobaric melt compositions. Let us consider the case of decompression melting starting at 5 GPa and terminating at about 1·5 GPa along the path designated at 5’ in Fig. 7a and b. The aggregate melt composition has 20·5% MgO and 10·1% FeO and is formed at a melt fraction of 0·40. This same melt composition is formed isobarically at 4 GPa, also at an average melt fraction of 0·40 (Fig. 8b). The aggregate magma formed polybarically therefore records in its geochemistry an average pressure of 4 GPa, as defined by isobaric 4 GPa FeO–MgO–F relations.
For melting regimes in oceanic ridges and mantle plumes, there will be an infinite number of streamlines, with horizontal and vertical components, along which fractional melts are formed and in local equilibrium with their residues. The melting regime may then be visualized as a spider’s web of streamlines, and the primary aggregate magma is an integrated product of all fractional melts that collect in the melting regime. Any true forward melting model must therefore compute the compositions of all fractional melts along all streamlines, and then perform the integration within the melting regime. The complexity of this procedure is immediately apparent. The importance of isobaric FeO–MgO–F systematics is that they provide a simple means of constraining the composition of a primary aggregate melt for any melting regime, regardless of the polybaric streamline complexity. This is explored in the subsequent discussion.
Forward models for FeO–MgO–F systematics specific to accumulated perfect fractional melting (APFM) of depleted and iron-rich peridotite source
Liquids in equilibrium with olivine [L + Ol] and harzburgite residues [L + Ol + Opx] were discussed above (Fig. 5b). The bulk distribution coefficients D for FeO and MgO were used together with F and Shaw’s (1970) equation, (24), to calculate liquids formed by accumulated perfect fractional melting. Results are illustrated below in the discussions on Gorgona and Hawaiian magmatism. We cannot provide pressure information for the aggregate liquids because it is not known for equilibrium melting.
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INVERSE MODELS
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We restrict our inverse models to well-documented high-MgO aphyric
and olivine-phyric lavas that are related to each other in space
and time by fractional crystallization of olivine. We assume
that olivine was the sole fractionating phase that relates all
lavas to each other and all lavas to the primary magma from
the melting regime. The inversion method consists of selecting
a representative lava composition into which olivine is incrementally
added or from which olivine is incrementally subtracted. The
composition of olivine in local equilibrium with the liquid
is computed by the method discussed above, where
KDOl/LFeO/MgO is adjusted for changes in liquid composition, and each increment
represents 1 wt % addition or subtraction of olivine. These
inverse calculations produce a loci of compositions that can
be compared with the compositions of liquids in the various
forward models discussed above. A computational algorithm is
provided in Electronic Appendix 5 on the
Journal of Petrology Web site at
http://www.petrology.oupjournals.org so that the
reader can replicate our calculations.
Several workers, in attempts to compute mid-ocean ridge basalt (MORB) and hotspot primary magmas, have assumed that all Fe in published lava analyses was FeO (i.e. FeOT; Langmuir et al., 1992), whereas others have attempted to consider only the true amount of FeO in the lava that is exchangeable with olivine (Albarède, 1992; Nisbet et al., 1993; Larsen & Pedersen, 2000). We adopt the latter approach because the amount of Fe2O3 can be large, with Fe3+/Fe ranging from about 0·07 to 0·15 in most MORB and komatiite occurrences reviewed below. Only when both FeO and Fe2O3 are evaluated in a lava suite of interest can we make a comparison with our forward models where iron has been calculated strictly as FeO from the exchange coefficient KDOl/LFeO/MgO. Failure to do so can result in substantial errors. For example, in the case where MgO = 20·0%, FeOT = 10·0% and Fe3+/Fe = 0·10, it can be determined that Fe2O3 = 1·11% and FeO = 9·0%. Inspection of Fig. 4 reveals that use of 10% FeOT instead of 9·0% FeO would yield a pressure for an equilibrium primary magma that is about 2 GPa too high.
For Kilauea and Baffin Island lavas we use FeO and Fe2O3 that have been directly measured by wet chemistry (Fe3+/Fe = 0·1; Wright et al., 1975; Robillard et al., 1992). In all cases we treat lavas that move from the melting regime to the surface as a system that is closed to oxygen, and assume no change in Fe3+/Fe for both primary and derivative lavas. A small but additional source of uncertainty is that we compare lavas for which both FeO and Fe2O3 have been constrained with forward models that contain no Fe2O3, as for fertile peridotite KR-4003 and its Fe-rich analogue. Although it is possible to include Fe2O3 in the forward model computations for olivine- and harzburgite-saturated liquids, as has been done for the depleted peridotite composition, the partition coefficients are not well constrained for assemblages containing garnet and clinopyroxene. Primary komatiite magmas are expected to contain 1–2% Fe2O3, and this will result in a modest dilution of all oxide elements in our computed forward models. For example, a primary magma with 10% FeO we calculate in a forward model would actually contain 9·8% FeO if it also had 2% Fe2O3 (10% FeO x 98/100). Our forward and inverse models should therefore be useful in situations where the amount of Fe3+/Fe > 0·1.
In cases where FeO and Fe2O3 have not been directly measured in the lavas (i.e. West Greenland and Gorgona), they have been computed from FeOtotal using the method of Kress & Carmichael (1991) and estimates of oxygen fugacity (Canil, 1999; Larsen & Pedersen, 2000). Oxygen fugacities are compared with those for the following buffers: nickel–nickel oxide (NNO) from O’Neill & Pownceby (1993), fayalite–quartz–magnetite (FQM) from O’Neill (1987), and iron–wüstite (IW) from O’Neill & Pownceby (1993). For example, Christie et al. (1986) determined Fe3+/Fe = 0·07 ± 0·03 for 78 MORB glasses. An fO2 = 2·5 log units more reducing than the NNO buffer (i.e. NNO - 2·5) would yield Fe3+/Fe = 0·07 for MORB using the method of Kress & Carmichael (1991), although different parameters in Kilinc et al. (1983) provide the same Fe3+/Fe with NNO = -2·3 (Christie et al., 1986). Data of Wright et al. (1975) on eruptions between 1968 and 1971 exhibit Fe3+/Fe = 0·10, only slightly more oxidizing than MORB (Fe3+/Fe = 0·07; Christie et al., 1986). A ratio of Fe3+/Fe = 0·10 is characteristic of an fO2 = 1·3 log units more reducing than the NNO buffer (i.e. NNO - 1·3; O’Neill & Pownceby, 1993).
Another minor difficulty with the inverse method is that addition and subtraction of olivine will yield a primary magma with Fe3+/Fe that differs somewhat from the selected lava composition because olivine accepts no Fe2O3. For example, the primary magma we calculate for Kilauea by adding olivine to sample DAS69-5-1 (Wright et al., 1975) contains 1·01–1·03% Fe2O3, whereas it should contain 1·18–1·19% Fe2O3 at NNO - 1·3 (Table 4). We have made no corrections for this effect because the error is small and overwhelmed by uncertainties in KD. Another difficulty is that we have completely ignored the effects of chromite precipitation. Our estimates for Cr2O3 in primary magmas are therefore unreliable.
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ABSTRACT
INTRODUCTION
, data of 
, data of 
