Melting Depths and Mantle Heterogeneity Beneath Hawaii and the East Pacific Rise

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 104, NO. B2, PAGES 2817–2829, FEBRUARY 10, 1999

Melting depths and mantle heterogeneity beneath Hawaii and the East Paciﬁc Rise: Constraints from Na/Ti and rare earth element ratios Keith Putirka Lawrence Livermore National Laboratory, Livermore, California.

Abstract. Mantle melting calculations are presented that place constraints on the mineralogy of the basalt source region and partial melting depths for oceanic basalts. Melting depths are obtained from pressure-sensitive mineral-melt partition coefficients for Na, Ti, Hf, and the rare earth elements (REE). Melting depths are estimated by comparing model aggregate melt compositions to natural basalts from Hawaii and the East Pacific Rise (EPR). Variations in melting depths in a peridotite mantle are sufficient to yield observed differences in Na/Ti, Lu/Hf, and Sm/Yb between Hawaii and the EPR. Initial melting depths of 95–120 km are calculated for EPR basalts, while melting depths of 200–400 km are calculated for Hawaii, indicating a mantle that is 300ЊC hotter at Hawaii. Some isotope ratios at Hawaii are correlated with Na/Ti, indicating vertical stratification to isotopic heterogeneity in the mantle; similar comparisons involving EPR lavas support a layered mantle model. Abundances of Na, Ti, and REE indicate that garnet pyroxenite and eclogite are unlikely source components at Hawaii and may be unnecessary at the EPR. The result that some geochemical features of oceanic lavas appear to require only minor variations in mantle mineral proportions (2% or less) may have important implications regarding the efficiency of mantle mixing. Heterogeneity required by isotopic studies might be accompanied by only subtle differences in bulk composition, and material that is recycled at subduction zones might not persist as mineralogically distinct mantle components.

1. Introduction sensitive to both P and mineralogy. Partition coefficients for these elements have also recently been calibrated to high P and Fundamental questions in the Earth sciences concern the T [Putirka, 1998a, b; Salters, 1996], making these elements mineralogy of the basalt source region and the temperatures particularly useful for examining mineralogic heterogeneity and depths at which basalts form. It has been proposed that and potential P-dependent geochemical variations. isotopic and other compositional differences between basalts The nature and degree of heterogeneity impact upon issues reflect mineralogical heterogeneity [Langmuir et al., 1977; Hof- of mantle composition and the efficiency of mantle mixing mann and White, 1982; Zindler et al., 1984; Allegre and Turcotte, [Hofmann et al., 1986; Kellogg, 1992; Farber et al., 1994], as well 1986] (and more recently, Hirschmann and Stolper [1996] and as the thermal structure of the mantle. It is thus essential to Hauri [1996]). However, isotopic differences need not be ac- differentiate between heterogeneity with respect to mineral- companied by substantial differences in mineralogy (compare ogy, isotope ratios, or differences in major or minor element whole rocks and mineral separates from Okano and Tatsumoto composition. To examine issues of heterogeneity and the con- [1996] and Xu et al. [1998]). Moreover, variations in the pres- ditions of partial melting, alkalic and tholeiitic basalts from sures (P) and temperatures (T) of partial melting have a Hawaii and tholeiites from the EPR are compared. Hawaii is significant impact on basalt composition [Klein and Langmuir, the type example for a mantle plume, while EPR basalts are 1987; Kinzler and Grove, 1992b; Kinzler, 1997]. The nature and representative of mid-ocean ridges [Langmuir, 1988]. As Ha- degree of mantle heterogeneity cannot be fully ascertained waii represents a mantle hot spot [Wilson, 1963; Morgan, 1972; until such effects are evaluated. To investigate the potential Sleep et al., 1988], melting depths should be deep compared to effects of P and T on melt composition, melting models are the EPR, where melting occurs in response to passive up- developed here, and the results are compared to tholeiites welling [Oxburgh and Turcotte, 1968; Cawthorn, 1975; Ahern from the East Pacific Rise (EPR) and tholeiitic and alkalic and Turcotte, 1979; Spiegelman, 1996]. The Hawaiian island lavas from Hawaii. The models test whether some of the geo- chain is also underlain by thick lithosphere (70–100 km [Bock, chemical variations at these localities can be explained by dif- 1991; Woods and Okal, 1996]). Faced with such geologic differences in the P-T conditions of melting. These calculations ferences, we might ask: Can differences in mantle temperature or lithosphere thickness explain some of the geochemical dif- also constrain minimum degrees of source region heterogene- ferences between Hawaii and the EPR? This question is ad- ity. The models use Na, Ti, Hf, and rare earth element (REE) dressed by comparing natural basalts to calculated melt com- abundance’s since their mineral/melt partition coefficients are positions derived from a homogenous depleted peridotite Copyright 1999 by the American Geophysical Union. source (see the appendix and Table 1). While the mantle is Paper number 1998JB900048. known to be heterogeneous, such calculations constrain heter- 0148-0227/99/1998JB900048$09.00 ogeneity. Geochemical variations that are unexplained by such 2817 2818 PUTIRKA: MELTING DEPTHS AND MANTLE HETEROGENEITY

Table 1. Model Compositions tholeiitic rocks are examined (Figure 1). The melting models test whether P-T conditions during melting can explain such Major Oxides Value Mineral Modes Value variations.

SiO2 46.316 olivine 0.60 TiO2 0.174 orthopyroxene 0.09 2. Geochemical Data and Corrections Al2O3 3.935 clinopyroxene 0.17 To examine geochemical variation due to mantle melting, it FeO 7.653 garnet 0.14 MgO 38.44 is essential to minimize the effects of shallow level fraction- CaO 3.192 ation. As a test for shallow level fractionation, Na/Ti and Na2O 0.281 Sm/Yb ratios are compared to MgO (Figure 2). For basaltic rocks, MgO is a useful indicator of fractionation, since olivine is normally crystallized at shallow depths. While some scatter exists, Na/Ti and Sm/Yb ratios are independent of MgO for models provide minimum estimates on source region differences. To test for mineralogic heterogeneity, melting models using eclogite and various garnet pyroxenite starting compositions are also developed. Basalts from Hawaii and the EPR exhibit notable geochemical differences. Both tholeiites and mildly alkalic Hawaiian basalts have lower Na/Ti ratios, due to higher Ti and lower Na (Figure 1). Lower melt fractions at Hawaii could account for increased Ti but not for Na if Na is also incompatible. This conundrum might be explained if mineral-melt partition coef- ﬁcients for Na increase with increased P [Frey et al., 1994; Kinzler, 1997]. Hawaiian basalts also exhibit high Sm/Yb and low Lu/Hf ratios compared to EPR lavas [Salters, 1996; Salters and Hart, 1991, 1989], and greater melting depths at Hawaii have been invoked to explain such differences [Salters, 1996]. Finally, there exist signiﬁcant intershield variations in Na/Ti at Hawaii; these intershield differences hold whether alkalic or

Figure 2. (a) Na/Ti cation fraction ratios are compared to MgO (weight percent) for EPR and Hawaiian basalts. Note Figure 1. Weight percent Na2O and TiO2 are compared for that alkalic and tholeiitic lavas from Loihi and Mauna Kea tholeiites from the East Pacific Rise (EPR) and from several feature similar Na/Ti ratios and are distinct compared to Hawaiian volcanoes. The Mauna Kea and Loihi groups also Koolau, Mauna Loa or EPR tholeiites. At Hawaii, Na/Ti ratios include alkalic lavas. Most Hawaiian basalts have lower Na/Ti are insensitive to MgO content. Na/Ti ratios at Hawaii are thus due to both lower Na and higher Ti contents. Basalts from the unlikely affected by low-pressure fractionation and should re- Koolau shield have intermediate Na/Ti ratios. Data are for flect source composition and melting conditions. In contrast, Loihi from Garcia et al. [1993, 1995]; Mauna Kea from Frey et EPR basalts are affected by low-pressure fractionation. Only al. [1991], Yang et al. [1996], Rhodes [1996], and Rhodes and EPR basalts with Ͼ8 wt % MgO were used to constrain EPR Hart [1995]; Mauna Loa from Rhodes [1988], Yang et al. [1996], melting depths; Na/Ti ratios for such EPR basalts are higher and Rhodes [1996]; Kilauea from Garcia et al. [1992] and Chen than at Hawaii. (b) The concentration ratio Sm/Yb is com- et al. [1996]; and Koolau from Frey et al. [1994]. East Pacific pared to wt % MgO for the same samples as in Figure 2a. Rise basalt compositions are from Langmuir [1988] (see also Sm/Yb ratios are independent of MgO content and should thus Langmuir et al. [1986]). reflect melting conditions and mantle composition. PUTIRKA: MELTING DEPTHS AND MANTLE HETEROGENEITY 2819

Hawaiian tholeiites and alkalic lavas and thus unaffected by Crough, 1978; Liu and Chase, 1989]. However, heat flow [Von- shallow level processing (Figure 2). Since accumulation or Herzen et al., 1989] and seismic studies [Woods and Okal, 1996] fractionation of olivine does not affect Na/Ti or Sm/Yb ratios, are inconsistent with such thinning, and an average lithosphere Hawaiian basalts with 7–13 wt % MgO are examined. An thickness of 100 km is indicated [Woods and Okal, 1996]. interesting interisland difference is apparent (Figure 2a): ba- Lithosphere thickness, though, is unlikely to be constant along salts from Mauna Kea, Loihi, and Kilauea have Na/Ti ϭ 2–2.5, the Hawaiian chain and may influence magma production while basalts from Mauna Loa are somewhat higher at 2.5–3.0, [Morgan et al., 1995; Wessel, 1993]. Since estimates of 75–80 km and Koolau basalts are higher still with Na/Ti, ranging from 3 lithosphere have been obtained at Oahu [Bock, 1991], a 75–120 to 4. km range was explored. In contrast to Hawaiian lavas, EPR basalts display Na/Ti When thick lithosphere is present, Na/Ti and Sm/Yb ratios ratios that decrease sharply with decreasing MgO (Figure 2a); decrease as initial melting depth (or Tp) increases (Figure 3). this probably reflects plagioclase fractionation. Ratios of Na/Ti ratios are higher beneath thin lithosphere and decrease Sm/Yb do not vary with MgO (Figure 2b) and are thus appar- as initial melting depth increases (Figure 3a). Na/Ti ratios cpx/melt ently unaffected by such fractionation. Experimental studies decrease with increased melting depth because the KNa ϭ cpx melt indicate that plagioclase saturation for mid-ocean ridge basalts (Na partition coefficient for clinopyroxene/melt, CNa /CNa , i (MORB) occurs near 8–10 wt % MgO [Tormey et al., 1987; where CNa is the concentration of Na in the superscripted Grove and Bryan, 1983]. The highest Na/Ti ratios (Figure 2a) phase) increases with increased P, while clinopyroxene and min/melt may thus approach primitive values. To minimize the effects of garnet KTi remain constant or decrease [Langmuir et al., fractionation on Na/Ti, only basalts with Ͼ8 wt % MgO will be 1992; Blundy et al., 1995; Kinzler, 1997; Walter, 1998; Putirka, compared to model values for constraining partial melting 1998a, b]. Most importantly, without the P-induced change in cpx/melt depths. Na/Ti ratios for such EPR basalts (4–5) are signifi- KNa , Ti and Na are not significantly fractionated from one cantly higher, and Sm/Yb ratios are lower, compared to Ha- another, and aggregate melt Na/Ti ratios are nearly invariant. waiian tholeiites and alkalic lavas. Low Na/Ti ratios thus indicate a contribution from melts produced at substantial depth. The decrease in Sm/Yb beneath thick lithosphere is due to 3. Results the progressive removal of garnet from the residue during The melting model of this study follows the work of Lang- partial melting. When melting begins, the amount of garnet is sol/melt garnet/melt muir et al. [1992] (see the appendix) and examines the compo- highest, and so is DYb , (since KYb is high). As melt- sitions of aggregate melts, i.e., melts that are pooled from a ing progresses, though, garnet is removed from the residue, sol/melt range of depths within a melting column. Thus each choice for and DYb decreases. By increasing initial melting depths mantle potential temperature (Tp) corresponds to a unique (i.e., increasing mean and maximum F) the amount of garnet initial depth of partial melting, and the choice of lithosphere in the total melting column is decreased, as is the average sol/melt thickness corresponds to a final depth of melting. In addition, DYb in the melting column. Aggregate melts at the surface sol/melt for a particular starting composition, when lithosphere thick- reflect this average DYb . When lithosphere thickness ex- ness and Tp are specified, there exists a unique maximum and ceeds 75 km, all melting occurs in the garnet stability field mean extent of partial melting, or F (melt fraction). Since only [Takahashi et al., 1993; Longhi, 1995; Kinzler, 1997; Walter, two variables (Tp, initial melting depth, lithosphere thickness, 1998], and the progressive consumption of garnet dominates and mean F) need be specified for a given source composition, the Sm/Yb signal. For both Na/Ti and Sm/Yb the aggregate the following discussion will refer to differences in initial melt- melt curves flatten with depth because melt productivity is ing depths and lithosphere thickness; differences in mean F reduced at increased P [Putirka, 1997]. The Na/Ti curves ex- and Tp are implied. hibit less flattening with depth, compared to Sm/Yb, because cpx/melt Initial melting depths and lithosphere thickness both signif- KNa increases steadily with depth throughout the melting sol/melt icantly affect Na/Ti and Sm/Yb ratios in aggregate melts. This column. In contrast, DYb , which depends upon the modal is true for both peridotite and eclogite or garnet pyroxenite abundance of garnet, does not vary greatly due to the small mantle sources. In general, partial melting of a garnet pyrox- amount of partial melt that is produced (and hence the small enite leads to aggregate melts that have higher Na/Ti and amount of garnet that is consumed) at high P. Sm/Yb ratios, compared to aggregate melts from a peridotite In the case of thin lithosphere, changes in Sm/Yb ratios are source. High Na/Ti for garnet pyroxenite partial melts result, in less dramatic (Figure 3b) because melts produced deep in the part, from higher Na/Ti in the source (5, compared to 4 for column (in the presence of garnet) are overwhelmed by the peridotite). More significant, though, is the greater amount of comparatively large amounts of melt produced at shallow garnet in the garnet pyroxenite (see the appendix), which in- depths (Ͻ75 km). With 10 km lithosphere, Sm/Yb first decreases the garnet pyroxenite bulk mineral/melt distribution creases then exhibits a rapid increase once the garnet stability ϭ sol/melt ϭ sol melt sol coefficient for Ti ( DTi CTi /CTi , where CTi is the field is entered (75 km). The initial decrease in Sm/Yb, be- melt concentration of Ti in the total solid and CTi is the concen- tween initial melting depths of 50 and 75 km, is due to varia- sol/melt Ͼ sol/melt tration of Ti in the melt). High Sm/Yb ratios similarly reflect tions in mean F. At these depths DYb DSm ;inthe Ͻ the high modal proportion of garnet, which results in an in- absence of garnet ( 75 km), though, these DREE are very sol/melt creased DYb . For both peridotite and pyroxenite starting small, and Sm and Yb are only fractionated from one another compositions, Na/Ti ratios decrease and Sm/Yb ratios increase when F is very low. As melting depths increase from 75 to 50 in aggregate melts, as lithosphere thickness increases. km, both maximum and mean F increase, and Sm/Yb ratios Mid-ocean ridge basalts were modeled using a 10-km litho- approach initial (unfractionated) values. Sm/Yb ratios for ag- sphere; at Hawaii, lithosphere thickness’ are less certain. For gregate melts increase sharply when initial melting depths gar/liq example, convective thinning is presumed to reduce an initially reach the garnet stability field (75 km), since KYb is very 90–100 km thick lithosphere to 50 km or less [Detrick and high. Sm/Yb ratios are also sensitive to melting stoichiometry 2820 PUTIRKA: MELTING DEPTHS AND MANTLE HETEROGENEITY

(Figure 3c). As an illustration, peridotite 1 (melting coefficient for garnet is 0.2) is compared to peridotite 2 (coefficient is 1.0). These values range beyond observed values (0.7 [Walter, 1998]), but Figure 3c shows the magnitude by which melting stoichiometry might influence Sm/Yb systematics at depth.

4. Discussion Variations in the P-T conditions of melting alone might account for substantial geochemical variations in natural basalts (Figures 3–5). Such variations encompass the large-scale differences between the EPR and Hawaii, as well as some intershield variation at the Hawaiian islands. In particular, the present model supports the Frey et al. [1994] and Kinzler [1997] hypotheses regarding the importance of melting depth for rec-

onciling variations in Na2O and TiO2 in oceanic basalts. These results do not imply that the mantle is homogenous; heterogeneity appears to be required at both Hawaii and the EPR [Langmuir and Hanson, 1980; Roden et al., 1994; Prinzhofer et al., 1989; Hekinian et al., 1989; Reynolds et al., 1992]. However, such heterogeneity might not encompass all major oxides, let alone involve major differences in source region mineralogy. Since the P-T conditions of melting can account for signiﬁcant major and minor element systematics, source region differences may be limited.

4.1. Estimates of Melting Depths and Temperatures At the EPR, initial melting depths of 120 Ϯ 15 km reproduce the approximate concentrations of Na, Ti, Sm, and Yb (Figure 4). These depths overlap with depth estimates implied by Salt- ers [1996, Figure 2] and are consistent with depths of low- velocity and electromagnetic anomalies at mid-ocean ridges [MELT Seismic Team, 1998; Zhang and Tanimoto, 1993; Anderson et al., 1992]. Mantle temperature estimates are sensitive to the temperature of the mantle solidus and are much less robust than melting depth estimates (see the appendix). If the mantle has a composition similar to KLB-1, a melting Њ depth of 110 km suggests a Tp of 1831 K (1558 C). While mantle temperatures are not well constrained from geophysical

studies [Parsons and Sclater, 1977; Stein and Stein, 1992], Tp inferred using a KLB-1 composition overlaps with mantle temperatures of 1723 Ϯ 250 K (at 95 km depth), obtained from global studies of heat flow and ocean bathymetry [Stein and Stein, 1992]. It cannot be overemphasized, though, that temperature estimates are only as reliable as our knowledge of mantle composition and solidus temperatures. Experimental studies show a range of melting temperatures for different peridotite compositions [Hirose and Kushiro, 1993]; actual temperatures could be lower by as much as 50 K, or more, if the mantle is more fertile than KLB-1. Much greater initial melting depths are implied for Hawai- Figure 3. (a) Na/Ti ratios (cation fraction) of aggregate ian tholeiite and alkalic lavas. Abundances of Na, Ti, Hf, and melts produced from peridotite and garnet pyroxenite sources REE can be produced using the same depleted mantle com- are compared at different P-T conditions. Lithosphere thick- position as that for the EPR but with increased lithosphere ness indicates depth to the top of the melting column; “initial thickness and initial melting depths of 200–400 km. An unde- melting depth” represents depth to the base of the melting pleted mantle source would yield higher initial Na/Ti ratios column and hence also reflects mantle potential temperature. (Figure 5); to achieve the low Na/Ti ratios of Hawaii for an (b) Sm/Yb ratios for aggregate melt compositions are com- undepleted source, increased initial melting depths (by ϳ50– pared, and (c) a close-up view of the 10-km lithosphere calcu- 100 km) would be required. lations is given. In Figure 3c the “peridotite 1” model uses a garnet melting coefficient of 0.2; the “peridotite 2” model uses Estimates of melting depths at Hawaii exceed those ob- a garnet melting coefficient of 1. For a given lithosphere thick- tained by Watson and McKenzie [1991]. There are numerous ness a garnet pyroxenite source yields higher Na/Ti and Sm/Yb reasons for these differences. First, it should be noted that the ratios compared to a peridotite source. Watson and McKenzie [1991] model does not successfully re- PUTIRKA: MELTING DEPTHS AND MANTLE HETEROGENEITY 2821

in a melt productivity that is too high. High melt productivity results in (1) elevated estimates of mean F and (2) lower incompatible element concentrations for a given initial depth of melting. The present model, with greater initial melting ⌬ ϳ depths and a more realistic Sf ( 420 J/kg), successfully yields Na, Ti, and REE concentrations for Hawaiian and EPR lavas (Figure 4). Since garnet is gradually consumed during melting, a garnet- free residue is produced at the top of the melting column at Hawaii. If the melting coefﬁcient for clinopyroxene is Ͼ0.5, then clinopyroxene is also consumed by depths of 100 km, leaving a harzburgite residue at shallow depths. This predicted residue might resolve the apparent conﬂict that high-MgO Kilauea tholeiites are harzburgite saturated at pressures Ͻ3.5 GPa [Eggins, 1992], yet show a garnet trace-element signature [Budahn and Schmitt, 1985; see also Frey et al., 1994]. Using the Њ solidus of KLB-1, a Tp of 2130 K (1857 C), is implied to achieve melting at 300 km. Such temperatures represent a mantle that is approximately 300 K hotter at Hawaii compared to the EPR, which is consistent with temperature differences inferred from tomographic [Romanowicz, 1994; Anderson et al., 1992] and geodynamic studies [Sleep, 1990; Ribe and Chris- tensen, 1994]. Calculated melting depths are also consistent with depths for low seismic velocities and high seismic wave attenuation [Bhattacharyya et al., 1996; Romanowicz, 1995; Zhang and Tanimoto, 1993]. The temperature difference between Hawaii and the EPR is probably more robust compared to absolute temperature estimates at Hawaii, which are subject to the same uncertainties as noted above for the EPR.

4.2. Mantle Heterogeneity The degree and nature of heterogeneity in the basalt source region can be constrained when the potential P-T effects on partial melt compositions are evaluated. Geochemical variations that are unexplained by a homogenous peridotite mantle model provide minimum estimates on source region differ- Figure 4. (a) Natural and model Sm concentrations (ppm) and Sm/Yb ratios are compared. (b) Calculated and observed ences. In some cases, such as at Hawaii, differences in P-T concentrations for Na and Ti are compared. Hawaiian basalts conditions are probably not sufficient to explain all geochemi- were modeled using a 100-km-thick lithosphere and an initial cal variations, and minimum differences in modal mineralogy melting depth of 300 km; EPR basalts were modeled using a for source regions are calculated. In addition to peridotite, 10-km lithosphere and an initial melting depth of 115 km; eclogite and various garnet pyroxenite starting compositions these model calculations are indicated with the letters H (Ha- are also examined to resolve whether such sources are consis- waii) and E (EPR) (circled). Observed abundance’s of Na, Ti, tent with observed geochemical signals. and some REE can be reproduced by varying the P-T melting 4.2.1. Heterogeneity beneath the EPR. Hirschmann and conditions of a mantle that has a depleted pyrolite bulk com- Stolper [1996] have proposed that garnet pyroxenite exists in position and a peridotite mineralogy. the MORB source region. Their argument was in part based upon the apparent discrepancy between the deep levels of melting required to produce the garnet signature in MORB produce Na2O and TiO2 contents at Hawaii. Their predicted and the relatively thin crust that is formed at oceanic spreading Na/Ti ratios [Watson and McKenzie, 1991, Table 2] are much centers. As noted by Putirka [1997], though, fractional melting too high, indicating that their melting depth estimates (parti- processes limit melt productivity and may be invoked to satisfy tion coefficients for Na) are too low. Watson and McKenzie both observed crustal thickness [White et al., 1992] and inferred [1991] also use a final melting depth of 82 km and assume that melting depths of Ͼ100 km [Salters, 1996]. Regarding geo- spinel peridotite is stable to depths apparently exceeding 100 chemical variation, Na/Ti and Sm/Yb ratios at the EPR are km. The lithosphere beneath some parts of Hawaii is conceiv- consistent with partial melting of a peridotite source. Some ably as thin as proposed by Watson and McKenzie [1991], but mixing with a garnet pyroxenite source is allowed, since the spinel peridotite is probably not stable, even at depths as shal- EPR samples plot between the peridotite and garnet pyroxen- low as 82 km [Takahashi et al., 1993; Longhi, 1995; Kinzler, ite curves (Figure 5b). However, only the major oxides carry 1997; Walter, 1998]. Using a more realistic garnet lherzolite any significant leverage on mineral abundances. It is possible mineralogy, such shallow melting depths yield Sm/Yb ratios that the observed geochemical differences, at least with respect that are too high compared to observed values (Figure 5). to Na and Ti, might be supported by minor mineralogic vari- ⌬ Finally, the entropy of fusion ( Sf) used by Watson and ations within a source that has an overall peridotite mineral- McKenzie [1991] is too low, perhaps by a factor of 2, resulting ogy. For example, a variation of Ϯ0.2 wt % Na in the EPR 2822 PUTIRKA: MELTING DEPTHS AND MANTLE HETEROGENEITY

source region could explain observed ranges of Na/Ti ratios in the high MgO EPR lavas; such differences can be accommodated by very small (Ͻ2%; see below) changes in peridotite mineral abundances. As recognized by Hirschmann and Stolper [1996], partial melts from neither garnet pyroxenite nor peridotite sources exhibit sufﬁcient variation to explain the full range of MORB Lu/Hf and Sm/Nd ratios. If the lithosphere thickness is increased to 30–50 km, peridotite partial melts can reproduce the low Lu/Hf and Sm/Nd of the MORB array (Figure 5c). Thicker lithosphere may not be surprising at such localities as the Atlantic-Antarctic Discordance (AAD), since cooler mantle temperatures are indicated from comparisons of mid-ocean ridge bathymetry and geochemistry [Klein and Langmuir, 1987; Langmuir et al., 1992; Salters, 1996]. Neither the garnet pyroxenite nor the peridotite models, though, are capable of repro- ducing the high Lu/Hf and Sm/Nd ratios observed at Kol- beinsy. In contrast, Salters’ [1996] peridotite melting model appears to account for all but the Kolbeinsy data by taking into account variations in the timing of source region depletion. 4.2.2. Heterogeneity beneath Hawaii. At Hawaii, eclogite has been hypothesized to exist in the source region, with eclogite partial melts contributing most greatly (up to 20%) to some Koolau basalts [Hauri, 1996]. Hauri’s [1996] hypothesis stems, in part, from the observation that Hawaiian lavas are

enriched in SiO2 compared to partial melts obtained from experimental studies of lherzolites. However, several isotope and trace element studies suggest that a recycled source at Koolau might be minimal [Roden et al., 1994; Bennett et al.,

1996]. Furthermore, Frey et al. [1994] interpret interisland SiO2 systematics as indicating depth of melting differences, rather than source region heterogeneity. Wagner and Grove [1998]

have also shown that basalts can obtain elevated SiO2 if orthopyroxene is assimilated at shallow depths. (Note: orthopyroxene assimilation does not affect Na/Ti or Sm/Yb. Using data from Wagner and Grove [1998], assimilation of 20% or-

Figure 5. (opposite) (a) Aggregate melt compositions are from a depleted peridotite source. High Na/Ti (cation fraction) at Koolau may be explained by the presence of thinner lithosphere and cooler mantle temperatures. Intravolcano variation probably reflects heterogeneity. Peridotite models use a depleted mantle composition (see the appendix and Table 1); “bulk composition uncertainty” reflects the increase in Na/Ti and Sm/Yb ratios that are obtained when an undepleted mantle source is input into the melting models (see the appendix). (b) Calculated aggregate melts are shown for eclogite and garnet pyroxenite sources (“HS” is the average garnet pyroxenite from Hirschmann and Stolper [1996]; “massif” refers to garnet pyroxenites from massif peridotites; see the appendix; K is the Koolau and ML is the Mauna Loa ϩ Mauna Kea ϩ Loihi fields, as in Figure 5a). Na/Ti and Sm/Yb ratios at Hawaii overlap only with some massif pyroxenites, but the predicted Na, Ti and REE abundances are too high compared to lava compositions (see text). (c) Lu/Hf and Sm/Nd from MORB [Salters, 1996] are compared to Hawaiian compositions (AAD, Atlantic-Antarctic Discordance). Initial melting depths for the 10-km lithosphere peridotite and garnet pyroxenite models range from 50 to 400 km, moving downward in the figure. Hawaiian data are adequately described with a 100-km lithosphere and initial melting depths of 200–400 km (increasing upward in the figure). Lu/Hf and Sm/Nd for other MORBs span a range of values that cannot be covered by varying the initial melting depths for eclogite or peridotite partial melting. PUTIRKA: MELTING DEPTHS AND MANTLE HETEROGENEITY 2823 thopyroxene decreases Na/Ti and Sm/Yb ratios by .015 and .05 compared to Hawaiian tholeiites and alkalic lavas (Figure 5). respectively). Finally, Okano and Tatsumoto [1996] observe Partial melts from some massif garnet pyroxenites exhibit that Hawaiian spinel lherzolite xenoliths exhibit a wide range Na/Ti and Sm/Yb ratios that overlap with some Hawaiian tho- of isotope ratios, with some isotopes approaching Koolau-like leiite and alkalic basalts. However, Na, Ti, Hf, and REE abun- values. This observation shows that a wide range of isotope dances from such sources are much higher than observed at ratios can be supported by a lherzolite mineralogy and that Hawaii. Partial melts from pyroxenite sources yield Na abun- isotope variations at Hawaii might not require an eclogite dances between 0.08–0.20 cation fraction, and Sm abun- source. It is thus unclear that eclogite is a necessary source dance’s of 6.2–12.5 ppm (compare to Figure 4) and are highest component at Hawaii. for massif pyroxenites. Minor element abundances might be Most of the interisland variation in Na/Ti and Sm/Yb at diluted if mixed with melts from a peridotite source. However, Hawaii can be accounted for by plausible ranges in the P-T to account for Na/Ti ratios at Koolau, massif pyroxenite partial conditions of melting for a peridotite mantle (Figure 5a). For melts would appear to dominate the Koolau aggregate melts example, Na/Ti-Sm/Yb partial melting arrays overlap the (up to 100%; Figure 5b). In addition, massif pyroxenites ex- Koolau field as lithosphere thickness decreases to 75 km, and hibit a wide range of garnet/pyroxene ratios; only when garnet initial melting depths decrease to 170 km. Owing to differences is Ͻ20% are Sm/Yb ratios in the correct range. Finally, the thin in initial melting depth (and Tp), different values for mean F lithosphere and cooler melting temperatures required in the are also obtained for the Hawaiian tholeiites (Figure 5a). For peridotite model (above) for Koolau are not avoided by as- comparison, estimates of F at Loihi are similar to, but slightly suming a pyroxenite source. Thus, in contrast to the peridotite higher than, those obtained by Garcia et al. [1995] and are model, pyroxenite and eclogite sources provide poor fits to Na, within the very wide range of values noted by Feigenson et al. Ti, and REE abundances at Hawaii. It would therefore appear [1996] for Mauna Kea. As noted above, though, differences in that such sources at Hawaii are not only unnecessary but per- melting depth (in the absence of heterogeneity) are required to haps also unlikely. fractionate Na from Ti; initial melting depth, rather than F,is As is evident from Figure 5, variations in lithosphere thick- the critical variable for explaining the range of Na/Ti ratios at ness may be invoked to explain interisland variations at Ha- Hawaii. waii. On the other hand, if the hypothesized lithosphere vari- Undoubtedly, some intraisland variation is due to heteroge- ations are incorrect, only small changes in the source region neity, especially since some Hawaiian lavas plot outside of the mineralogy are required based on Na and Ti abundances. Mass partial melting grid (Figure 5). Limited variations in melting balance calculations using a mantle peridotite and high- depths and lithosphere thickness at Hawaii, though, are at least pressure mineral compositions [Walter, 1998; Putirka, 1998a, b] plausible. Melting depths might vary depending upon the po- underscore this conclusion. For example, if the difference be- sition of the shield volcano and the plume axis [Farnetani and tween the lowest and highest Na2O values at Koolau and Richards, 1995], especially if shield positions are influenced by Kilauea (about 1 wt %; Figure 1) are due only to heterogeneity the state of stress in the lithosphere [Jackson and Shaw, 1975]. in the source region, mass balance implies that this difference Relative maximum melting depths for Koolau, Kilauea, Mauna can be accommodated by a source region difference in clinopy- Loa, and Loihi are qualitatively consistent with melting depths roxene ϩ garnet of Ͻ2.0% (assuming mean F is 0.15, mean min/melt inferred from major oxide systematics [Frey et al., 1994]; the DNa is 0.06, and minerals have constant composition). model is furthermore consistent with trace element and isoto- Such source differences are reduced if any Na2O variation pic observations [Bennett et al., 1996; Roden et al., 1994] that results from the P-T conditions of melting, assimilation in the indicate a peridotite source for Hawaiian lavas. Moreover, shallow mantle, adjustments in mineral composition in the Koolau lies north of the Molokai fracture zone [Mammerickx, source region, or shallow level fractional crystallization. It 1989; Atwater, 1989], and seismic work [Bock, 1991] at Oahu should be noted that while these calculations are based only on indicates a 75–80 km lithosphere in this region. Na2O, this oxide carries more leverage on calculated mineral If the Koolau lithosphere approaches 100 km, the mantle proportions compared to other major oxides. This is because source at Koolau must differ from that beneath Loihi and Na occurs only in clinopyroxene to any great extent, and even Mauna Kea. Additionally, since lithosphere thickness probably at high pressure it is never the dominant component in this does not vary greatly at any single volcano, intraisland heter- phase. Large changes in source Na2O concentrations therefore ogeneity is also implied by the range of Na/Ti ratios displayed translate into large changes in clinopyroxene modal abun- at each of the Hawaiian shields (Figure 5a). The lowest Na/Ti dances. Na2O is thus an ideal oxide for determining whether a ratios at Mauna Kea are also not explained by the present mantle source is comprised of peridotite or pyroxenite. While model. These low Na/Ti ratios can only be explained if (1) the an analysis of other elements, especially Ca or Al, might also Ͼ top of the melting column exceeds 150 km depth or (2) the be useful (given suitable high-pressure calibrations of Kd), it is mantle source has higher clinopyroxene (by 2%) and lower tentatively concluded that small modal variations in a perido- garnet (by 2%) compared to the mineralogy of Table 1. Option tite assemblage of minerals can probably accommodate ob- 2 seems more likely, but lower garnet results in lower Sm/Yb served geochemical variations at Hawaii. ratios, perhaps indicating REE heterogeneity. Mantle heterogeneity is a flexible hypothesis and cannot be While peridotite partial melting may explain interisland vari- excluded. If eclogite is not required to describe geochemical ation at Hawaii, can garnet pyroxenite or eclogite sources also variations in oceanic lavas, though, there are important impli- yield observed Na, Ti, and REE abundances at Koolau? To cations for mixing in Earth’s mantle. It seems likely that small illustrate the potential range of such sources, several starting amounts of recycled material contribute to the trace element compositions were explored, including eclogite, and garnet and isotopic signature of some oceanic lavas [Hofmann and pyroxenites from various sources (see the appendix). As is White, 1982; Zindler et al., 1984; Hauri et al., 1996]. Such ma- evident from Figure 5b, most pyroxenites and eclogites are terial, though, might not survive the recycling process as a unsuitable as source components, since Sm/Yb ratios are high distinct mineralogical component. Mantle mixing might be ef- 2824 PUTIRKA: MELTING DEPTHS AND MANTLE HETEROGENEITY

Figure 6. Hawaiian shield averages for isotopes and major oxides [Hauri, 1996] are compared to test for depth-dependent isotopic heterogeneity at Hawaii. Na/Ti ratios are correlated with (a) 87Sr/86Sr, (b) 206Pb/ 204Pb, and (c) 187Os/188Os. (Note that Hauri [1996] gives two averages for Loihi: one for alkalics and one for tholeiites; both are plotted. R2 values are for Hauri’s [1996] shield averages.) The Loa trend volcanoes are consistent with two-component mixing between an upper isotopically enriched mantle component and a deeper more isotopically depleted/less enriched source. Kea trend volcanoes are not consistent with two- component mixing and may indicate a third component [Chen, 1987]. Interestingly, Loihi lavas [Garcia et al., 1995; Lanphere, 1983; Frey and Clague, 1983] and Mauna Loa lavas [Rhodes and Hart, 1995] show local internal correlations for 87Sr/86Sr-Na/Ti that are opposite to the intershield trend but directed toward MORB (Figure 7).

ficient at erasing such heterogeneity, or perhaps the melting (Figure 7) indicate a large-scale vertical component to isotopic process is itself a homogenizing agent. heterogeneity in the Pacific upper mantle. The Hawaii-EPR comparison supports the conventional layered mantle model, 4.3. Spatial Variability of Isotope Sources or perhaps a “marble cake” mantle with a systematic depth To test for depth distributions of isotopic heterogeneity in distribution of isotopically distinct blobs. the Hawaiian mantle, compositional averages for the Hawaiian shields [Hauri, 1996] were examined. Such shield averages yield good correlation’s between Na/Ti and some isotope ratios 5. Summary (Figure 6). Since, as noted above, Na can only be fractionated A mantle melting model was developed to estimate partial from Ti at depth, it appears that melts produced at depth (low melting depths for oceanic lavas and to constrain mantle het- Na/Ti ratios) tap mantle sources that are isotopically distinct erogeneity, using Na/Ti and REE ratios. Na/Ti ratios are par- from melts produced at more shallow levels of the mantle ticularly useful since Na and Ti are only strongly fractionated (higher Na/Ti). The ordering of the Loa trend volcanoes is the from one another at high P. Hafnium and the REE’s are also same in each plot in Figure 6 and is thus consistent with mixing useful since their mineral/melt partition coefficients are sensi- between two, vertically stratified, mantle sources. This order- tive to pressure and mineralogy [Salters, 1996; Kinzler, 1997; ing for the Loa trend holds, even for the more poorly corre- Walter, 1998; Putirka, 1998a, b]. Several important results are lated Sr isotope ratios (Figure 6), and supports prior argu- obtained from the models. First, the P-T conditions of melting ments for two-component mixing at Hawaii [Bennett et al., alone appear to be capable of explaining both local variation at 1996; Chen, 1987; Chen and Frey, 1985]. It is also possible, Hawaii, as well as some large-scale geochemical differences though, that isotope ratios vary continuously but systematically between Hawaii (an ocean island) and the EPR (a mid-ocean with depth in the mantle. So far as Na/Ti ratios represent ridge spreading center). This implies that bulk compositional melting depth, Koolau lavas reflect partial melting of a shallow differences between Hawaiian and EPR source regions might and variably enriched/depleted [see Richardson et al., 1982] be minimal; this is consistent with near-uniform, but nonprimi- mantle component (Figure 7). A two-component mixing tive, minor element ratios for oceanic basalts [Hofmann et al., scheme is not consistent with Kea trend lava compositions, 1986] and high-pressure diffusion experiments which indicate which may indicate a less vertically stratified source [Staudigel efficient homogenization in parts of the upper mantle [Farber et al., 1984; Stille et al., 1983; Chen, 1987]. et al., 1994]. Mantle heterogeneity is also constrained; inferred Interestingly, Sr isotopes for individual lavas at Loihi and source region differences can be accommodated by small (2%)

Mauna Loa show a local, or internal, correlation that is oppo- variations in peridotite phase proportions. Na2O, TiO2, and site to the intershield trend (Figure 6) but directed toward REE abundances at Hawaii also appear to be inconsistent with MORB. The intershield trend would appear to indicate a lat- a variety of potential eclogite or garnet pyroxenite sources. The eral (along-strike) component as well as a vertical component mantle is undoubtedly mineralogically heterogeneous, but this to local heterogeneity at the Hawaiian islands. This might be and other work [Sims and Depaolo, 1997] reveal the need to an enriched shallow layer, perhaps at or near the base of the test models of heterogeneity against possible P-T dependent Hawaiian lithosphere, that is most strongly sampled at Koolau. variations in melt composition. In contrast, both the local trend at Hawaii and the differences Abundances of Na, Ti, Hf, and the REE for EPR lavas are between isotope and Na/Ti ratios at Hawaii and the EPR best reproduced when melting begins at 120 Ϯ 15 km, consis- PUTIRKA: MELTING DEPTHS AND MANTLE HETEROGENEITY 2825

Figure 7. Isotopes and Na/Ti ratios for Hawaiian lavas are compared to lavas from the EPR. Differences in Na/Ti between EPR and Hawaii indicate that the shallow upper mantle has experienced greater extents of long-term depletion of (a) Rb relative to Sr and (b) Nd relative to Sm. Isotopic field for EPR lavas (and neighboring seamounts) are from Zindler et al. [1984]. Note that individual Loihi and Mauna Loa lavas appear to trend toward MORB, perpendicular to the mean interisland trend. Symbols and data are as in Figure 6. tent with recent seismic work [MELT Seismic Team, 1998] and decrease with increasing depth in the mantle [Kinzler, 1997; prior depth estimates [Salters, 1996]. In contrast, Hawaiian Walter, 1998]. This appears not to be an intrinsic pressure tholeiites can be modeled using a 100-km-thick lithosphere and effect but instead results from the low Al content of near initial melting depths of 200–400 km. This implies a temper- solidus liquids at high pressure [Putirka, 1998b]. A decrease in ature difference between Hawaii and the EPR of 300ЊC, close the partition coefficient for Ti amplifies the pressure depen- to estimates inferred from geodynamic studies [Sleep, 1990; dence of Na/Ti and decreases estimates of initial melting Schilling, 1991] and mantle tomography [Romanowicz, 1994]. depths. Since the clinopyroxene-melt partition coefficients for The compositional dependencies of peridotite solidus temper- Ti observed by Kinzler [1997] and Walter [1998] are probably atures, though, need to be explored so that these depth esti- most appropriate for modeling mantle melting, they were mates may be used to better resolve the thermal structure of adopted for this study. Earth’s upper mantle. The present model also indicates that garnet is consumed during melting, while aggregate melts re- A1. Mantle Composition tain a garnet signature. This result may help to resolve the One set of mantle mineral proportions used for peridotite apparent conflict between trace element abundances, which calculations (Table 1) are from Ita and Stixrude [1992, Figure indicate garnet in the source region [Budahn and Schmitt, 4]. The Ita and Stixrude [1992] estimates were obtained as a 1985; Frey et al., 1994], and experimental studies which indicate best fit to seismic data for mineral elastic properties. Such that some primitive Kilauea basalts are not garnet saturated at mineral modes are consistent with other similar studies of P Ͻ 3.5 GPa [Eggins, 1992]. upper mantle mineralogy [Weidner and Ito, 1987] and provide a reasonable starting point for modeling an initial mantle mineralogy. Initial element concentrations for a peridotite mantle Appendix: Mantle Melting Model are from Kinzler and Grove [1992b] and Hirschmann and Stol- Oceanic basalt compositions can be successfully explained per [1996] for a depleted mantle and McDonough and Sun by polybaric partial melting models [Klein and Langmuir, 1987; [1995] for an undepleted source. Minerals compositions from Kinzler and Grove, 1992b; Langmuir et al., 1992; Kinzler, 1997]. high-pressure experimental studies [Walter, 1998; Putirka, Aggregate melt compositions were thus calculated for batch 1998a] were used to compare the major oxide [Kinzler and and fractional melting processes using the equations of Lang- Grove, 1992b] and mineral modes [Ita and Stixrude, 1992] of muir et al. [1992] and Plank and Langmuir [1992] and the Table 1. Mass balance calculations indicate overlap between mineral-melt partitioning relationships of Putirka [1998a, b] the major oxide composition and mineral proportions, but and Salters [1996]. The calculations employ a step-wise ap- these estimates are very sensitive to the mineral compositions proach [Putirka, 1997]. In this method, degrees of partial melt- selected for mass balance. Using the Kinzler and Grove [1992b] ing (F) and aggregate melt compositions are calculated at major element abundances, it is possible to obtain mineral depth increments of 2 km. The residual mineralogy is adjusted modes that have lower garnet (by 2%) and higher clinopyrox- at each step using the estimated value for F and the stoichio- ene (up to 6%) balanced by lower olivine; these mineralogys metric coefficients of the pertinent melting equilibria (see below). were also explored for modeling purposes. A model mantle Recent experimental work indicates that at near-solidus con- with slightly higher clinopyroxene and lower garnet and olivine ditions the clinopyroxene-melt partition coefficient for Ti may abundances results in lower depth estimates for Hawaiian la- 2826 PUTIRKA: MELTING DEPTHS AND MANTLE HETEROGENEITY vas. Such a mineralogy can also more easily explain the lowest peridotite solidi have not been measured with the same tem- Na/Ti ratios observed at Mauna Kea, although lower-than- perature precision (Walter [1998] and Zhang and Herzberg observed Sm/Yb ratios are also obtained. The mineralogy of [1994] account for thermal gradients in their experiments; see Table 1 appears to be the most successful mineralogy for si- Zhang and Herzberg [1994] for comparisons), and composi- multaneously explaining EPR and Hawaiian lava compositional effects on the mantle solidus cannot yet be quantified. tions. Model results are less sensitive to small changes in initial The data presented by Hirose and Kushiro [1993], though, Na/Ti ratio, and a range of depleted mantle starting composi- indicate that Tsolidus differences of up to 50 K are possible, tions are successful at explaining major element variations in depending on mantle composition. oceanic basalts. The peridotite bulk composition uncertainty (Figure 5) re- A3. Melting Stoichiometry flects the difference between depleted and undepleted sources Melting stoichiometry affects the estimation of mineral pro- when these sources are input into the melting models. The portions throughout the melting column and thus impacts average garnet pyroxenite composition is from Hirschmann sol/melt upon Di . Stoichiometric coefficients to depths of 0–75 and Stolper [1996], and their modal mineralogy is used. Eclo- km are from J. Longhi [see Salters, 1996], Longhi [1995], and gite compositions are from Griffin and Brueckner [1985], Grif- Kinzler and Grove [1992a]. These coefficients (experimentally fiths and Cornichet [1985], Miller et al. [1988], Taylor and Neal determined at P Ͻ 3.5 GPa) might not extrapolate to high P. [1989], and Beard et al. [1992]; model calculations use a garnet With increased pressure, clinopyroxene and garnet survive to fraction of 0.25. Eclogite garnet contents vary widely (0.25– greater extents of melting [Wei et al., 1990; Takahashi et al., 0.50), and higher amounts of garnet yield partial melts with 1993]. In work by Takahashi et al [1993], clinopyroxene disap- higher Sm/Yb and Na/Ti ratios (Figure 5). Garnet pyroxenites pears at 38% melting at 3 GPa, while at 7 GPa clinopyroxene from massifs are from Loubet et al. [1982], Bodineir et al. survives to Ͼ70% melting. Less clinopyroxene must be con- [1987], and Stosch and Lugmair [1990]; a garnet fraction of 0.2 sumed for each increment of melt produced at 7 GPa, and was used for model calculations. As with eclogites, pyroxenites melting coefficients should be reduced. At depths Ͼ75 km the feature a wide range of garnet fractions (0–50%), and in- models (Figures 3–5) use Walter’s [1998] coefficients, although creased garnet yields increased Sm/Yb and Na/Ti ratios for lower coefficients were explored. partial melts (Figure 5). The amount of orthopyroxene on the mantle solidus is ex- pected to change with depth since solid solution between or- A2. The Mantle Liquidus and Solidus and Mantle thopyroxene and clinopyroxene increases with increased tem- Adiabat perature [Lindsley, 1983; Longhi and Bertka, 1996]. While The mantle melting model uses a mantle adiabat of 1.2 orthopyroxene appears in the products side of the melting K/GPa and liquidus and solidus curves from Zhang and Her- equilibrium at 3.0–3.5 GPa [Longhi, 1995], orthopyroxene may zberg [1994]. Liquidus and solidus pressures were converted to disappear from the melting equilibria at high pressure [Zhang depth using the preliminary reference Earth model [Anderson, and Herzberg, 1994; Takahashi et al., 1993]. However, the pre- 1989]. cise P at which orthopyroxene disappears is unclear [see Canil, The spinel-garnet transition was placed at 2.3 GPa [Gud- 1992; Walter, 1998; Bertka and Holloway, 1993]. Orthopyroxene finnsson and Presnall, 1996; Kinzler, 1997]; a cusp on the solidus was treated as being absent from the melting interval at P Ͼ at the spinel-garnet phase transition was not modeled. While a 6.5 GPa. Since orthopyroxene exerts little leverage on Na/Ti change in slope must occur at the spinel-garnet transition, no or REE ratios, small errors regarding the placement of or- clear constraints on the magnitude of this change exist. A cusp thopyroxene in the melting interval do not affect model calcu- is not clearly detectable in the data of Takahashi et al. [1993] lations. for KLB-1, nor in the CaO-MgO-Al2O3-SiO2 (CMAS) system [Gudfinnsson and Presnall, 1996], which may indicate that the transition is not sharp. Any error introduced by ignoring small Acknowledgments. I thank Charlie Langmuir for many helpful dis- cussions concerning this project and for introducing to me some of the cusps is also insignificant compared to error on the solidus problems concerning Na and Ti abundances in oceanic basalts. I also temperature. greatly appreciate the reviews of Michael Garcia, Vincent Salters, and Langmuir et al. [1992] showed that compositional differences Kenneth Cameron, which resulted in a much improved version of this between batch and fractional melting may not be very great manuscript. Finally, I thank David Walker, Rosamond Kinzler, and when polybaric aggregate melts are compared. The present John Longhi for helpful comments and reviews of earlier versions of this manuscript and Rick Ryerson for his support. UCRL-JC-131482 calculations support this notion. The results of fractional and batch melting models are similar, though batch melting results compare somewhat better to the geochemical data (fractional References melting results in greater degrees of depletion for elements Ahern, J. L., and D. L. Turcotte, Magma migration beneath an ocean with low partition coefficients), in agreement with Feigenson et ridge, Earth Planet. Sci. Lett., 45, 115–122, 1979. al. [1996]. Such differences, though, do not greatly impact P-T Allegre, C. J., and D. L. 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