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Earth and Planetary Science Letters 230 (2005) 29 – 46 www.elsevier.com/locate/epsl Flow and melting of a heterogeneous mantle: 1. Method and importance to the geochemistry of ocean island and mid-ocean ridge basalts Garrett Ito*, John J. Mahoney School of Ocean and Earth Science and Technology, POST 810, University of Hawaii, Honolulu, HI 96822, USA Received 5 May 2004; received in revised form 1 September 2004; accepted 26 October 2004 Available online 24 December 2004 Editor: B. Wood Abstract Understanding the partial melting process is key to our ability to relate geochemical characteristics of hotspot and midocean ridge lavas to the dynamics and chemical structure of the mantle. We present a method of computing the trace-element and isotopic compositions of magmas generated by melting a heterogeneous source in mantle plumes and beneath mid-ocean ridges. The method simulates fractional melting with thermodynamically consistent melting functions of three mantle lithologies, each with a distinct trace-element and isotopic composition. A key assumption is that enriched mantle peridotite (EM) and pyroxenite (PX) both begin melting deeper than depleted mantle peridotite (DM). Model calculations can explain many features observed in a compilation of ocean island basalt (OIB) and mid-ocean ridge basalt (MORB) data. In particular, La/Sm and Sr, Nd, and Pb isotope ratios are most variable and extend to compositions most distinct from average MORB compositions in islands formed on relatively old seafloor (N~16 m.y.). The compositions of hotspot islands erupting on younger seafloor are less variable and overlap more appreciably with common MORB compositions. Models predict these observations to result from the effect of lithospheric thickness in limiting the extent of partial melting. Beneath old seafloor where the lithosphere is thick, models predict the overall extent of partial melting and the extent of DM melting to be small; therefore, magma compositions are most sensitive to changes in the relative proportions of EM and PX, as well as to mantle temperature. Beneath young seafloor where the lithosphere is thin, models predict more extensive melting of all lithologies. Progressive extraction of the different components during melting can also explain the general topology of isotopic arrays defined by OIBs globally. Our models not only predict testable variations in trace-element and isotopic ratios with mean extent of partial melting, but also show that pyroxenite can complicate such correlations because it can melt to very high extents, in many cases, completely. If the thickness of the mantle plume layer beneath the lithosphere exceeds that of the DM melting zone, an increase in the mantle flow rate with depth, which is predicted for mantle plumes, can enhance the flux of incompatible elements and isotopes derived from PX and EM, relative to the case of the more uniform flow profile expected beneath mid-ocean ridges. Thus, differences in both mantle flow and lithospheric thickness between mid-ocean ridges and hotspots can lead to important distinctions in the isotopic and trace-element characteristics of MORBs and OIBs, independent * Corresponding author. Tel.: +1 808 956 9717; fax: +1 808 956 5154. E-mail addresses: [email protected] (G. Ito)8 [email protected] (J.J. Mahoney). 0012-821X/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.epsl.2004.10.035 30 G. Ito, J.J. Mahoney / Earth and Planetary Science Letters 230 (2005) 29–46 of any compositional differences between their respective mantle sources. In addition, variations in mantle flow alone can contribute to geographic variations in hotspot geochemistry observed both in intraplate settings and where hotspots interact with mid-ocean ridges. D 2004 Elsevier B.V. All rights reserved. Keywords: ocean island basalt (OIB); mid-ocean ridge basalt (MORB); mantle heterogeneity; partial melting; mantle plume; mantle convection 1. Introduction The geochemistry of ocean island basalt (OIB) and mid-ocean ridge basalt (MORB) reflects physical and chemical processes in the mantle ranging from the global [1–3] to the local scale [4–8]. One key linkage between the geochemical properties that we can measure in volcanic rocks and those of the mantle source materials is the process of melting. A great deal has been learned about mantle melting through laboratory experiments, geochemical observations, and theory [9–16]. To date, studies of mantle melting have focused largely on mid-ocean ridge melting, owing in part to the relative simplicity of the structure and composition of most oceanic crust. Correspondingly, most theoretical treatments have focused on melting of peridotite having relatively limited heterogeneity. The greater diversity of hotspot-related magmatism in terms of both tectonic settings and geochemical compositions offers an opportunity to extend our understanding of the mantle but requires consideration of the upper-mantle dynamics beneath hotspots, as well as the process of melt generation and accumulation from a heterogeneous mantle. The concept that compositional heterogeneity is present in the mantle as veins, streaks, or blobs smaller than typical volumes of upper mantle melting zones is widely discussed in the geochemical literature [17–22]. Compelling evidence for such heterogeneity is recognized at hotspots [4,23–29] and at mid-ocean ridges [19,30–37]. Both the differences in source composition and associated melting behavior can strongly influence magma composition, possibly contributing to large and often correlated changes in incompatible element and isotope ratios [32,33,38]. For example, mafic materials may be important melting components [2,24– 26,39–42] and the low melting temperature of pyroxenite [43,44] relative to peridotite can cause variations in the fraction of each component sampled by melting and give rise to chemical mixing trends in erupted magmas [38,42,44]. Furthermore, the sensitivity of the solidus of peridotite to incompatible element and volatile content [15,33,46,47] can allow for variable extraction of heterogeneous peridotite [32,48]. Although its importance is well recognized, the melting of a veined mantle has received relatively little quantitative, theoretically based treatment. The purpose of this manuscript is to quantitatively explore the consequences of melting a heterogeneous mantle on the incompatible-element and isotopic composition of OIBs and MORBs. We begin by describing a simple method for calculating the composition of melts as they form and mix. Melting and melt mixing are both coupled to mantle flow. We assume that narrow, buoyant upwellings cause OIB volcanism and show that the difference between such bmantle plumeQ flow and the flow beneath midocean ridges is one factor that can contribute to differences between OIB and MORB geochemistry. A second important factor is lithospheric thickness, which limits the extent to which different lithologies melt. Comparisons between model predictions and existing data sets are used to examine possible causes for global OIB and MORB systematics, and for local variability within individual ocean island groups. 2. Method: Melting model 2.1. Governing equations Partial melting beneath hotspots and mid-ocean ridges predominantly occurs as the asthenosphere ascends and decompresses. Melting ceases as the G. Ito, J.J. Mahoney / Earth and Planetary Science Letters 230 (2005) 29–46 asthenosphere is diverted sideways beneath the lithosphere (Fig. 1). A simple way to compute the composition and volume of melts integrated over the whole melting zone is to relate them to the properties of the residue flowing out of the melting zone [10– 13]. This material forms a bresidual mantle columnQ (RMC) [11] beneath mid-ocean ridges and, as we describe below, forms a bresidual mantle cylinderQ (also RMC) beneath intraplate hotspots. The traceelement concentration C i of pooled magmas derived from mantle source i can be calculated by assuming 31 perfect mixing of melts derived from each depth, or pressure P of the RMC, Z P2i C0i Ei ðFi ÞFi ð PÞU ð PÞdP P1i : ð1Þ Ci ¼ Z P2i Fi ð PÞU ð PÞdP P1i Here, C 0i is the concentration of a trace element in source i, E i ( F i ) is the factor by which the melt is enriched relative to the source after melting to a mass Fig. 1. (a) Solidi for enriched mantle (EM, dashed), pyroxenite (PX, gray), and depleted mantle (DM, black line); also shown are the adiabat (dotted) and predicted temperature T profile (black curve) for a starting potential temperature of 1450 8C. (b) Predicted isobaric productivity for each lithology as labeled with their respective mass fraction in the mantle, / i. For EM and DM, values assumed for K D , D C*sol/liq, DH Afus, TAfus (variables are defined by [15]), are 0.25, 0.02, 10 kJ/mol, and 1336 8C, respectively [15]. For EM, assumed proportions for major component A (defined in [15]) and minor, incompatible component I are 0.598 and 0.012, respectively; for DM, they are 0.606 and 0.004. (c) Predicted melt productivity for each lithology. (d) Isoviscous, axisymmetric flow (arrow with size proportional to flow rate; streamlines in bold) due to a cylinder of buoyant fluid beneath a rigid top boundary. The thickness of the plume layer exiting the melting zone H is shown schematically. (e) Predicted radial flow along the black curve in Panel (d), where upwelling and melting have stopped (solid); radial flow predicted by lubrication theory (dashed curve, see text), and horizontal flow driven passively by plate spreading at a mid-ocean ridge (vertical line). These curves represent the horizontal flow of the residue exiting the melting zone U( P) and are proportional to the width of the residual mantle cylinder (RMC). (f) Predicted melting functions F( P) for the mantle lithologies, as labeled in Panel (c). 32 G. Ito, J.J. Mahoney / Earth and Planetary Science Letters 230 (2005) 29–46 fraction F i , and U is the speed at which the residue is exiting the melting zone. Both F i and U are functions of pressure P. The pressure range of the RMC for source i is defined by the beginning P 1i and ending melting pressures P 2i . Eq. (1) simply describes an average concentration, C 0i E i ( F i ), of accumulated incremental melts that were extracted from each portion of the RMC, weighted by the amount of melt extracted, F i ( P)U( P)dP. To solve Eq. (1) we must define functions of E i ( F i ), F i ( P), and U( P). 2.2. Enrichment function E( F) [54]. With the above assumptions, the melt productivity of lithology i depends on thermal coupling with the other j lithologies, each comprising a mass fraction / j of the mantle assemblage approximately according to: BF BPi BT aTi T X BT =BPi jF BT =BPj jF þ DS / j j BPi F qc p cp jpi BT =BFj jp : ¼ X BT T DSi T BT =BFi jP þ / þ DS / j j BF c c BT =BF j i p p p jpi j P ð2Þ The enrichment function E i ( F i ) describes an idealization of elemental extraction from the solid resulting from melting and melt–solid interaction. Here, we consider accumulated, fractional melting [49], which assumes that infinitesimal melt increments form in chemical equilibrium with the solid but are immediately taken out of equilibrium with the solid prior to mixing with other melt increments. The composition of an infinitesimal melt increment is governed by the modal mineralogy of each solid lithology ([13,40,44]; assuming that they do not chemically equilibrate, as discussed below), liquid– mineral partition coefficients [13,50], and pressuredependent phase transitions ([47,51]; see Table 1 of Background Dataset in Appendix A). The accumulated enrichment functions E i ( F i ) are analytical solutions of fractional melt compositions normalized by C 0i and integrated (i.e., accumulated) over F through the different solid-phase intervals ([13,52]; i.e., Eq. 11 of [13]). 2.3. Melting function F( P) A key quantity in describing the melting function F( P) is melt productivity BF/BP, the fraction of melt generated per increment of decompression. Following [45], we assume that the system remains in thermal equilibrium (implying characteristic dimensions of heterogeneities b102 m) but in chemical disequilibrium. Although the likelihood of chemical disequilibrium in a partially molten mantle has been questioned [53], an analysis of compaction and chemical diffusion time scales demonstrates that disequilibrium can exist, given reasonable properties of many upper mantle systems See Table 1 for the definition of variables and [15,45,55] for further explanation. We consider a mantle composed of three lithologies: benrichedQ mantle (EM) peridotite, bdepletedQ mantle (DM) peridotite, and pyroxenite (PX). For peridotite melting, we use basic thermodynamic and mass-balance principles to describe the dependence of BT/BF i |p (=BF/BTi 1| p) on F [15]. This simple method treats peridotite as an assemblage of three compositional components: two major components forming a solid solution and a small quantity of a third, incompatible component I. This ternary system captures many of the essential aspects of more complex calculations that consider nine oxide components in peridotite [14,15,55–57], notably, minimal BF/BP at the onset of melting and an increase in BF/ BP with F up to the point of clinopyroxene exhaustion, where BF/BP suddenly drops ([55]; Fig. 1). We assume that DM behaves as nominally dry peridotite and thus calibrate its melting behavior (see Fig. 1 caption) to qualitatively match that predicted by [14]. The DM solidus-depth function is derived empirically [58]. We simulate enriched mantle (EM) with a higher concentration of the incompatible component I compared with DM, which represents an elevated water content. Consequently, EM begins melting at a greater pressure than DM and has a greater depth zone over which melt productivity is low (Fig. 1). The increase in I is such that the change in solidus and BF/BP functions relative to DM is comparable with adding 0.05 wt.% water according to the parameterization of [51]. For pyroxenite melting, we use the experimentally constrained solidus pressure and BF/BT|p functions of G. Ito, J.J. Mahoney / Earth and Planetary Science Letters 230 (2005) 29–46 Table 1 Definition of variables Variable Meaning Value Unit cp 1200 J kg1 8C1 9.8 m s2 km C C 0i Ci C pm Ei F g H H DM P P0 R DS T U z a /l q Specific heat at constant pressure Concentration of a trace element in the eruptible magma Concentration of a trace element in starting source i Concentration in the melt arising from source i Concentration in estimated primitive mantle [62] Concentration of accumulated, incremental melt normalized by C 0i Weight fraction of partial melting Acceleration of gravity Characteristic thickness of plume layer exiting melting zone Thickness of DM melting zone beneath lithosphere Pressure Pressure at the base of the lithosphere Isotope ratio Change in entropy in converting solid to melt Potential temperature Normalized horizontal flow rate out of the melting zone Depth below the lithosphere Coefficient of thermal expansion Mass fraction of lithology i in mantle Mantle density km GPa GPa 200 J8C1 kg1 8C km 3105 3300 kg m3 [43] (experiments were done at 2–3 GPa, therefore, applying these functions for higher pressures is an extrapolation). From the known functions of BF/ BTi | p, we use Eq. (2) to calculate BF/BP i for each lithology present (i.e., / j N0). We then numerically integrate over pressure to yield F i ( P) (Fig. 1f) for application in Eq. (1). 2.4. Mantle flow function U( P) We assume that hotspot or OIB volcanism is caused by decompression melting of a cylindrical 33 upwelling (mantle plume) of low-density material interacting with the base of a stationary lithospheric plate. To derive the appropriate function, U( P), we examine the two-dimensional (2D) axisymmetric flow of an isoviscous (asthenospheric) fluid contained in a half-space with a rigid top boundary (i.e., the base of the lithosphere; Fig. 1d). Buoyant fluid is contained in a (plume) cylinder of radius R, extending from a depth z=H below the lithosphere to a sublithospheric depth of z=11H (hence, the base of the plume stem is sufficiently deep to minimize its effects on shallow flow), where H is the characteristic thickness of the plume layer that forms beneath the lithosphere and exits the melting zone. Following [59], we solve for mantle flow by filling the cylinder with buoyant particles and numerically integrating analytical solutions of the momentum equation for incompressible flow from each particle [60]. Material is predicted to rise in the cylinder and turn horizontal as it interacts with the lithosphere. The most rapid flow is predicted to be deep below the lithosphere, decreasing to zero at the base of the lithosphere to satisfy the boundary condition. Decompression melting rate will be zero where the vertical component of flow is zero. Along a contour of zero-upwelling, the rate of (radial) flow out of the melting zone decreases toward the lithosphere (Fig. 1e). This radial flow profile is one form of U( P). Another way to evaluate U( P) is to approximate the portion of material flowing radially beneath the lithosphere as a thin layer, using lubrication theory. Buoyancy drives radial flow subject to the boundary conditions of zero-flow at the base of the lithosphere and zero-shear stress at the base of the plume layer. These conditions are appropriate for an isoviscous fluid [61] and yield a flow rate that increases as quadratic function of depth (Fig. 1e). Normalized by the flow rate at the base of the layer, the horizontal flow as a function of depth z is: U ð zÞ ¼ 2ð z=H Þ ð z=H Þ2 : ð3Þ Eq. (3) is converted to a function of pressure with the relation P =P 0+qgz, where P 0 is the pressure at the base of the lithosphere, q=3300 kg/m3, and g is the acceleration of gravity. This function is very similar to the profile computed above for 2D 34 G. Ito, J.J. Mahoney / Earth and Planetary Science Letters 230 (2005) 29–46 axisymmetric flow (cf. curves in Fig. 1e); for simplicity, we will use Eq. (3) for U( P). The thickness of the plume layer exiting the melting zone is H (Fig. 1d). This variable controls the maximum pressure P 1i in the integral of Eq. (1); P 1i is either the solidus pressure of lithology i or the pressure at the base of the plume layer ( P 1i = P 0+qgH), whichever is less. This means that the RMC could extend as deep as the solidus but could be shorter if buoyancy pushes material to shallower depths prior to exiting the melting zone. The minimum pressure corresponds to the base of the lithosphere P 2i =P 0. In the following calculations, we assume H=100 km, saving a discussion of the effects of varying H for Section 5.3. This form of mantle flow contrasts with that commonly assumed for mid-ocean ridge melting [11,12,62]. Instead of decreasing toward the base of the lithosphere, horizontal mantle flow that is driven kinematically by two diverging plates is nearly uniform with depth (Fig. 1e) and approximately equal to the half spreading rate of the plates. The normalized flow function U( P) is therefore equal to one and does not appear in the equivalent equations presented previously [11,12]. Buoyancy associated with melting can drive a type of active flow [62], but in contrast to deep mantle plume buoyancy, this relatively shallow, melt-related buoyancy tends to push the mantle more rapidly through the upper portion of the melting zone. This would effectively widen the RMC near its top, producing a nearly opposite effect to that of the deeper plume buoyancy simulated here. 2.5. Melt mixing and composition of eruptible magmas Using Eq. (1), we solve for the concentrations of trace elements in melts derived from each mantle lithology. The final concentration in the eruptible magma is then calculated by weighting the concentrations by the amount of melt derived from each source Z P2i 3 X Ci /i Fi ð PÞU ð PÞdP C¼ i¼1 3 X i¼1 Z P1i : P2i /i P1i Fi ð PÞU ð PÞdP ð4Þ If C i is the concentration of an element with a radiogenic isotope, then the isotope ratio in the eruptible magma R is: 3 X R¼ Z i¼1 3 X i¼1 P2i Fi ð PÞU ð PÞdP Ri Ci /i Z P1i ; P2i ð5Þ Fi ð PÞU ð PÞdP Ci /i P1i where R i is the ratio in source i. Eqs. (4) and (5) are simply mixing equations. Oftentimes, simpler mixing equations are used to infer the proportions that each component contributes to a given magma composition, and these proportions are assumed to be the same as those in the source material (i.e., / i ). However, Eqs. (1), (4), and (5) reveal how melting and mantle flow can contribute to mixing proportions. Eq. (5) is conceptually the same as the isotope mixing equation in [38], but the integrals in Eq. (5) describe a specific mechanism that controls mixing proportion, namely, melt flux, which is controlled by mantle flow. 3. Model predictions 3.1. Mantle source compositions The composition of magmas clearly depends on the starting composition of the lithologies melting, C 0i . We define a single composition for each of the three lithologies considered in this paper (see Background Datasets, Table 2, in Appendix A). Not varying C 0i minimizes the number of free variables and allows us to focus on the effects of melting. Compared to estimated primitive mantle [63], EM is assumed to be enriched in the most incompatible trace elements, and DM is assumed to be depleted in the most incompatible trace elements, with relative concentration increasing with increasing compatibility. PX is assumed to have the median incompatibleelement composition of the MORB data set that we have used (see Section 4). We also assume that each lithology has a different radiogenic isotope composition. We assume EM to have isotope ratios similar to the postulated bEM1Q or bEM2Q end-members, PX to G. Ito, J.J. Mahoney / Earth and Planetary Science Letters 230 (2005) 29–46 be isotopically similar to the proposed bHIMUQ [2], and DM to be similar to bDMMQ [5]. 3.2. Changes in composition with extent of partial melting We now show some predictions of Eqs. (1)–(5). Our purpose is to build an intuitive understanding of the process of melting in the presence of heterogeneities and mantle flow. In these calculations, we assume an anomalously hot plume mantle with a potential temperature of 1450 8C, or a temperature excess of DT=100 8C. In reality, temperature is likely to vary significantly in a mantle plume, but the simplicity of our models limits our calculations to simulating only the average mantle temperature. We consider DT=100 8C to represent a moderate, average excess temperature. For a given mantle lithology, Eqs. (1)–(5) predict the well-understood behavior of maximum incompatible-element concentrations C i being produced at the onset of melting, when the (maximum) extent of 35 melting F imax ( F imax=F i ( P 2i )) is near zero. Continued melting leads to decreasing C i roughly in proportion to 1/F imax (see Background Dataset in Appendix A for the evolution of C i with F imax). Enrichment E i =C i /C 0 is greater for more incompatible elements than for less incompatible elements; therefore, ratios like La/Sm also decrease with increasing F imax. For a case in which only EM is present (/ EM=1, max / DM = 0), La/Sm is maximized for all F EM (Fig. 2a). Cases that also include DM (/ DMN0) predict concentration curves that diverge from and fall below the max curve for / EM =1, once DM begins to melt ( F EM c0.065). With regard to isotope ratios, when only EM is melting, isotope ratios remain constant and equal to those of EM (Fig. 2b and c). As DM melts, isotope ratios become more DM-like with increasing extent of melting. The greater / DM is, the closer the max isotope ratios are to DM for a given value of F EM . The converse is also true. Fig. 2d–f shows predictions with PX added. Here, DM is always assumed to be 90% of the source mantle, and EM and PX make up the remaining portion. Again, Fig. 2. (a–c) Predicted melt compositions from mantle made of only EM and DM, with various fractions of EM as labeled. (d–f) Predicted ratios from mantle made of EM, DM, and pyroxenite with fraction / DM=0.9 and labeled fractions of EM. Gray curves in right column are the same as those in left column. Source compositions are shown as circles (EM, i.e., EM2), triangles (PX), and squares (DM). Kinks in the curves near max F EM =0.2 correspond to the sudden drop in EM and DM melt productivity, BF/BP, associated with the exhaustion of clinopyroxene as a melting phase (see Fig. 1c and f). A decrease in BF/BP means that a greater vertical length of mantle experiences a given change in melt fraction (i.e., max DP=(BP/BF)DF), and this translates to a larger volume of high-degree DM melts added to the mixture over a given change in F EM . 36 G. Ito, J.J. Mahoney / Earth and Planetary Science Letters 230 (2005) 29–46 at the onset of melting, only EM controls the commax positions. Once PX begins to melt ( F EM = ~ 0.01), 87 86 La/Sm and Sr / Sr decrease, while 206Pb / 204Pb increases toward the PX source value. As melting max continues, DM begins to melt at F EM =~ 0.07. From 87 86 206 this point, La/Sm, Sr/ Sr, and Pb/204Pb decrease gradually toward values of the DM source. The large and rapid change in all compositions at the onset of PX melting reflects a large influx of elements from PX caused by two factors. First, PX is assumed to be enriched in incompatible elements relative to peridotite. Second, PX melts very quickly, in this case, melting 100% over a pressure interval of b2 GPa (Fig. 1). This behavior results because peridotite is more abundant than PX, EM melts at a much lower rate (i.e., BF/BT j | p) than PX does, and DM is largely subsolidus; therefore, peridotite melting consumes very little latent heat and more is available for PX melting (Eq. (2)). By comparison, if PX were the only material present, then complete melting would require ~ 4 GPa of decompression. These results show how a small amount of PX in the mantle can have a large influence on the trace-element and isotopic composition of eruptible magmas. 3.3. Mantle plume flow versus mid-ocean ridge flow The above calculations include the increasing rate of mantle flow with depth given by Eq. (3). To illustrate the importance of such plume flow, we compare solutions using the same starting sources, but with the uniform flow appropriate for mid-ocean ridges (U( P)=1). Predicted compositions with midocean ridge flow are subtracted from those with plume flow to quantify the relative benrichmentQ caused by mantle plume flow alone (indicated by D in Fig. 3). Over most of the interval that DM is melting, calculations with mantle plume flow predict higher values of La/Sm, as well as more EM- and/or PX-like isotope signatures compared with the calculations with mid-ocean ridge flow. This result is caused by the relatively high mantle plume flow U( P) near the base of the melting zone, where melting is limited to low degrees and where incompatible elements are extracted most efficiently from EM and PX. Shallower in the melting zone, the decreasing rate of mantle exiting the melting zone Fig. 3. Excesses in La/Sm, 87Sr / 86Sr, and 206Pb / 204Pb caused by mantle plume flow compared with mid-ocean ridge mantle flow. Numbers indicate the fraction of EM (/ EM) composing the mantle mixture; / DM = 0.9 and PX make up the remaining fraction. U( P) decreases the flux of incompatible-elementmax depleted melts (generated at higher F EM ), as well as the DM isotope signatures. The enrichment caused by mantle plume flow tends to be largest nearest the max onset of DM melting ( F EM = 0.07– 0.12) and generally decreases with continued melting. Because of the assumed composition of the EM end-member, plume flow elevates La / Sm and 87Sr / 86Sr most substantially, relative to mid-ocean ridge flow, when EM is most abundant in the starting mantle. Similarly, the degree to which Pb isotope ratios are elevated by mantle plume flow increases with the amount of PX originally present. Thus, mantle plume flow could be one cause for the heavier sampling of PX and EM components at hotspots than at midocean ridges, independent of any mantle source differences. G. Ito, J.J. Mahoney / Earth and Planetary Science Letters 230 (2005) 29–46 4. Importance to OIB and MORB genesis 4.1. Chemical variations with seafloor age The above calculations predict systematic changes in magma geochemistry as a function of the maximum fraction of partial melting F max. One factor that limits F max is lithospheric thickness (proportional to P 2 in Eqs. (1), (4), and (5)). We thus anticipate a dependence of magma geochemistry on seafloor age at the time of volcanism. We compiled geochemical data for various hotspot island groups, primarily from the GEOROC database (http://georoc. mpch-mainz.gwdg.de). Seafloor age at the time of volcanism was determined by subtracting known or 37 estimated sample ages from the magnetically determined ages of the surrounding abyssal seafloor [64]. We also compiled geochemical data for the MidAtlantic Ridge (MAR), East Pacific Rise, and Indian Ocean ridges, principally from the PETDB database (http://petdb.ldeo.columbia.edu/petdb/). To isolate bnormalQ from anomalous MORBs, we only used data for samples collected within the depth range of 2500–3500 m. This depth range is meant to eliminate potential regions in which the mantle is anomalously hot or cool. We also eliminate regions identified as hotspot-influenced by [65] and [66]. Fig. 4 shows several key, frequently measured geochemical ratios versus the square-root of seafloor age at the time of volcanism. The MORB data are Fig. 4. Observed ratios of tholeiitic basalts from various ocean island groups (circles) vs. the square-root of seafloor age at the time of volcanism. Data for some hotspots are gray and some are colored: Iceland (black), Galápagos (dark blue), Easter (red), Pitcairn (yellow), Cook-Austral (light blue), Hawaii and Hawaiian-Emperors (purple), Society (white), Canary (brown), and Samoa (orange). Green histograms summarize data from bnormalQ sections of mid-ocean ridges (see text). Red curves encompassed by light orange shading are calculations with EM (isotopically similar to EM 2 [5]) fraction / EM = 0.1 and pyroxenite fraction / PX = 0; blue curves and light green shaded area are for / EM = 0.02 and / PX = 0.08. Solid curves show predictions for mantle plume flow (U( P) given in Eq. (3)), with excess temperatures DT of 0–200 8C (Normal mantle potential temperature, assumed to be 1350 8C, is the lower limit for mantle plumes. Temperature increases to the right between curves.) The mantle fraction of DM is / DM = 0.9. Dashed curves are solutions for DT = 0 8C and mid-ocean ridge flow (U( P) = 1). 38 G. Ito, J.J. Mahoney / Earth and Planetary Science Letters 230 (2005) 29–46 represented as histograms along the vertical axis at zero seafloor age. A simple change in compositions with seafloor age, as would be predicted by a given model calculation, is not evident. Indeed, variability within island chains can be as large as or larger than the variability between different chains. However, what is evident is that both the greatest compositional ranges and the compositions most distinct from those of average MORB tend to be among islands on older seafloor (N~16 m.y.). In contrast, islands erupting on relatively young seafloor (b~16 m.y.) or thin lithosphere exhibit comparatively li- mited variability in the ratios shown, overlapping appreciably with the MORB values. We compare predictions of a few models (curves in Fig. 4) with these data. Here, we assume that lithospheric thickness is 7 km for zero-age seafloor and thickens in proportion to the square root of age (e.g., thickness is ~90 km beneath the recent Hawaiian islands). We consider mean excess mantle temperatures of DT=0, 100, and 200 8C and two starting compositions: a mixture of EM (isotopically similar to EM2) and DM (/ EM|/ DM=0.1|0.9), and a mixture of all three lithologies (/ EM|/ PX|/ DM=0.02|0.08|0.9). Fig. 5. Isotope ratios of basalts from mid-ocean ridges (green) and the same ocean island groups as in Fig. 4. Dashed curves show calculations using the same source compositions as in Fig. 4. Solid (gray) curves show results for a different EM end-member, similar to EM1. Numbers indicate fraction of EM in the mantle (/ EM) with / DM = 0.9; note that / PX = 1/ DM/ EM. Large open circles show assumed isotope ratios of each mantle component. The dashed curves are broadly consistent with the Easter (red), Canary (brown), Galápagos (dark blue), and Iceland (black) hotspot trends. Solid curves would better predict the Cook-Austral (light blue) trend if PX began melting deeper than EM1. Like those of many ocean islands, the trends of the Society (white), Samoa (orange), Hawaiian (purple), and Pitcairn (yellow) data could be better explained by mixing of EM with a material having less radiogenic Pb (not shown) than the pyroxenite composition shown. This source could be a different PX, a fifth end-member, such as bCQ [67] or bFOZOQ [5], or a mixture of the two. G. Ito, J.J. Mahoney / Earth and Planetary Science Letters 230 (2005) 29–46 Models predict magma composition to be most sensitive to both mantle temperature and starting composition for older plate ages, where F max is relatively low, and least sensitive to these variables for younger plates, where F max is relatively high. In addition, predicted compositions are always most MORB-like on younger seafloor. It is notable that the model magma compositions encompass a large fraction of the total Nd–Sr–Pb isotopic and La/Sm range observed in OIBs globally with changes in only two model variables (lithospheric thickness and temperature) and with only two starting mantle compositions. The observed Pb isotope ratios in detail show a maximum total range of composition near seafloor ages of 20–40 m.y., with lower variability at both younger and older seafloor ages. Models successfully explain this general behavior and do so because PX is predicted to largely control the Pb isotope signature at the intermediate seafloor ages, with DM and EM becoming increasingly important at the younger and older ages, respectively. We also note that the low 208 Pb / 206Pb ratios of Hawaii could be predicted with an EM source with lower 208Pb / 206Pb, more similar to EM1 (see also Fig. 5). Finally, we illustrate the importance of mantle flow. Most of the curves shown in Fig. 4 assume mantle plume flow Eq. (3); however, the dashed curves assume mid-ocean ridge flow (U( P)=1 and DT=0). At zero seafloor age, these curves fall within the range of observed mid-ocean ridge compositions. They illustrate the natural tendency for mid-ocean ridge flow to produce melts with higher mean extents of melting and to more heavily sample DM. 4.2. OIB and MORB isotopic arrays Melting of a heterogeneous mantle also may contribute to the formation of elongate barraysQ in isotope space observed in OIB and MORB data [2,5,67]. Such arrays suggest important mixing processes between distinct isotopic end-members, but the mixing processes are not well understood. One possibility is that mixing occurs primarily in the solid state as a consequence of mantle convection [5,67,68]. Alternatively, mixing trends can arise by the progressive melting of a heterogeneous mantle [32,38,48]. Both processes may be occurring, but 39 here we show that melting of a heterogeneous mantle alone can account for a large fraction of the observed isotopic variability in such arrays. Predicted and observed isotope arrays are displayed in Fig. 5. For starting mantle mixtures of only EM and DM, isotope ratios are predicted to begin near those of EM and then trend toward DM values with increasing extent of partial melting. Likewise, starting mixtures of only PX and DM yield mixing arrays between PX and DM values. For mixtures of all three lithologies, magma compositions start near EM, trend toward PX, and then turn toward DM values. Although details of the curves depend on the precise nature of the model mantle source, source end-members representing only four isotopic starting compositions yield predictions that largely encompass the OIB and MORB data; moreover, the predicted trends are broadly consistent with many of the observed trends [e.g., Samoa (orange dots), Pitcairn (yellow), Easter (red), Canary (brown), Iceland (black), Galápagos (blue), and Cook-Austral (light blue)]. An observation that appears to be diagnostic of the melting process that we are simulating is the apparent bend in the Hawaiian hotspot (purple) array, from moderate 206Pb/204Pb (18.5–19) towards low 206Pb/204Pb (V18) at moderate values of 87 Sr/ 86 Sr (0.7035–0.7040) and 143 Nd/144Nd (0.5129–0.5130). Nevertheless, many of the observed arrays would be matched better by including a source similar to our PX end-member, but with lower 206Pb/204Pb and 208Pb/204Pb, resembling the proposed bcommonQ (C or FOZO) isotopic end-member [5,67]. We do not explicitly model this end-member, but we anticipate that the process that we are simulating could explain the isotopic trends toward this composition found in many data arrays, including MORB data [67], if this end-member usually begins melting shallower than EM and PX, but deeper than DM. In any case, it is clear that a large portion of the mixing implied in OIB isotopic arrays could be accomplished by the partial melting process. Moreover, magma compositions in Fig. 4 can be seen to extend well into the MORB range for cases with high F max; thus, as noted in the previous section, the melting process alone can contribute significantly to the isotopic and incompatible-element differences between OIBs and MORBs. 40 G. Ito, J.J. Mahoney / Earth and Planetary Science Letters 230 (2005) 29–46 5. Discussion 5.1. Incomplete magma mixing factor f i . This factor is 1 for peridotite (EM and DM) but b1 for PX. Setting f PX=0.15, for example, implies that 100% melting of PX yields magma compositions equivalent to melting peridotite by 15%. An important limitation to our method is that we only model complete mixing of melts generated between the base of the melting zone and a specified minimum pressure ( P 2). What we are therefore effectively assuming when comparing predictions with observations (Figs. 4 and 5) is that individual lavas or magma batches (commonly represented by data for a single sample) from a hotspot represent mixtures of melts aggregated from the base of the melting zone to different heights. Only in this way does our model address the possibility of incomplete mixing of melts derived from different parts of the melting zone. In addition, if incomplete mixing of melts contributes to the compositional variability within a group of lavas from a hotspot erupting on seafloor of a given age, the predicted composition for the corresponding seafloor age (Fig. 4) is most relevant to the average or median composition. We therefore expect lava compositions to scatter about the individual predicted compositions at a given seafloor age. 5.2. Mean degree of melting and importance of pyroxenite The above restrictions noted, our calculations reveal some potential complexities in relationships between isotopes, incompatible elements, and extent of melting that may not have been recognized without this or a similar quantitative treatment. Incompatible element concentrations are known to be related, in part, to the mean degree of melting F̄. We define F̄ as a weighted average, Z P2 Fi ð PÞ2 U ð PÞdP X P1 F¼ F̄ fi /i Z P2 : ð6Þ i Fi ð PÞU ð PÞdP P1 Most relations between magma composition and F̄ in the current literature pertain to peridotite melting; however, pyroxenite is likely to melt much more extensively than peridotite. To define a quantity F̄ that can be related to peridotite melting, we incorporate a Fig. 6. Predicted variations with mean extent of melting as defined in text. DM is 90% of the mantle (/ DM=0.9). Numbers indicate the fraction of EM in the mantle, and PX composes the remaining portion. Here, the isotopic composition of EM is EM2. G. Ito, J.J. Mahoney / Earth and Planetary Science Letters 230 (2005) 29–46 Intuitively, the mean extent of melting is always less than the total extent of melting F imax. For reference, if mantle flow U and productivity BF/BP were uniform and only one lithology were present, F̄ would equal F max/2. Mixtures of only the two max peridotite lithologies (EM and DM) yield F̄bF EM /2 because BF/BP increases with melting and because max max F DM bF EM (Fig. 6). With our assumption of complete mixing, calculations predict the most extreme EM-type isotopic signatures (e.g., 87Sr/86SrN0.7050) to be present only at low extents of melting (F̄b ~ 0.03 max and F EM b0.1 for / EMj/ DMj/ PX=0.1j0.9j0; see Fig. 6). It may be possible to test these predictions using major element compositions of lavas possessing strongly EM1- or EM2-type isotopic compositions, although careful consideration should be taken if EMtype peridotite contains material derived from subducted marine sediments. The presence of pyroxenite adds some complexity. First, pyroxenite drastically increases F̄ for the same max F EM (Fig. 6a), yielding strongly HIMU-type isotopic compositions (e.g., 206Pb/204PbN20) at appreciable values of F̄ (0.04–0.06). Second, our calculations predict more complex correlations between isotope ratios, La/Sm, and F̄ when pyroxenite is present. For example, Sr and Pb isotopic compositions are predicted to change minimally over a wide range of F̄ (0.02–0.08), whereas La/Sm decreases gradually by 30–55%. Also, radiogenic Pb content both increases (for F̄b ~ 0.02) and decreases (for F̄ N ~ 0.06) with increasing F̄ and decreasing La/Sm. These outcomes are simple to understand in the context of melting of a heterogeneous mantle, but they highlight the potential complexities that should be considered in future efforts to relate isotope ratios, incompatible element concentrations, and extent of partial melting. 5.3. Mantle plume flow and thickness, and implications for spatial variations at hotspots As we have illustrated, mantle flow can strongly influence magma compositions. This prediction allows for the possibility that spatial variations in mantle flow can contribute to geographic variations in the geochemistry of hotspot volcanoes [69–71] in the absence of spatial variations in mantle composition. For example, in the case in which a mantle plume is rising beneath a mid-ocean ridge, lavas erupted 41 directly over the mantle plume will be most influenced by mantle plume flow, which can enhance the melting of EM and PX relative to DM. On the other hand, lavas erupting along the ridge axis, well away from the plume, will be most influenced by mid-ocean ridge flow and will tend to possess compositions more like normal MORB, all else being equal. Could this type of difference in mantle flow contribute significantly to along-axis geochemical gradients, such as those documented for the Iceland–MAR system [72,73]? If so, the effects of mantle plume flow in enhancing magmatic concentrations of incompatible elements and EM and PX isotopic signals would have to overcome the opposing effect of elevated mantle plume temperatures to increase the extent of partial melting. The ability of plume flowUas we have treated itUto enhance EM and PX melting depends on the characteristic thickness H of plume material flowing out of the melting zone (Fig. 2d) relative to the thickness of the melting zone. So far, we have considered a single value of H and compared solutions with and without plume flow for the same mantle temperatures and lithospheric thicknesses (Figs. 3 and 4). To address plume–ridge interaction, we modify these parameters. We consider an average potential temperature of T p=1450 8C, a lithospheric thickness of 30 km (i.e., the thickness of the Icelandic crust is 30–46 km [74,75]), and we vary H. To simulate mid-ocean ridge melting, we assume T p=1350 8C, a lithospheric thickness of 7 km, and uniform mantle flow. We then calculate La/Sm, 87 Sr/87Sr, and 206Pb/204Pb for each case and then take the difference between the two cases, DLa/Sm, D87Sr/87Sr, and D206Pb/204Pb. These results are compared with the difference in median values of the above ratios for Iceland and for sections of the MAR not influenced by hotspots. Fig. 7 illustrates how increasing H relative to the thickness of the DM melting zone H DM (DM solidus depth for T p=1450 8C minus the lithospheric thickness of 30 km gives H DM=63 km) increases DLa/Sm, D87Sr/87Sr, and D206Pb/204Pb. Plume flow leads to lower values of these ratios than does midocean ridge flow when H/H DMb1.3 for the Sr and Pb isotopes and when H/H DMb1 for La/Sm. Plume flow produces greater ratios than does mid-ocean ridge flow when H/H DMN1–1.3. For these relatively 42 G. Ito, J.J. Mahoney / Earth and Planetary Science Letters 230 (2005) 29–46 enhancement of EM and PX [36,69,72] in the Icelandic hotspot magmas compared with the normal MAR magmas. Indeed, the trace-element inversions of [77] have already suggested that rapid plume flow deep in the melting zone is important beneath Iceland. Studies that incorporate 3D mantle flow and melting are needed to test more completely the importance of each on spatial geochemical variations. In addition, although the current models do not address the elevated 3He/4He ratios of Iceland basalts, future efforts to do so will have to consider a high 3He/4He component and at what depth it is likely to begin melting relative to the other lithologies. Finally, we hope that the above illustration of the importance of plume thickness H will help motivate future geophysical studies to place improved bounds on H at Iceland and other hotspots. 5.4. Implications for large-scale mantle structure Fig. 7. Differences in La/Sm, 87Sr/86Sr, and 206Pb/204Pb between a plume model (T p=1450 8C, lithospheric thickness of 30 km, plumedriven mantle flow) and a mid-ocean ridge model (T p=1350 8C, lithospheric thickness of 7 km, uniform mantle flow) increase with plume layer thickness, H. In both models, / DM=0.9, the amount of EM is labeled, and PX makes up the remaining portion. Left axes show the differences normalized by the difference between median Iceland values (La/Sm=1.96; 87Sr/86Sr=0.7032; 206Pb/204Pb=18.49) and median MAR values (La/Sm=1.0; 87 Sr/ 86 Sr=0.7027; 206 Pb/204Pb=18.33). thick plume layers, predicted differences in the above ratios can be appreciable fractions of the observed differences between the Iceland and MAR median values. A recent seismological study suggests that the layer of plume material beneath Iceland is ~200 km [76], whereas a mean excess plume temperature of 100–200 8C [76] implies that the DM melting zone extends 60–100 km beneath the lithosphere. It is thus possible that the plume flow of a heterogeneous mantle can contribute substantially to the apparent It is important to note that the model calculations that we have used for comparison with MORB and OIB data assume only small variations in the starting source compositions. The amount of DM was fixed at 90%, and we varied only the proportions of EM and PX. Yet, in many cases, melts derived from this restricted range of source mixtures span almost the full range of hotspot La/ Sm and Nd–Pb–Sr isotopic compositions and often extend well into the MORB range. The general implication is that mantle plumes may not be as compositionally different from MORB source mantle as commonly believed. In turn, this leads to the question of whether there is a need for compositional layering in the mantle to account for the geochemical differences between OIBs and MORBs [22], and if so, how significant is the distinction between mantle layers, at least in the portion of the mantle that feeds OIB and MORB volcanism. We leave these questions to our companion study [78]. 6. Conclusions We have taken a rudimentary approach to simulating flow and melting of a heterogeneous mantle. We assume that the mantle is composed of G. Ito, J.J. Mahoney / Earth and Planetary Science Letters 230 (2005) 29–46 three source materials (EM, PX, and DM) with distinct trace-element and isotopic compositions and with different melting functions. Magma composition is assumed to be governed by the perfect mixing of fractional melts. Magma composition is also controlled by the rate at which the residue flows through the melting zone as a function of depth. For an isoviscous mantle plume, this rate is predicted to be a maximum at the base of the plume layer and to decrease upward toward the lithosphere, in contrast to a uniform flow profile expected beneath mid-ocean ridges. A compilation of OIB data shows that incompatible-element ratios (e.g., La/Sm) and Sr, Nd, and Pb isotope ratios are most variable and extend to compositions most distinct from those of average MORB in OIBs erupted on lithosphere older than ~16 m.y. Ocean island volcanoes erupting on younger seafloor exhibit much more limited variability, and their compositional range overlaps more with that of MORBs. These general systematics are explained well by our calculations, in which thick lithosphere limits the maximum extent of melting and the amount of DM melting to low values, and therefore magma composition is very sensitive to (a) differences in mantle temperature and (b) the relative proportions of EM and PX. Decompression beneath thinner lithosphere or younger seafloor more extensively melts all three source materials and therefore minimizes differences in magma composition. Our models can also explain many aspects of OIB isotopic arrays if individual OIB lavas (or more realistically, magma batches) represent melts extracted at different depths in the melting column. In addition to predicting a wide range of OIB compositions, the models predict compositions that extend well into the MORB range, all with the same starting mantle source composition. Relative to mid-ocean ridge flow, mantle plume flow can enhance the incompatible element concentration and isotopic expression of EM and PX if the plume thickness exceeds the thickness of the DM melting zone by ~30%. Thus, differences in mantle flow, in addition to lithospheric thickness, can lead to geochemical differences between intraplate OIBs and MORBs. Differences in mantle flow may also contribute to geographic variations in magma composition at hotspots, including hotspots near or at midocean ridges. All of these results suggest that mantle 43 plume material may be more similar in composition to MORB source mantle than previously thought. Our calculations, however, are limited to simulating the mean compositions of whole melting zones. More sophisticated 3D models are needed to evaluate more completely the importance of variable flow and melting of a heterogeneous mantle on correlations among incompatible elements, isotope ratios, and mean extent of melting on intra-hotspot geochemical variations and on the differences between hotspots and mid-ocean ridges. Acknowledgements We appreciate the thorough reviews provided by Marc Hirschmann, Yaoling Niu, and Paula Smith. We thank R. Batiza, C. Lesher, and J. Sinton for discussions during the earlier stages of this work. This project was funded by NSF grants OCE02-21889 and OCE00-04498. 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