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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 3008C 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 Fundamental questions in the Earth sciences concern the mineralogy of the basalt source region and the temperatures and depths at which basalts form. It has been proposed that isotopic and other compositional differences between basalts reflect mineralogical heterogeneity [Langmuir et al., 1977; Hofmann and White, 1982; Zindler et al., 1984; Allegre and Turcotte, 1986] (and more recently, Hirschmann and Stolper [1996] and Hauri [1996]). However, isotopic differences need not be accompanied by substantial differences in mineralogy (compare whole rocks and mineral separates from Okano and Tatsumoto [1996] and Xu et al. [1998]). Moreover, variations in the pressures (P) and temperatures (T) of partial melting have a significant impact on basalt composition [Klein and Langmuir, 1987; Kinzler and Grove, 1992b; Kinzler, 1997]. The nature and degree of mantle heterogeneity cannot be fully ascertained until such effects are evaluated. To investigate the potential effects of P and T on melt composition, melting models are developed here, and the results are compared to tholeiites from the East Pacific Rise (EPR) and tholeiitic and alkalic lavas from Hawaii. The models test whether some of the geochemical variations at these localities can be explained by differences in the P-T conditions of melting. These calculations also constrain minimum degrees of source region heterogeneity. The models use Na, Ti, Hf, and rare earth element (REE) abundance’s since their mineral/melt partition coefficients are Copyright 1999 by the American Geophysical Union. Paper number 1998JB900048. 0148-0227/99/1998JB900048$09.00 sensitive to both P and mineralogy. Partition coefficients for these elements have also recently been calibrated to high P and T [Putirka, 1998a, b; Salters, 1996], making these elements particularly useful for examining mineralogic heterogeneity and potential P-dependent geochemical variations. The nature and degree of heterogeneity impact upon issues of mantle composition and the efficiency of mantle mixing [Hofmann et al., 1986; Kellogg, 1992; Farber et al., 1994], as well as the thermal structure of the mantle. It is thus essential to differentiate between heterogeneity with respect to mineralogy, isotope ratios, or differences in major or minor element composition. To examine issues of heterogeneity and the conditions of partial melting, alkalic and tholeiitic basalts from Hawaii and tholeiites from the EPR are compared. Hawaii is the type example for a mantle plume, while EPR basalts are representative of mid-ocean ridges [Langmuir, 1988]. As Hawaii represents a mantle hot spot [Wilson, 1963; Morgan, 1972; Sleep et al., 1988], melting depths should be deep compared to the EPR, where melting occurs in response to passive upwelling [Oxburgh and Turcotte, 1968; Cawthorn, 1975; Ahern and Turcotte, 1979; Spiegelman, 1996]. The Hawaiian island chain is also underlain by thick lithosphere (70 –100 km [Bock, 1991; Woods and Okal, 1996]). Faced with such geologic differences, we might ask: Can differences in mantle temperature or lithosphere thickness explain some of the geochemical differences between Hawaii and the EPR? This question is addressed by comparing natural basalts to calculated melt compositions derived from a homogenous depleted peridotite source (see the appendix and Table 1). While the mantle is known to be heterogeneous, such calculations constrain heterogeneity. Geochemical variations that are unexplained by such 2817 2818 Table 1. PUTIRKA: MELTING DEPTHS AND MANTLE HETEROGENEITY Model Compositions Major Oxides Value Mineral Modes Value SiO2 TiO2 Al2O3 FeO MgO CaO Na2O 46.316 0.174 3.935 7.653 38.44 3.192 0.281 olivine orthopyroxene clinopyroxene garnet 0.60 0.09 0.17 0.14 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 coefficients 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 1. Weight percent Na2O and TiO2 are compared for tholeiites from the East Pacific Rise (EPR) and from several Hawaiian volcanoes. The Mauna Kea and Loihi groups also include alkalic lavas. Most Hawaiian basalts have lower Na/Ti due to both lower Na and higher Ti contents. Basalts from the Koolau shield have intermediate Na/Ti ratios. Data are for Loihi from Garcia et al. [1993, 1995]; Mauna Kea from Frey et al. [1991], Yang et al. [1996], Rhodes [1996], and Rhodes and Hart [1995]; Mauna Loa from Rhodes [1988], Yang et al. [1996], and Rhodes [1996]; Kilauea from Garcia et al. [1992] and Chen et al. [1996]; and Koolau from Frey et al. [1994]. East Pacific Rise basalt compositions are from Langmuir [1988] (see also Langmuir et al. [1986]). tholeiitic rocks are examined (Figure 1). The melting models test whether P-T conditions during melting can explain such variations. 2. Geochemical Data and Corrections To examine geochemical variation due to mantle melting, it is essential to minimize the effects of shallow level fractionation. As a test for shallow level fractionation, Na/Ti and 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 Figure 2. (a) Na/Ti cation fraction ratios are compared to MgO (weight percent) for EPR and Hawaiian basalts. Note that alkalic and tholeiitic lavas from Loihi and Mauna Kea feature similar Na/Ti ratios and are distinct compared to Koolau, Mauna Loa or EPR tholeiites. At Hawaii, Na/Ti ratios are insensitive to MgO content. Na/Ti ratios at Hawaii are thus unlikely affected by low-pressure fractionation and should reflect source composition and melting conditions. In contrast, EPR basalts are affected by low-pressure fractionation. Only EPR basalts with .8 wt % MgO were used to constrain EPR melting depths; Na/Ti ratios for such EPR basalts are higher than at Hawaii. (b) The concentration ratio Sm/Yb is compared to wt % MgO for the same samples as in Figure 2a. Sm/Yb ratios are independent of MgO content and should thus reflect melting conditions and mantle composition. PUTIRKA: MELTING DEPTHS AND MANTLE HETEROGENEITY Hawaiian tholeiites and alkalic lavas and thus unaffected by shallow level processing (Figure 2). Since accumulation or fractionation of olivine does not affect Na/Ti or Sm/Yb ratios, Hawaiian basalts with 7–13 wt % MgO are examined. An interesting interisland difference is apparent (Figure 2a): basalts from Mauna Kea, Loihi, and Kilauea have Na/Ti 5 2–2.5, while basalts from Mauna Loa are somewhat higher at 2.5–3.0, and Koolau basalts are higher still with Na/Ti, ranging from 3 to 4. In contrast to Hawaiian lavas, EPR basalts display Na/Ti ratios that decrease sharply with decreasing MgO (Figure 2a); this probably reflects plagioclase fractionation. Ratios of Sm/Yb do not vary with MgO (Figure 2b) and are thus apparently unaffected by such fractionation. Experimental studies indicate that plagioclase saturation for mid-ocean ridge basalts (MORB) occurs near 8 –10 wt % MgO [Tormey et al., 1987; Grove and Bryan, 1983]. The highest Na/Ti ratios (Figure 2a) may thus approach primitive values. To minimize the effects of fractionation on Na/Ti, only basalts with .8 wt % MgO will be compared to model values for constraining partial melting depths. Na/Ti ratios for such EPR basalts (4 –5) are significantly higher, and Sm/Yb ratios are lower, compared to Hawaiian tholeiites and alkalic lavas. 3. Results The melting model of this study follows the work of Langmuir et al. [1992] (see the appendix) and examines the compositions of aggregate melts, i.e., melts that are pooled from a range of depths within a melting column. Thus each choice for mantle potential temperature (T p ) corresponds to a unique initial depth of partial melting, and the choice of lithosphere thickness corresponds to a final depth of melting. In addition, for a particular starting composition, when lithosphere thickness and T p are specified, there exists a unique maximum and mean extent of partial melting, or F (melt fraction). Since only two variables (T p , initial melting depth, lithosphere thickness, and mean F) need be specified for a given source composition, the following discussion will refer to differences in initial melting depths and lithosphere thickness; differences in mean F and T p are implied. Initial melting depths and lithosphere thickness both significantly affect Na/Ti and Sm/Yb ratios in aggregate melts. This is true for both peridotite and eclogite or garnet pyroxenite mantle sources. In general, partial melting of a garnet pyroxenite leads to aggregate melts that have higher Na/Ti and Sm/Yb ratios, compared to aggregate melts from a peridotite source. High Na/Ti for garnet pyroxenite partial melts result, in part, from higher Na/Ti in the source (5, compared to 4 for peridotite). More significant, though, is the greater amount of garnet in the garnet pyroxenite (see the appendix), which increases the garnet pyroxenite bulk mineral/melt distribution melt sol coefficient for Ti (5D sol/melt 5 C sol Ti Ti /C Ti , where C Ti is the concentration of Ti in the total solid and C melt is the concenTi tration of Ti in the melt). High Sm/Yb ratios similarly reflect the high modal proportion of garnet, which results in an increased D sol/melt . For both peridotite and pyroxenite starting Yb compositions, Na/Ti ratios decrease and Sm/Yb ratios increase in aggregate melts, as lithosphere thickness increases. Mid-ocean ridge basalts were modeled using a 10-km lithosphere; at Hawaii, lithosphere thickness’ are less certain. For example, convective thinning is presumed to reduce an initially 90 –100 km thick lithosphere to 50 km or less [Detrick and 2819 Crough, 1978; Liu and Chase, 1989]. However, heat flow [VonHerzen et al., 1989] and seismic studies [Woods and Okal, 1996] are inconsistent with such thinning, and an average lithosphere thickness of 100 km is indicated [Woods and Okal, 1996]. Lithosphere thickness, though, is unlikely to be constant along the Hawaiian chain and may influence magma production [Morgan et al., 1995; Wessel, 1993]. Since estimates of 75– 80 km lithosphere have been obtained at Oahu [Bock, 1991], a 75–120 km range was explored. When thick lithosphere is present, Na/Ti and Sm/Yb ratios decrease as initial melting depth (or T p ) increases (Figure 3). Na/Ti ratios are higher beneath thin lithosphere and decrease as initial melting depth increases (Figure 3a). Na/Ti ratios decrease with increased melting depth because the K cpx/melt Na melt (Na partition coefficient for clinopyroxene/melt, 5 C cpx Na /C Na , i where C Na is the concentration of Na in the superscripted phase) increases with increased P, while clinopyroxene and garnet K min/melt remain constant or decrease [Langmuir et al., Ti 1992; Blundy et al., 1995; Kinzler, 1997; Walter, 1998; Putirka, 1998a, b]. Most importantly, without the P-induced change in K cpx/melt , Ti and Na are not significantly fractionated from one Na another, and aggregate melt Na/Ti ratios are nearly invariant. 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 the progressive removal of garnet from the residue during partial melting. When melting begins, the amount of garnet is highest, and so is D sol/melt , (since K garnet/melt is high). As meltYb Yb ing progresses, though, garnet is removed from the residue, and D sol/melt decreases. By increasing initial melting depths Yb (i.e., increasing mean and maximum F) the amount of garnet in the total melting column is decreased, as is the average D sol/melt in the melting column. Aggregate melts at the surface Yb reflect this average D sol/melt . When lithosphere thickness exYb ceeds 75 km, all melting occurs in the garnet stability field [Takahashi et al., 1993; Longhi, 1995; Kinzler, 1997; Walter, 1998], and the progressive consumption of garnet dominates the Sm/Yb signal. For both Na/Ti and Sm/Yb the aggregate melt curves flatten with depth because melt productivity is reduced at increased P [Putirka, 1997]. The Na/Ti curves exhibit less flattening with depth, compared to Sm/Yb, because K cpx/melt increases steadily with depth throughout the melting Na column. In contrast, D sol/melt , which depends upon the modal Yb abundance of garnet, does not vary greatly due to the small amount of partial melt that is produced (and hence the small amount of garnet that is consumed) at high P. In the case of thin lithosphere, changes in Sm/Yb ratios are less dramatic (Figure 3b) because melts produced deep in the column (in the presence of garnet) are overwhelmed by the comparatively large amounts of melt produced at shallow depths (,75 km). With 10 km lithosphere, Sm/Yb first decreases then exhibits a rapid increase once the garnet stability field is entered (75 km). The initial decrease in Sm/Yb, between initial melting depths of 50 and 75 km, is due to variations in mean F. At these depths D sol/melt . D sol/melt ; in the Yb Sm absence of garnet (,75 km), though, these D REE are very small, and Sm and Yb are only fractionated from one another when F is very low. As melting depths increase from 75 to 50 km, both maximum and mean F increase, and Sm/Yb ratios approach initial (unfractionated) values. Sm/Yb ratios for aggregate melts increase sharply when initial melting depths reach the garnet stability field (75 km), since K gar/liq is very Yb 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 reconciling 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. Figure 3. (a) Na/Ti ratios (cation fraction) of aggregate melts produced from peridotite and garnet pyroxenite sources are compared at different P-T conditions. Lithosphere thickness indicates depth to the top of the melting column; “initial melting depth” represents depth to the base of the melting column and hence also reflects mantle potential temperature. (b) Sm/Yb ratios for aggregate melt compositions are compared, and (c) a close-up view of the 10-km lithosphere calculations is given. In Figure 3c the “peridotite 1” model uses a garnet melting coefficient of 0.2; the “peridotite 2” model uses a garnet melting coefficient of 1. For a given lithosphere thickness a garnet pyroxenite source yields higher Na/Ti and Sm/Yb ratios compared to a peridotite source. Estimates of Melting Depths and Temperatures At the EPR, initial melting depths of 120 6 15 km reproduce the approximate concentrations of Na, Ti, Sm, and Yb (Figure 4). These depths overlap with depth estimates implied by Salters [1996, Figure 2] and are consistent with depths of lowvelocity 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 depth of 110 km suggests a T p of 1831 K (15588C). While mantle temperatures are not well constrained from geophysical studies [Parsons and Sclater, 1977; Stein and Stein, 1992], T p inferred using a KLB-1 composition overlaps with mantle temperatures of 1723 6 250 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 Hawaiian tholeiite and alkalic lavas. Abundances of Na, Ti, Hf, and REE can be produced using the same depleted mantle composition as that for the EPR but with increased lithosphere thickness and initial melting depths of 200 – 400 km. An undepleted mantle source would yield higher initial Na/Ti ratios (Figure 5); to achieve the low Na/Ti ratios of Hawaii for an undepleted source, increased initial melting depths (by ;50 – 100 km) would be required. Estimates of melting depths at Hawaii exceed those obtained by Watson and McKenzie [1991]. There are numerous reasons for these differences. First, it should be noted that the 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 depths and a more realistic DS f (;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 garnetfree residue is produced at the top of the melting column at Hawaii. If the melting coefficient for clinopyroxene is .0.5, 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 ,3.5 GPa [Eggins, 1992], yet show a garnet trace-element signature [Budahn and Schmitt, 1985; see also Frey et al., 1994]. Using the solidus of KLB-1, a T p of 2130 K (18578C), 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 Christensen, 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. Figure 4. (a) Natural and model Sm concentrations (ppm) and Sm/Yb ratios are compared. (b) Calculated and observed concentrations for Na and Ti are compared. Hawaiian basalts were modeled using a 100-km-thick lithosphere and an initial melting depth of 300 km; EPR basalts were modeled using a 10-km lithosphere and an initial melting depth of 115 km; these model calculations are indicated with the letters H (Hawaii) and E (EPR) (circled). Observed abundance’s of Na, Ti, and some REE can be reproduced by varying the P-T melting conditions of a mantle that has a depleted pyrolite bulk composition and a peridotite mineralogy. produce Na2O and TiO2 contents at Hawaii. Their predicted Na/Ti ratios [Watson and McKenzie, 1991, Table 2] are much too high, indicating that their melting depth estimates (partition coefficients for Na) are too low. Watson and McKenzie [1991] also use a final melting depth of 82 km and assume that spinel peridotite is stable to depths apparently exceeding 100 km. The lithosphere beneath some parts of Hawaii is conceivably as thin as proposed by Watson and McKenzie [1991], but spinel peridotite is probably not stable, even at depths as shallow as 82 km [Takahashi et al., 1993; Longhi, 1995; Kinzler, 1997; Walter, 1998]. Using a more realistic garnet lherzolite mineralogy, such shallow melting depths yield Sm/Yb ratios that are too high compared to observed values (Figure 5). Finally, the entropy of fusion (DS f ) used by Watson and McKenzie [1991] is too low, perhaps by a factor of 2, resulting 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 differences. In some cases, such as at Hawaii, differences in P-T conditions are probably not sufficient to explain all geochemical variations, and minimum differences in modal mineralogy for source regions are calculated. In addition to peridotite, eclogite and various garnet pyroxenite starting compositions are also examined to resolve whether such sources are consistent with observed geochemical signals. 4.2.1. Heterogeneity beneath the EPR. Hirschmann and Stolper [1996] have proposed that garnet pyroxenite exists in 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 and the relatively thin crust that is formed at oceanic spreading centers. As noted by Putirka [1997], though, fractional melting processes limit melt productivity and may be invoked to satisfy both observed crustal thickness [White et al., 1992] and inferred melting depths of .100 km [Salters, 1996]. Regarding geochemical variation, Na/Ti and Sm/Yb ratios at the EPR are consistent with partial melting of a peridotite source. Some mixing with a garnet pyroxenite source is allowed, since the EPR samples plot between the peridotite and garnet pyroxenite curves (Figure 5b). However, only the major oxides carry any significant leverage on mineral abundances. It is possible that the observed geochemical differences, at least with respect to Na and Ti, might be supported by minor mineralogic variations within a source that has an overall peridotite mineralogy. For example, a variation of 60.2 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 (,2%; 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 reproducing the high Lu/Hf and Sm/Nd ratios observed at Kolbeinsy. 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 1 Mauna Kea 1 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 thopyroxene decreases Na/Ti and Sm/Yb ratios by .015 and .05 respectively). Finally, Okano and Tatsumoto [1996] observe that Hawaiian spinel lherzolite xenoliths exhibit a wide range of isotope ratios, with some isotopes approaching Koolau-like values. This observation shows that a wide range of isotope ratios can be supported by a lherzolite mineralogy and that isotope variations at Hawaii might not require an eclogite source. It is thus unclear that eclogite is a necessary source component at Hawaii. Most of the interisland variation in Na/Ti and Sm/Yb at Hawaii can be accounted for by plausible ranges in the P-T conditions of melting for a peridotite mantle (Figure 5a). For example, Na/Ti-Sm/Yb partial melting arrays overlap the Koolau field as lithosphere thickness decreases to 75 km, and initial melting depths decrease to 170 km. Owing to differences in initial melting depth (and T p ), different values for mean F are also obtained for the Hawaiian tholeiites (Figure 5a). For comparison, estimates of F at Loihi are similar to, but slightly higher than, those obtained by Garcia et al. [1995] and are within the very wide range of values noted by Feigenson et al. [1996] for Mauna Kea. As noted above, though, differences in melting depth (in the absence of heterogeneity) are required to fractionate Na from Ti; initial melting depth, rather than F, is the critical variable for explaining the range of Na/Ti ratios at Hawaii. Undoubtedly, some intraisland variation is due to heterogeneity, especially since some Hawaiian lavas plot outside of the partial melting grid (Figure 5). Limited variations in melting depths and lithosphere thickness at Hawaii, though, are at least plausible. Melting depths might vary depending upon the position of the shield volcano and the plume axis [Farnetani and Richards, 1995], especially if shield positions are influenced by the state of stress in the lithosphere [Jackson and Shaw, 1975]. Relative maximum melting depths for Koolau, Kilauea, Mauna Loa, and Loihi are qualitatively consistent with melting depths inferred from major oxide systematics [Frey et al., 1994]; the model is furthermore consistent with trace element and isotopic observations [Bennett et al., 1996; Roden et al., 1994] that indicate a peridotite source for Hawaiian lavas. Moreover, Koolau lies north of the Molokai fracture zone [Mammerickx, 1989; Atwater, 1989], and seismic work [Bock, 1991] at Oahu indicates a 75– 80 km lithosphere in this region. If the Koolau lithosphere approaches 100 km, the mantle source at Koolau must differ from that beneath Loihi and Mauna Kea. Additionally, since lithosphere thickness probably does not vary greatly at any single volcano, intraisland heterogeneity is also implied by the range of Na/Ti ratios displayed at each of the Hawaiian shields (Figure 5a). The lowest Na/Ti ratios at Mauna Kea are also not explained by the present model. These low Na/Ti ratios can only be explained if (1) the top of the melting column exceeds .150 km depth or (2) the mantle source has higher clinopyroxene (by 2%) and lower garnet (by 2%) compared to the mineralogy of Table 1. Option 2 seems more likely, but lower garnet results in lower Sm/Yb ratios, perhaps indicating REE heterogeneity. While peridotite partial melting may explain interisland variation at Hawaii, can garnet pyroxenite or eclogite sources also yield observed Na, Ti, and REE abundances at Koolau? To illustrate the potential range of such sources, several starting compositions were explored, including eclogite, and garnet pyroxenites from various sources (see the appendix). As is evident from Figure 5b, most pyroxenites and eclogites are unsuitable as source components, since Sm/Yb ratios are high 2823 compared to Hawaiian tholeiites and alkalic lavas (Figure 5). Partial melts from some massif garnet pyroxenites exhibit Na/Ti and Sm/Yb ratios that overlap with some Hawaiian tholeiite and alkalic basalts. However, Na, Ti, Hf, and REE abundances from such sources are much higher than observed at Hawaii. Partial melts from pyroxenite sources yield Na abundances between 0.08 – 0.20 cation fraction, and Sm abundance’s of 6.2–12.5 ppm (compare to Figure 4) and are highest for massif pyroxenites. Minor element abundances might be diluted if mixed with melts from a peridotite source. However, to account for Na/Ti ratios at Koolau, massif pyroxenite partial melts would appear to dominate the Koolau aggregate melts (up to 100%; Figure 5b). In addition, massif pyroxenites exhibit a wide range of garnet/pyroxene ratios; only when garnet is ,20% are Sm/Yb ratios in the correct range. Finally, the thin lithosphere and cooler melting temperatures required in the peridotite model (above) for Koolau are not avoided by assuming a pyroxenite source. Thus, in contrast to the peridotite model, pyroxenite and eclogite sources provide poor fits to Na, Ti, and REE abundances at Hawaii. It would therefore appear that such sources at Hawaii are not only unnecessary but perhaps also unlikely. As is evident from Figure 5, variations in lithosphere thickness may be invoked to explain interisland variations at Hawaii. On the other hand, if the hypothesized lithosphere variations are incorrect, only small changes in the source region mineralogy are required based on Na and Ti abundances. Mass balance calculations using a mantle peridotite and highpressure mineral compositions [Walter, 1998; Putirka, 1998a, b] underscore this conclusion. For example, if the difference between the lowest and highest Na2O values at Koolau and Kilauea (about 1 wt %; Figure 1) are due only to heterogeneity in the source region, mass balance implies that this difference can be accommodated by a source region difference in clinopyroxene 1 garnet of ,2.0% (assuming mean F is 0.15, mean D min/melt is 0.06, and minerals have constant composition). Na Such source differences are reduced if any Na2O variation results from the P-T conditions of melting, assimilation in the shallow mantle, adjustments in mineral composition in the source region, or shallow level fractional crystallization. It should be noted that while these calculations are based only on Na2O, this oxide carries more leverage on calculated mineral proportions compared to other major oxides. This is because Na occurs only in clinopyroxene to any great extent, and even at high pressure it is never the dominant component in this phase. Large changes in source Na2O concentrations therefore translate into large changes in clinopyroxene modal abundances. Na2O is thus an ideal oxide for determining whether a mantle source is comprised of peridotite or pyroxenite. While an analysis of other elements, especially Ca or Al, might also be useful (given suitable high-pressure calibrations of K d ), it is tentatively concluded that small modal variations in a peridotite assemblage of minerals can probably accommodate observed geochemical variations at Hawaii. Mantle heterogeneity is a flexible hypothesis and cannot be excluded. If eclogite is not required to describe geochemical variations in oceanic lavas, though, there are important implications for mixing in Earth’s mantle. It seems likely that small amounts of recycled material contribute to the trace element and isotopic signature of some oceanic lavas [Hofmann and White, 1982; Zindler et al., 1984; Hauri et al., 1996]. Such material, though, might not survive the recycling process as a 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/ 204 Pb, and (c) 187Os/188Os. (Note that Hauri [1996] gives two averages for Loihi: one for alkalics and one for tholeiites; both are plotted. R 2 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 twocomponent 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 process is itself a homogenizing agent. 4.3. Spatial Variability of Isotope Sources To test for depth distributions of isotopic heterogeneity in 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 (Figure 6). Since, as noted above, Na can only be fractionated from Ti at depth, it appears that melts produced at depth (low Na/Ti ratios) tap mantle sources that are isotopically distinct from melts produced at more shallow levels of the mantle (higher Na/Ti). The ordering of the Loa trend volcanoes is the same in each plot in Figure 6 and is thus consistent with mixing between two, vertically stratified, mantle sources. This ordering for the Loa trend holds, even for the more poorly correlated Sr isotope ratios (Figure 6), and supports prior arguments for two-component mixing at Hawaii [Bennett et al., 1996; Chen, 1987; Chen and Frey, 1985]. It is also possible, though, that isotope ratios vary continuously but systematically with depth in the mantle. So far as Na/Ti ratios represent melting depth, Koolau lavas reflect partial melting of a shallow and variably enriched/depleted [see Richardson et al., 1982] mantle component (Figure 7). A two-component mixing scheme is not consistent with Kea trend lava compositions, which may indicate a less vertically stratified source [Staudigel et al., 1984; Stille et al., 1983; Chen, 1987]. Interestingly, Sr isotopes for individual lavas at Loihi and Mauna Loa show a local, or internal, correlation that is opposite to the intershield trend (Figure 6) but directed toward MORB. The intershield trend would appear to indicate a lateral (along-strike) component as well as a vertical component to local heterogeneity at the Hawaiian islands. This might be an enriched shallow layer, perhaps at or near the base of the Hawaiian lithosphere, that is most strongly sampled at Koolau. In contrast, both the local trend at Hawaii and the differences between isotope and Na/Ti ratios at Hawaii and the EPR (Figure 7) indicate a large-scale vertical component to isotopic heterogeneity in the Pacific upper mantle. The Hawaii-EPR comparison supports the conventional layered mantle model, or perhaps a “marble cake” mantle with a systematic depth distribution of isotopically distinct blobs. 5. Summary A mantle melting model was developed to estimate partial melting depths for oceanic lavas and to constrain mantle heterogeneity, using Na/Ti and REE ratios. Na/Ti ratios are particularly useful since Na and Ti are only strongly fractionated from one another at high P. Hafnium and the REE’s are also useful since their mineral/melt partition coefficients are sensitive to pressure and mineralogy [Salters, 1996; Kinzler, 1997; Walter, 1998; Putirka, 1998a, b]. Several important results are obtained from the models. First, the P-T conditions of melting alone appear to be capable of explaining both local variation at Hawaii, as well as some large-scale geochemical differences between Hawaii (an ocean island) and the EPR (a mid-ocean ridge spreading center). This implies that bulk compositional differences between Hawaiian and EPR source regions might be minimal; this is consistent with near-uniform, but nonprimitive, minor element ratios for oceanic basalts [Hofmann et al., 1986] and high-pressure diffusion experiments which indicate efficient homogenization in parts of the upper mantle [Farber et al., 1994]. Mantle heterogeneity is also constrained; inferred source region differences can be accommodated by small (2%) variations in peridotite phase proportions. Na2O, TiO2, and REE abundances at Hawaii also appear to be inconsistent with a variety of potential eclogite or garnet pyroxenite sources. The mantle is undoubtedly mineralogically heterogeneous, but this and other work [Sims and Depaolo, 1997] reveal the need to test models of heterogeneity against possible P-T dependent variations in melt composition. Abundances of Na, Ti, Hf, and the REE for EPR lavas are best reproduced when melting begins at 120 6 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 prior depth estimates [Salters, 1996]. In contrast, Hawaiian tholeiites can be modeled using a 100-km-thick lithosphere and initial melting depths of 200 – 400 km. This implies a temperature difference between Hawaii and the EPR of 3008C, close to estimates inferred from geodynamic studies [Sleep, 1990; Schilling, 1991] and mantle tomography [Romanowicz, 1994]. The compositional dependencies of peridotite solidus temperatures, though, need to be explored so that these depth estimates may be used to better resolve the thermal structure of Earth’s upper mantle. The present model also indicates that garnet is consumed during melting, while aggregate melts retain a garnet signature. This result may help to resolve the apparent conflict between trace element abundances, which indicate garnet in the source region [Budahn and Schmitt, 1985; Frey et al., 1994], and experimental studies which indicate that some primitive Kilauea basalts are not garnet saturated at P , 3.5 GPa [Eggins, 1992]. Appendix: Mantle Melting Model Oceanic basalt compositions can be successfully explained by polybaric partial melting models [Klein and Langmuir, 1987; Kinzler and Grove, 1992b; Langmuir et al., 1992; Kinzler, 1997]. Aggregate melt compositions were thus calculated for batch and fractional melting processes using the equations of Langmuir et al. [1992] and Plank and Langmuir [1992] and the mineral-melt partitioning relationships of Putirka [1998a, b] and Salters [1996]. The calculations employ a step-wise approach [Putirka, 1997]. In this method, degrees of partial melting (F) and aggregate melt compositions are calculated at depth increments of 2 km. The residual mineralogy is adjusted at each step using the estimated value for F and the stoichiometric coefficients of the pertinent melting equilibria (see below). Recent experimental work indicates that at near-solidus conditions the clinopyroxene-melt partition coefficient for Ti may decrease with increasing depth in the mantle [Kinzler, 1997; Walter, 1998]. This appears not to be an intrinsic pressure effect but instead results from the low Al content of near solidus liquids at high pressure [Putirka, 1998b]. A decrease in the partition coefficient for Ti amplifies the pressure dependence of Na/Ti and decreases estimates of initial melting depths. Since the clinopyroxene-melt partition coefficients for Ti observed by Kinzler [1997] and Walter [1998] are probably most appropriate for modeling mantle melting, they were adopted for this study. A1. Mantle Composition One set of mantle mineral proportions used for peridotite calculations (Table 1) are from Ita and Stixrude [1992, Figure 4]. The Ita and Stixrude [1992] estimates were obtained as a best fit to seismic data for mineral elastic properties. Such mineral modes are consistent with other similar studies of 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 are from Kinzler and Grove [1992b] and Hirschmann and Stolper [1996] for a depleted mantle and McDonough and Sun [1995] for an undepleted source. Minerals compositions from high-pressure experimental studies [Walter, 1998; Putirka, 1998a] were used to compare the major oxide [Kinzler and Grove, 1992b] and mineral modes [Ita and Stixrude, 1992] of Table 1. Mass balance calculations indicate overlap between the major oxide composition and mineral proportions, but these estimates are very sensitive to the mineral compositions selected for mass balance. Using the Kinzler and Grove [1992b] major element abundances, it is possible to obtain mineral modes that have lower garnet (by 2%) and higher clinopyroxene (up to 6%) balanced by lower olivine; these mineralogys were also explored for modeling purposes. A model mantle with slightly higher clinopyroxene and lower garnet and olivine 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 Na/Ti ratios observed at Mauna Kea, although lower-thanobserved Sm/Yb ratios are also obtained. The mineralogy of Table 1 appears to be the most successful mineralogy for simultaneously explaining EPR and Hawaiian lava compositions. Model results are less sensitive to small changes in initial Na/Ti ratio, and a range of depleted mantle starting compositions are successful at explaining major element variations in oceanic basalts. The peridotite bulk composition uncertainty (Figure 5) reflects the difference between depleted and undepleted sources when these sources are input into the melting models. The average garnet pyroxenite composition is from Hirschmann and Stolper [1996], and their modal mineralogy is used. Eclogite compositions are from Griffin and Brueckner [1985], Griffiths and Cornichet [1985], Miller et al. [1988], Taylor and Neal [1989], and Beard et al. [1992]; model calculations use a garnet fraction of 0.25. Eclogite garnet contents vary widely (0.25– 0.50), and higher amounts of garnet yield partial melts with higher Sm/Yb and Na/Ti ratios (Figure 5). Garnet pyroxenites from massifs are from Loubet et al. [1982], Bodineir et al. [1987], and Stosch and Lugmair [1990]; a garnet fraction of 0.2 was used for model calculations. As with eclogites, pyroxenites feature a wide range of garnet fractions (0 –50%), and increased garnet yields increased Sm/Yb and Na/Ti ratios for partial melts (Figure 5). A2. The Mantle Liquidus and Solidus and Mantle Adiabat The mantle melting model uses a mantle adiabat of 1.2 K/GPa and liquidus and solidus curves from Zhang and Herzberg [1994]. Liquidus and solidus pressures were converted to depth using the preliminary reference Earth model [Anderson, 1989]. The spinel-garnet transition was placed at 2.3 GPa [Gudfinnsson and Presnall, 1996; Kinzler, 1997]; a cusp on the solidus at the spinel-garnet phase transition was not modeled. While a change in slope must occur at the spinel-garnet transition, no clear constraints on the magnitude of this change exist. A cusp is not clearly detectable in the data of Takahashi et al. [1993] 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 cusps is also insignificant compared to error on the solidus temperature. Langmuir et al. [1992] showed that compositional differences between batch and fractional melting may not be very great when polybaric aggregate melts are compared. The present 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 melting results in greater degrees of depletion for elements with low partition coefficients), in agreement with Feigenson et al. [1996]. Such differences, though, do not greatly impact P-T estimates (compare the fractional melting curve in Figure 5a). Additionally, estimates of depth are more robust than T since K cpx/melt is much more sensitive to P than T [Putirka, 1998b], Na and the K min/melt for Ti, Hf, and REEs are expressed only as a d function of P [Salters, 1996]. Reported T estimates rely on experimental measurements of solidus temperatures. Recently, solidus temperatures have been measured at high pressure for two similar peridotite nodules KR003 [Walter, 1998] and KLB-1 [Zhang and Herzberg, 1994]. Unfortunately, other peridotite solidi have not been measured with the same temperature precision (Walter [1998] and Zhang and Herzberg [1994] account for thermal gradients in their experiments; see Zhang and Herzberg [1994] for comparisons), and compositional effects on the mantle solidus cannot yet be quantified. The data presented by Hirose and Kushiro [1993], though, indicate that T solidus differences of up to 50 K are possible, depending on mantle composition. A3. Melting Stoichiometry Melting stoichiometry affects the estimation of mineral proportions throughout the melting column and thus impacts upon D sol/melt . Stoichiometric coefficients to depths of 0 –75 i km are from J. Longhi [see Salters, 1996], Longhi [1995], and Kinzler and Grove [1992a]. These coefficients (experimentally determined at P , 3.5 GPa) might not extrapolate to high P. With increased pressure, clinopyroxene and garnet survive to greater extents of melting [Wei et al., 1990; Takahashi et al., 1993]. In work by Takahashi et al [1993], clinopyroxene disappears at 38% melting at 3 GPa, while at 7 GPa clinopyroxene survives to .70% melting. Less clinopyroxene must be consumed for each increment of melt produced at 7 GPa, and melting coefficients should be reduced. At depths .75 km the models (Figures 3–5) use Walter’s [1998] coefficients, although lower coefficients were explored. The amount of orthopyroxene on the mantle solidus is expected to change with depth since solid solution between orthopyroxene and clinopyroxene increases with increased temperature [Lindsley, 1983; Longhi and Bertka, 1996]. While orthopyroxene appears in the products side of the melting equilibrium at 3.0 –3.5 GPa [Longhi, 1995], orthopyroxene may disappear from the melting equilibria at high pressure [Zhang and Herzberg, 1994; Takahashi et al., 1993]. However, the precise P at which orthopyroxene disappears is unclear [see Canil, 1992; Walter, 1998; Bertka and Holloway, 1993]. Orthopyroxene was treated as being absent from the melting interval at P . 6.5 GPa. Since orthopyroxene exerts little leverage on Na/Ti or REE ratios, small errors regarding the placement of orthopyroxene in the melting interval do not affect model calculations. Acknowledgments. I thank Charlie Langmuir for many helpful discussions concerning this project and for introducing to me some of the problems concerning Na and Ti abundances in oceanic basalts. I also greatly appreciate the reviews of Michael Garcia, Vincent Salters, and Kenneth Cameron, which resulted in a much improved version of this manuscript. 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