{'fraction_non_alphanumeric': 0.03377017624936933, 'fraction_numerical': 0.028152413094263945, 'mean_word_length': 4.6014439404374565, 'pattern_counts': {'":': 0, '<': 26, '<?xml version=': 0, '>': 10, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 2, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Geochemical and Fluid Dynamic Investigations Into the Nature of Chemical Heterogeneity in the Earth's Mantle

Variations in the abundances of elements and radiogenic isotopes in mantle derived peridotites and volcanic rocks are chemical integrals over time, space, and process, which ultimately contain information about the role of convection in the earth's mantle in creating, maintaining, and destroying geochemical heterogeneities. Successful inversion of these integrals requires extensive knowledge of the geochemical behavior of elements, the length scales of chemical variability, the evolution with time of geologic systems, the physical properties of mantle rocks, and the driving forces of phenomena which govern heat and mass transport in a dynamic earth. This dissertation attempts to add to this knowledge by examining the trace element and isotope geochemistry of mantle peridotites and oceanic island basalts, and by studying aspects of the flow of viscous fluids driven by thermal buoyancy. The trace element and isotopic systematics of peridotites and associated mafic layers from the Ronda Ultramafic Complex, southern Spain (Chapter 2), provides information bearing on the geochemical behavior of the highly incompatible elements U, Th, and Pb in the mantle, and on the length scales of geochemical variability in a well exposed peridotite massif. Garnet is demonstrated to be a significant host for U in the mantle, and together with clinopyroxene, these two minerals control the abundances and partitioning relationships of U and Th during the melting of anhydrous peridotite. Clinopyroxene, plagioclase, and to a lesser extent garnet are hosts for Pb in mantle peridotite; however, the role of trace sulfide may exert some control over the abundance and partitioning of Pb in some samples. Due to the possibility that Pb is partitioned into sulfide, the U/Pb, Th/Pb, and Ce/Pb ratios measured in clinopyroxene are likely to be higher than the bulk rock. U-Pb age systematics of garnet-clinopyroxene pairs from Ronda peridotites and mafic layers indicate Pb isotopic equilibrium in these samples up to 20-50 Ma ago. The Pb-Pb systematics of garnetand spinel-facies peridotites and mafic layers indicate a heterogeneity on the order of 3 Ga old. This Pb isotope signature may have been created within the massif 3 Ga ago, or may have been metasomatically imprinted on the massif 1.3 Ga ago by basaltic melts with island arc affinities. The isotopic evolution of Ronda is consistent with an origin as ancient (3 Ga) MORB source mantle which experienced a partial melting event at 1.3 Ga ago, and was subsequently incorporated into the subcontinental lithosphere. The very low U, Th, and Pb concentrations in depleted peridotite indicate that recycled crustal materials, with U-Th-Pb concentrations 102-104 times higher than peridotite, will have a larger influence on the isotopic composition of Pb in the mantle than on the Sr and Nd isotopic composition. An investigation of the trace element and isotopic compositions of clinopyroxenes in peridotite xenoliths from Savaii, Western Samoa and Tubuai, Austral Islands (Chapter 3) reveals geochemical signatures which are not present in basalts from these islands, due to the inherent averaging of melting processes. The data indicate similarities in the melting and melt segregation processes beneath these isotopically extreme islands. Samples with LREE depleted clinopyroxenes, with positive Zr and negative Ti anomalies, are the result of polybaric fractional melting of peridotite in the garnetand spinel lherzolite stability fields, with the Savaii samples having experienced a larger mean degree of melting than the Tubuai samples. The extreme fractionation of HREE in the Savaii samples requires that they have melted to the clinopyroxene-out point (about 20%) while retaining residual garnet; the low concentrations of HREE in these same samples requires a further 10-20% melting in the spinel lherzolite stability field. The extremely high total degrees of melting experienced by the Savaii samples (33-42%), as well as the high degree of melting in the garnet lherzolite stability field, suggests a mantle plume origin for these xenoliths. A large majority of the xenolith clinopyroxenes from both Savaii and Tubuai are LREE enriched to varying degrees, and many samples display significant intergrain trace element heterogeneity. This highly variable yet systematic heterogeneity was the result of metasomatism by percolating melts undergoing chromatographic trace element fractionation. The trace element compositions of some LREE enriched clinopyroxenes are consistent with the percolating melt being typical oceanic island basalt. The clinopyroxenes with the highest LREE concentrations from both islands, which also have very low Ti and Zr concentrations and large amounts of grain-boundary hosted Ba, require that the percolating melt in these cases had the trace element signature of carbonatite melt. The isotopic composition of one of these "carbonatitic" samples from Tubuai is similar to basalts from this island. The isotopic composition of clinopyroxene in a "carbonatitic" sample from Savaii records 87Sr/86Sr and 14 3Nd/144 Nd values of .71284 and .512516 respectively, far in excess of the most extreme Samoa basalt values (87 Sr/86Sr=.70742, 143Nd/144Nd=.51264). These "carbonatitic" signatures indicate the presence of volatilerich, isotopically extreme components in the mantle beneath Tubuai and Savaii, which likely have their origins in recycled crustal materials. The Re-Os isotope systematics of oceanic island basalts from Rarotonga, Savaii, Tahaa, Rurutu, Tubuai, and Mangaia are examined (Chapter 4). Os concentration variations suggest that olivine, or a low Re/Os phase associated with olivine, controls the Os concentration in basaltic magmas. The Savaii and Tahaa samples, with high 87Sr/86Sr and 207Pb/204Pb ratios (EMII), as well as basalts from Rarotonga, have 1870s/1860s ratios of 1.026-1.086, within the range of estimates of bulk silicate earth and depleted upper mantle. The basalts from Rurutu, Tubuai, and Mangaia (Macdonald hotspot), characterized by high Pb isotope ratios (HIMU), have 1870s/1860s ratios of 1.117-1.248, higher than any estimates for bulk silicate earth, and higher than Os isotope ratios of metasomatized peridotites. The high 1870s/1860s ratios indicate the presence of recycled oceanic crust in the mantle sources of Rurutu, Tubuai, and Mangaia. Inversion of the isotopic data for Mangaia (endmember HIMU) indicate that the recycled crustal component has Rb/Sr, Sm/Nd, Lu/Hf, and Th/U ratios which are very similar to fresh MORB glasses, and U/Pb and Th/Pb ratios which are within the range of MORB values, but slightly higher than average N-MORB. These results indicate that the low-temperature alteration signature of altered oceanic crust may be largely removed during subduction, and that oceanic crust was recycled into to the lower mantle source of the Macdonald hotspot plume. Furthermore, the high 1870s/ 1860s ratios of the Tubuai and Mangaia basalts indicates that percolation through depleted mantle peridotite (1870s/1860s= 1.00-1.08), observed to occur in the Tubuai xenoliths, had little influence on the composition of the erupted basalts. A fluid dynamic model for mantle plumes is developed (Chapter 5) by examining a vertical, axisymmetric boundary layer originating from a point source of heat, and incorporating experimentally constrained rheological and physical properties of the mantle. Comparison of linear (n=l) and non-Newtonian (olivine, n=3) rheologies reveals that nonNewtonian plumes have narrower radii and higher vertical velocities than corresponding Newtonian plumes. The non-Newtonian plumes also exhibit "plug flow" at the conduit axis, providing a mechanism for the transport of deep mantle material, through the full depth of the mantle, in an unmixed state. Plumes are demonstrated to entrain ambient mantle via the horizontal conduction of heat, which increases the buoyancy and lowers the viscosity of mantle at the plume boundary. Streamlines calculated from the fluid dynamic model demonstrate that most of the entrained mantle originates from below 1500 km depth. Parameterization of the entrainment mechanism indicates that the factional amount of entrained mantle is lower in stronger, hotter plumes due to their higher vertical velocities. Examination of the global isotopic database for oceanic island basalts reveals the presence of a mantle component (FOZO), common to many hotspots worldwide, characterized by depleted 87Sr/86Sr and 143Nd/144Nd, radiogenic 206,207,208Pb/204Pb, and high 3He/4He. This component is isotopically distinct from the source of MORB; thus, with the exception of ridge centered hotspots such as Iceland and the Galapagos, upper mantle does not appear to be a component in most hotspots, in agreement with entrainment theory. The combined fluid dynamic and isotopic results indicate that both FOZO and the enriched mantle components (EMI, EMII, and HIMU) are located in the lower mantle. Furthermore, high 3He/4He in FOZO preculdes an origin for FOZO-bearing plumes in a thermal boundary layer at 670 km depth in the mantle. Since a 670 km thermal boundary layer would be replenished by the downward motion of the upper mantle, an origin for FOZO at 670 km would require either 1) a high 3He/4He signature in the MORB source, or 2) entrainment of MORB mantle into intraplate plumes, neither of which is observed in the OIB isotope data. This indicates that the 670 km discontinuity is not a barrier to mantle convection. The preservation of isotopically different upper and lower mantles does not require layered convection, but is probably the result of an increasing residence time with depth in the mantle, possibly caused by an increase in the mean viscosity of the mantle with depth. Thesis Supervisor: Stanley R. Hart Senior Scientist Woods Hole Oceanographic Institution

The trace element and isotopic systematics of peridotites and associated mafic layers from the Ronda Ultramafic Complex, southern Spain (Chapter 2), provides information bearing on the geochemical behavior of the highly incompatible elements U, Th, and Pb in the mantle, and on the length scales of geochemical variability in a well exposed peridotite massif. Garnet is demonstrated to be a significant host for U in the mantle, and together with clinopyroxene, these two minerals control the abundances and partitioning relationships of U and Th during the melting of anhydrous peridotite. Clinopyroxene, plagioclase, and to a lesser extent garnet are hosts for Pb in mantle peridotite; however, the role of trace sulfide may exert some control over the abundance and partitioning of Pb in some samples. Due to the possibility that Pb is partitioned into sulfide, the U/Pb, Th/Pb, and Ce/Pb ratios measured in clinopyroxene are likely to be higher than the bulk rock. U-Pb age systematics of garnet-clinopyroxene pairs from Ronda peridotites and mafic layers indicate Pb isotopic equilibrium in these samples up to 20-50 Ma ago. The Pb-Pb systematics of garnet-and spinel-facies peridotites and mafic layers indicate a heterogeneity on the order of 3 Ga old. This Pb isotope signature may have been created within the massif 3 Ga ago, or may have been metasomatically imprinted on the massif 1.3 Ga ago by basaltic melts with island arc affinities. The isotopic evolution of Ronda is consistent with To Tracy, who had the hardest job of all, and handled it with grace under pressure And to my mother Karen, for her unshakable optimism Introduction The geochemical variability expressed in the trace element and isotopic signatures of mantle derived peridotites and basalts is the end product of the processes of mantle mixing, melting, and melt segregation acting over various spatial and temporal scales. In addition to these processes, surficial weathering, mass transport, and alteration may contribute to the geochemical signatures of mantle derived materials if crustal components are recycled into the deep mantle. In attempting to relate specific geochemical signatures to specific mantle processes, one must have a firm understanding of the mechanisms by which these different processes influence the distribution of different elements over the spatial and temporal scales observable in mantle derived rocks. This dissertation attempts to place geochemical observations in mantle peridotites and basalts into the context of fluid dynamic processes in the earth's mantle, and thereby forge a better understanding of the ways in which physical process determine chemical signatures.
Chapter 2 applies a long-standing geochemical tool, the U-Th-Pb isotopic system, to an examination of the scales of chemical heterogeneity in peridotites and mafic rocks from the Ronda Ultramafic Complex, Southern Spain. Though the isotopic composition of Pb in the mantle was first shown to be demonstrably heterogeneous in 1964 (Gast et al., 1964), the application of the U-Th-Pb system has lagged far behind the pace of Sr and Nd isotopic studies of mantle peridotites. As a result, we know little about the geochemical behavior of these elements in the mantle, complicating the interpretations of the Pb isotopic signatures of basaltic rocks (Tatsumoto, 1966;Gast, 1969;Sun, 1980). The low concentrations (ppb) of U, Th, and Pb in the Ronda peridotites indicates that the Pb isotopic composition of the mantle will be strongly influence by any recycled crustal components. Compared with the more limited isotopic variability observed in other ultramafic massifs (Polv6 and Allegre, 1980;, the large degree of isotopic heterogeneity at Ronda, present at both small and large scale lengths, suggests a residence in the subcontinental lithosphere for about 1.3 Ga. The isotopic evolution of Ronda is consistent with an origin as ancient (>1.3 Ga) MORB source mantle incorporated into the subcontinental lithosphere 1.3 Ga ago.
Chapter 3 examines the trace element characteristics of clinopyroxene in peridotite xenoliths from the islands of Savaii (Western Samoa, Samoa hotspot) and Tubuai (Austral Islands, Macdonald hotspot) which were collected by the author during the fall of 1990.
Basaltic rocks from the Samoa and Macdonald hotspots are characterized by extreme isotopic compositions ( 87 Sr/ 86 Sr to .7075,207 Pb/204Pb to 15.70 (EMII) at Tutuila, American Samoa ; 206 Pb/2 04 Pb to 21.80 (HIMU) at Mangaia, Cook Islands , Chapter 4), and so the geochemical signatures of these xenoliths were expected to place constraints on the origins of these endmember signatures and the melt generation/segregation processes operative in their plume sources.
The trace element characteristics of LREE depleted xenoliths indicate an origin as residues of polybaric fractional melting in the stability fields of garnet and spinel lherzolite.
Compared with abyssal peridotites , the high degrees of melting in the garnet lherzolite stability field experienced by the Savaii samples (up to 22%), coupled with their high total degrees of melting (33-42%) suggest a mantle plume origin for these xenoliths. The extreme variability of LREE enrichment in most of the xenoliths is consistent with metasomatism by percolating basaltic and carbonatitic melts which were undergoing chromatographic trace element fractionation . The isotopic compositions of clinopyroxenes with "carbonatitic" trace element patterns from both Savaii and Tubuai indicate the presence of volatile-rich, isotopically extreme components in the Samoa and Macdonald mantle plumes. These components likely have their origins in recycled crustal materials.
Chapter 4 applies a relatively new geochemical tool, the Re-Os isotopic system, to the analysis of oceanic island basalts with extreme isotopic signatures for 87 Sr/86Sr (EMII, Savaii,Western Samoa and Tahaa, Society Islands) and 206 , 20 7 208 Pb/204pb (HIMU, Rurutu, Tubuai, and Mangaia, Cook-Austral Islands). Re and Os are both chalcophile (affinity for sulfide) and siderophile (affinity for metal) elements. Os is strongly depleted in basaltic melts compared with Re, and so basaltic melts have much higher Re/Os ratios than residual peridotites (Morgan, 1986). As a result of the different geochemcal properties of Re and Os compared with other parent-daughter systems, the analysis of Os isotopes in the South Pacific OIBs was expected to yield new constraints on the origins of these isotopically extreme mantle compositions. The 187 0s/ 186 0s ratios of the Savaii and Tahaa basalts lie within the range of estimates for primitive and depleted mantle, but the high 187 0s/ 186 0s ratios in the HIMU basalts indicate the presence of recycled oceanic crust in their mantle sources, in agreement with previous studies Hofmann and White, 1982), and indicating that subducted oceanic lithosphere is recycled into the lower mantle. In addition, the homogeneity of the Os isotope ratios in the basalts from Tubuai and Mangaia require that melt migration through depleted mantle had an insignificant effect on the chemistry of these basalts. The identification of a low 87 Sr/ 86 Sr-high 206 ,2 0 7 , 208 Pb/ 204 Pb signature with recycled oceanic crust suggests its presence in the mantle sources of other oceanic basalts, including some high 2 06Pb/ 2 04Pb mid-ocean ridge basalts.
Chapter 5 examines the mantle mixing consequences of fluid flow in mantle plumes, modelled as the axisymmetric boundary layer rising from a point source of heat. By incorporating experimentally and theoretically constrained mantle properties, the effects of these properties on the entrainment of ambient mantle into plumes is evaluated. The entrainment theory indicates that the entrained mantle originates almost entirely from below 1500 km depth. The Sr-Nd-Pb-He isotopic database on oceanic basalts indicates the presence of a mantle component (FOZO) which is present in many hotspots from around the world. The results from entrainment theory, and the isotopic signatures of OIB confirm, that the entrainment of MORB source mantle (upper mantle) in mantle plumes is minimal (except for ridge centered hotspots), and that both FOZO and the enriched mantle components (EMI-EMII-HIMU) are located in the lower mantle. The combined geochemical and fluid dynamic results suggest that mantle plumes may not originate from a thermal boundary layer at 670 km depth, evidence which probably rules out layered convection.
Finally, the most important results of this research are integrated in Chapter 6. The low concentrations of the most incompatible elements in mantle peridotite indicate that the signature of recycled crustal components should be most clear in the isotopic signatures of Th, Pb and Sr. The unique properties of the U-Pb system, due to the existence of two parent-daughter systems in a single element-element pair, make this system a powerful tool for studies of mantle peridotites. The U-Pb (and Th-Pb) isotopic systematics of peridotites are very sensitive to resetting by recent melting and metasomatic processes, due to the incompatibility of these elements. However, the age information contained in Pb-Pb isochrons is more difficult to reset, requiring perfect homogenization, and thus the Pb-Pb system is more likely to contain ancient age information than other isotopic systems. Similar to the situation at mid-ocean ridges , fractional melting in mantle plumes requires that erupted melt products are integrated collections of small batches of melt generated throughout the plume. However, the abundance of LREE enriched xenoliths from oceanic islands indicates that melt extraction processes, and thus probably also melt mixing processes, are more efficient at mid-ocean ridges than at hotspots. As a result, the degree of chemical variability of the upper mantle cannot be evaluated from the equivalent variability in MORB, and thus the upper mantle may not be as "well mixed" as is often suggested (White and Schilling, 1978;Ito et al., 1987). Although mixing processes are likely to occur in mantle plumes, the expression of plume-ambient mantle mixing in the chemistry of hotspot basalts is complicated by the mixing processes of plume-lithosphere interaction Griffiths and Campbell, 1991) and melt segregation (McKenzie, 1984;Kenyon, 1990). A more detailed inversion of 12 OIB geochemistry to examine the chemical structures of mantle plumes requires a better characterization of plume-lithosphere interactions, and knowledge of the mechanisms of melt extraction from the mantle beneath ridges and hotspots, both employing well constrained rheological and physical parameters for the upper mantle. 13

Introduction
Geochemical studies of mantle derived basalts and peridotites have established the unequivocal existence of chemical heterogeneities in the earth's mantle which require that various segments of the mantle have evolved independently over time scales of up to several billions of years (Tatsumoto, 1966;Gast, 1969;Brooks et al., 1976) The most direct approach for examining the origins of these heterogeneities is through the study of mantle peridotites, either xenoliths erupted to the surface by igneous processes, or tectonically emplaced orogenic peridotite massifs. Orogenic peridotites offer the advantage of examining mantle geochemistry within its geologic context, and their large size facilitates direct observation of the scale of mantle heterogeneity.
Orogenic peridotite massifs (alpine, or high temperature peridotites) are large bodies, up to several hundred square kilometers, typically composed of 90 -95% lherzolite and harzburgite with up to 5-10% mafic rocks occurring as bands or layers within the peridotite. They are distinguished from ophiolite peridotites (low temperature peridotites) by the lack of an associated volcanic section. Major element studies of orogenic peridotites (Dick, 1977;Sinigoi et al., 1980;Quick, 1981;Sinigoi et al., 1983; have determined that they are residues from various degrees of partial melting at mantle pressures and temperatures (Kornprobst, 1969;Dickey, 1970;Obata, 1980). Their trace element characteristics are consistent with this interpretation, but also suggest histories more complicated than a single melt extraction (Frey, 1969;Loubet et al., 1975;Loubet and Allegre, 1979;Loubet and Allegre, 1982). With a few exceptions , the peridotites are almost exclusively depleted in the light rare earth elements (LREE) relative to the heavy rare earths (HREE) (Bodinier et al., 1988), and in this way are quite different from mantle xenoliths, which are dominantly LREE enriched .
The origins of mafic layers in alpine peridotites have proven enigmatic. In some cases, such as at the Lherz peridotite massif, some mafic rocks containing hydrous phases, which exhibit cross-cutting relationships with an earlier generation of anhydrous mafic layers, likely represent magma conduits associated with basaltic volcanism (Bodinier et al., 1987). The origins and age relationships of mafic layers at other peridotite massifs are not as clear, and they likely do not have a simple relationship to the peridotites (Loubet and Allegre, 1982;. Unlike the dominantly LREE depleted peridotites in which they occur, the mafic layers often exhibit a variety of REE patterns. Theories pertaining to the mafic layers suggest their origins as crystal cumulates from basic magmas , melts of peridotite and/or an earlier generation of mafic layers (Loubet and Allegre, 1982), and subducted oceanic crust deformed during mantle convection .
Isotopic studies of orogenic peridotites have demonstrated that significant isotopic heterogeneities exist on a variety of scale lengths (Menzies and Murthy, 1976;Polv6 and Allfgre, 1980;Richard and Allegre, 1980;. Isotopic compositions of peridotites display large ranges both within and between individual massifs. Isotopic results on mafic layers from some massifs have demonstrated heterogeneities of the same range as associated peridotites (Zabargad, Beni Bousera), while mafic rocks from other massifs (Lherz) display a limited heterogeneity (Polve, 1983;. Sm-Nd mineral isochrons from Ronda and Beni Bousera mafic rocks are believed to date the time of emplacement of the peridotite bodies into the crust (Polv6 and Allegre, 1980;Zindler et al., 1983;. The long-term chemical variability of the mantle is reflected in the large range of the radiogenic isotope ratios of Sr, Nd and Pb measured in basaltic rocks from oceanic islands (ex. , as well as Sr and Nd isotopic studies of mantle peridotites (Menzies and Murthy, 1980a,b;Stosch and Seck, 1980;. However, investigations of the U-Th-Pb isotopic system in mantle peridotites have been hampered by the very low concentrations of these elements in peridotite. As a result, we know little about the geochemical behavior and residence sites of U, Th, and Pb in the mantle. Pb isotope analyses of whole rock peridotites are likely to be dominated by extraneous contaminants (basaltic veinlets, alteration products, groundwater precipitates, etc.), as has been demonstrated for the Rb-Sr and Sm-Nd systems . Thus the analysis of purified mineral separates is the only way in which reliable Pb isotope data can be obtained on mantle peridotite samples. This strategy presents a substantial analytical challenge in two ways. First, a mineral separate must be prepared which is free of crustal U, Th and Pb; this is even more crucial than for Sr and Nd analysis, because of the order of magnitude lower U-Th-Pb concentrations (ppb, 10-9 grams/g) in the constitutent minerals. Second, analytical blanks must be reduced to a very low level for the chemical separation procedure, in order to minimize their contribution to these small quantities of U, Th and Pb. This is particularly challenging for Pb because of the pervasive nature of anthropogenic Pb contamination. Once these potential sources of contamination are characterized and eliminated, reliable U-Th-Pb data can be obtained on peridotite mineral separates.
The Ronda peridotite, a 300 km 2 orogenic peridotite located in the Betic Cordillera of southern Spain, has been the focus of numerous investigations (Dickey, 1970;Lundeen, 1978;Dickey et al., 1979;Obata, 1980;Obata, 1982;Zindler et al., 1983;, and is perhaps the most well studied of the orogenic peridotites. The massif is mineralogically zoned from garnet peridotite facies in the northwest, through spinel peridotite to plagioclase peridotite facies to the southeast and east (Fig. 1, from Obata, 1980), and it is likely that this zonation reflects the polybaric cooling history of the massif (Obata, 1980). Investigations by , Zindler et al. (1983), ,  and Reisberg et al. (1990) have demonstrated that the massif underwent a partial melting event at about 1.3 Ga. This melting event is reflected in the depletions of basaltic constituents (Ca, Al, Fe, Ti, Na) in the peridotites, as well as depletions in Nd/Sm and Re/Os which resulted in isochronous relationships between whole rock samples in the Sm-Nd and Re-Os systems. This event was contemporaneous with the formation of the mafic layers, as indicated by a whole rock Re-Os isochron for the mafic layers with an age of 1.3 Ga (Reisberg et al., 1990). A small portion of the eastern end of the massif was subject to a metasomatic infiltration at about 300 Ma . The massif was subsequently emplaced into the crust, and cooled past the Sm-Nd closure temperature at about 22 Ma (Zindler et al., 1983). The Ronda ultramafic complex thus represents a well studied location in which to investigate the geochemical behavior of U, Th and Pb in the mantle. In addition, the purposes of this study are: 1) to demonstrate the feasibility of obtaining accurate and reproducible U-Th-Pb data from mantle peridotite by analysis of mineral separates, avoiding the contamination problems known to disturb the incompatible element systematics of whole rocks; 2) to examine the scale of trace element and Pb isotopic heterogeneity; 3) to examine correlations among the isotopes of Sr, Nd, and Pb at a variety of scale lengths, 4) to document the isotopic character of the mafic layers, and 5) to further evaluate models proposed for the origins of heterogeneity in the mantle, and at Ronda in particular.

Sample Descriptions and Analytical Procedures
The locations of all the samples in this study are shown in Fig. 1. Samples R140-R148 and R163-R166 from the plagioclase facies were selected from mapped sections of interlayered peridotite and mafic layers (Fig. 3). The remaining samples with the designation Rxxx were selected to cover the geographic expanse of the massif; some of these samples have been studied by Obata (1980), , and . A selection of samples from the spinel and garnet facies studied by Reisberg   , Reisberg (1988), and   Figure 2. Detailed maps of the fine-scale sampling areas in the garnet and plagioclase facies, after Reisberg (1988). A) Garnet facies sampling area. Shaded line marks the location of a garnet-rich band. Sample 060R is located 15 cm above the band, sample 056R is located 35 cm below the band. Isotopic data from Reisberg et al. (1989) (Sr-Nd) and Reisberg et al. (1990) (1989) were also analyzed. Samples 050R, 051R, 056R, and 060R are from an area of closely spaced sampling around a garnet-rich band of lherzolitic composition (Fig. 2). In addition, U-Th-Pb isotope data obtained by Alan Zindler on plagioclase facies samples studied by  are included in this chapter. Samples 002R, 008R, 009R, 013R, and 016R are from a small scale traverse in the plagioclase facies, and are all located within 150 meters of each other (Fig. 2). Sample descriptions, petrographic details, and additional data can be found in these references.

122
To avoid contamination during processing, samples were wrapped in plastic wrap and cotton towels and crushed to 50-100 mesh size with a plastic mallet on a wooden block. Plagioclase, clinopyroxene and garnet were concentrated magnetically and purified by repeated crushing (with an agate mortar and pestle) and handpicking following procedures similar to . Great care was taken to avoid inclusions, films and subgrain boundaries known to host incompatible elements. At this point, several representative grains of clinopyroxene and garnet were selected for analysis by ion microprobe. Clinopyroxene separates were leached using two different procedures: 1) 2.5 N HC1 at 100 0 C for 1 hr, followed by 5% HF at room temperature for 20 minutes, followed by 2.5 N HCI at 100 0 C for 30 minutes; 2) 2.5 N HCl at 100 0 C for 1 hr, followed by a solution of 8N HNO 3 -0.6N HCl-0.05N HF at 100'C for 2 hr. Garnets were leached using the first procedure. The second leaching procedure was later developed to ensure the solution of U and Th during the leaching procedure, though repeat analyses of R238 cpx indicate that the different leaching procedures did not fractionate U, Th, and Pb (see below). Grains were rinsed with water between acid leaching steps, and finally the grains were rinsed five times with water and dried at 75 0 C. Plagioclase was leached in 2.5 N HC1 at room temperature for 30 minutes. All leaching steps used reagents cleaned by subboiling distillation in teflon stills, and took place in clean, filtered air. A detailed description of the procedures for the sample dissolution, separation of U, Th, and Pb, and mass spectrometry of these elements are given in the appendix.
REE and the trace elements Sc, Cr, Ti, Zr and Sr were analyzed in situ using a Cameca IMS 3f ion microprobe, employing energy filtering to exclude molecular ion interferences . Concentrations were determined through the use of working curves based on a set of well determined standards. Precision of the analyses is 5-15%, except for Ce and Nd in garnet, where precision is estimated at 40-50% and 20-40% respectively. All concentrations with errors greater than 50% are reported as maximum values.  Table 2a. Isotope dilution trace element data for mineral separates from Ronda peridotites and mafic layers. Mineral facies describes location of the sample (Fig. 1) in the plagioclase-lherzolite (PL), spinellherzolite (SL), and garnet-lherzolite (GL) facies as defined by Obata (1980). Sr and Nd data for all LDGO samples are from  and . U-Th-Pb data for LDGO plagioclase-facies samples are from Zindler (unpublished data).   Table 2b. Isotopic composition data for mineral separates from Ronda peridotites and mafic layers. Mineral facies describes location of the sample (Fig. 1) in the plagioclase-lherzolite (FL), spinel-lherzolite (SL), and garnet-lherzolite (GL) facies as defined by Obata (1980). Pb isotope data for garnets was normalized relative to the 207Pb/204Pb ratio of cpx from the same sample (see text). Sr and Nd data for all LDGO samples are from  and . U-Th-Pb data for LDGO plagioclase-facies samples are from Zindler (unpublished data).

La Ce Nd Zr Sm Eu Gd* Ti Dy Er Yb
Ronda Spinel Peridotites I  I  I  I  I  I  I  I  I  I  I  I  I

La Ce
Nd Zr Sm Eu Gd*Ti Dy Er Yb Figure 4. G) Chondrite-normalized trace element patterns for clinopyroxenes from Ronda mafic layers. R256 is from the garnet facies, the rest are from the plagioclase facies.

Trace element concentrations
Ion microprobe results are given in Table 1 and Zr is only about a factor of 3, but Cr varies by a factor of 7. There is a large variation in Sr in cpx from both peridotites and mafic layers, but this is related to the partitioning of Sr into plagioclase in some of the samples (peridotites R25, R142, R145, R163; mafic layers R140, R141), though in most of the samples from the plagioclase facies studied by

U-Th-Pb Isotopic Data
In order to assess the accuracy of the U-Th-Pb concentrations, clinopyroxene separates from peridotite R238 and mafic layer R301 from the spinel facies were each split into two fractions and leached by different techniques: CPX#1) 2.5 N HCl-100 0 C-60 min.; 5% HF-25 0 C-20 min.; 2.5 N HCl-100 0 C-30 min.
CPX#2) 8N HNO 3 -0.6N HCl-0.05N HF mixture at 100 0 C for 2 hours In both cases, CPX#1 was leached so that about 10% of the sample was dissolved away, while CPX#2 experienced 30% partial dissolution. As shown in  Table 2). In this case, the two analyses for each sample correspond to different magnetic fractions of clinopyroxene, with the first analyses (cpx 1) corresponding to the more magnetic fractions. All of these aliquots were of very high quality, and leached using leaching method #2. However, during leaching, the more magnetic fractions experienced about 5-10% partial dissolution, whereas the less magnetic fractions were partially dissolved to 15-30% using exactly the same procedure. The reason for this is unclear. However, based on the difference in the Pb isotopic compositions of the pairs for each sample, it would seem that the different magnetic fractions may be slightly heterogeneous. This explanation is contrary to the work of , who demonstrated that different magnetic fractions of clinopyroxene from sample 407R were in Sr and Nd isotopic equilibrium. Data for the U-Th-Pb system is given in Table 2 and plotted in Fig. 5. Large variations in the abundances of these elements are evident: Pb varies from 8 to 357 ppb, U varies from <1 to 78 ppb, and Th varies from <1 to 286 ppb. For the plagioclase and spinel peridotite cpx, the U and Pb concentrations are similar to cpx from other orogenic peridotite massifs studied by , as well as cpx in xenoliths from San Carlos  and Dish Hill . The garnet peridotite cpx have Pb concentrations similar to some samples reported by (Kramers et al., 1983) and (Cohen et al., 1984), but are generally lower than cpx concentrations reported in other studies (Zartman and Tera, 1973;Kramers, 1977;Kramers, 1979). The Th analyses of Kramers (1977) are much higher than concentrations for Ronda cpx, but this may be due to the autolithic nature of those cpx from kimberlite. U concentrations are distinctly lower than cpx analyses reported by Kramers (1979) and fission track results (Kleeman et al., 1969;Haines and Zartman, 1973 Figure 6c. Sr-Pb diagram for clinopyroxenes separated from Ronda peridotites and mafic layers, relative to the field of oceanic basalts

Pb/ Pb
Figure 6d. Nd-Pb isotope diagram for clinopyroxenes separated from Ronda peridotites and mafic layers, relative to the field of oceanic basalts  and references therein). Samples are from garnet facies (squares), spinel facies (circles), plagioclase facies (triangles), and mafic layers (plusses). Several sample from Ronda lie outside the field of oceanic basalts; some spinel and garnet facies have higher 143Nd/144Nd than MORB, and several plagioclase facies samples have lower 143Nd/144Nd than HIMU basalts from Mangaia. Hatched lines enclose data for samples from the small scale sampling areas in the garnet and plagioclase facies. Analytical errors are smaller than the size of the symbols.
products. The low concentration of Pb in some plagioclase facies samples (peridotites R25, R142, R145, R163, 404R; mafic layers R140, R141) may be attributed to partitioning of Pb into plagioclase. Unfortunately, plagioclase in the peridotite samples is badly altered, and cannot be trusted to give reliable Pb isotopic information. In general, the range in concentration follows the relative incompatibility of the elements in cpx; the most highly incompatible elements display the greatest range. As a consequence, U238JU Pb (g) ranges from 1.17 to 78.8, and Th/U ranges from 0.45 to 6.94 for cpx. Garnets are characterized by very low abundances of U (2.7-4.3 ppb), Th (1.4-5.2 ppb) and Pb (1.5-9.7 ppb), but have high g (28-122). The single plagioclase analyzed is characterized by high Pb and low U and Th abundances. Clinopyroxenes from garnet facies peridotites show high abundances of U, Th and Pb relative to other peridotite cpx, with the exception of R85-32 from the spinel facies. The cpx data fall into two groups based on their U/Pb ratios (Fig. 5a). One group has generally high concentrations of Pb (>70 ppb) and low U/Pb ratios (average .=3.2, low-g group); the other group has generally lower Pb concentrations (<70 ppb) and higher U/Pb ratios (average g=13.6, high-p group). These two groups also have different Th/U ratios; the average Th/U of the low-. group is 2.5 whereas the high-g group has an average Th/U of 4.2. Lead isotope ratios are given in Table 2 and plotted in Figure 6. For the Pb isotopic analyses of the garnet separates, the amount of Pb analyzed was exceedingly small (150-500 pg), and suffered from a hydrocarbon interference on 2 04Pb during mass spectrometry. In order to correct for this effect, the garnet Pb isotope data was corrected by normalizing the measured 207 Pb/2°4Pb relative to 207 Pb/ 2°4 Pb measured for clinopyroxene from the same sample. The 207 Pb/24PPb ratio of cpx from sample R145 also likely suffers from this effect, and so the Pb isotope data for this sample is not plotted in Fig. 6 Bousera orogenic peridotite massif exhibits a similar range for  all the Pb isotope ratios, while Pb isotope data for whole rocks from the Lherz and Zabargad orogenic peridotites are more restricted and have lower 20 7 Pb/2Pb ratios . Pb isotope results for cpx separates from xenoliths from the southwestern United States reported by  and Meijer et al. (1990) are distinctly less radiogenic and have lower 20 7 Pb/24Pb. Peridotite xenoliths from Africa (Kramers, 1977(Kramers, , 1979Cohen et al., 1984) also show large ranges in Pb isotopes in their constitutent clinopyroxene. The normalized 2 06Pb/24Pb and 2 s 0 8 Pbfl4Pb ratios in garnets from samples R498, R521, R618, R740, and R256 are more radiogenic than the values for their corresponding cpx (   and . Sample R238 is notable for its very low 87 Sr/ 86 Sr and Pb isotopic compositions.
Sample 040R from the garnet facies has high 207 Pb/2nPPb, and lies to the left of the 3.1 Ga isochron and the 4.55 Ga geochron. This sample has high 1 43 Nd/144Nd, but also has fairly high 87 Sr/ 8 6Sr as noted by ; these characteristics are quite different from the other garnet-facies samples in which 87 Sr/ 8 6Sr and the Pb isotopes are well correlated.

Partitioning of U, Th, and Pb in Peridotite Minerals
In order to determine the host phases for U, Th, and Pb in mantle peridotites, analyses of olivine, orthopyroxene, and garnet were made on several samples, and the relevant mineral/mineral partition coefficients are given in Table 3. Olivine and orthopyroxene contain essentially no U and Th (measured amounts were essentially indistinguishable from blank levels), but were found to host a small amount of Pb.
Though the absence of U and Th in these minerals suggests minimal contamination, the olivine and orthopyroxene analyses are not in Pb isotopic equilibrium with their corresponding clinopyroxenes (  Figure 7. A) Sm-Nd and B) U-Pb isochron plots for garnet-cpx pairs from Ronda garnet peridotites (R521,R618,R740) and a garnet-bearing mafic layer (R256). Uncertainties (2a) are estimated at +0.0035% and 0.5% on 143Nd/144Nd and 147Sm/144Nd, respectively, and +0.14% and +0.5% on 206Pb/204Pb for cpx and garnet, respectively, and 20% on 238U/204Pb. The U-Pb ages of R618 and R256 are within error of Sm-Nd garnet-cpx ages from Ronda garnet peridotites  and Rb-Sr dates of anatectic country rocks (Priem et al., 1979). Isochron ages of R521 and R740 are within error of each other, but outside the range of previously reported garnet-cpx Sm/Nd ages. The Sm-Nd and U-Pb ages of R618 are concordant, but those of R521 are not, suggesting the possibility of a very slight U or Pb contamination of R521 garnet, and probably R740 garnet.
separates may have contained a small amount of a contaminant with low U/Pb and Th/Pb ratios. Thus the olivine/cpx and opx/cpx partition coefficients given in Table 3 are considered to be upper limits. Figure 7 shows the Sm-Nd and U-Pb systematics of garnet-cpx pairs from Ronda garnet peridotites (R 521, R618, R740) and a garnet bearing mafic layer (R256). The Sm-Nd ages are within error of a Sm-Nd isochron age on a garnet-bearing mafic layer analyzed by Zindler et al. (1983), and garnet-cpx Sm-Nd ages measured by  on Ronda garnet peridotites. The U/Pb ratios and Pb isotopic compositions of garnet from the garnet-bearing samples listed in Table 2 are distinctly higher than their corresponding clinopyroxenes. On a 23 8 U/o4Pb-2 06Pb/ 2°4 Pb isochron diagram, these garnet-cpx pairs display a range of ages from 17.3 Ma to 44.0 Ma, with large errors (Fig. 7b). The mineral isochron ages for R256 and R618 are within error of the Sm-Nd garnet-cpx ages determined by Zindler et al. (1983) for a Ronda garnet-clinopyroxenite (21.5±1.8 Ma), and by  for Ronda garnet peridotites (21.0+7.0 Ma to 24.5±7.3 Ma). In addition, these ages are in agreement with Rb-Sr ages of about 22 Ma for anatectic granites associated with the peridotite massif (Loomis, 1975;Priem et al., 1979). However, the garnet-cpx pairs for R521 and R740 are different from the above ages, though they are within error of each other. The Sm-Nd and U-Pb ages for R618 are concordant, but those for R521 are not. The most likely explanation for this discordance is a slight Pb contamination of the R521 garnet separate. For the 232 Th/204Pb-208 Pb/o4Pb system, two of the garnet-cpx pairs are essentially in equilibrium, while R618 gives a garnet-cpx age of 41.6 Ma, and R521 gives a garnet-cpx age of 140 Ma (not shown). The larger amount of noise in the Th-Pb system is probably the result of a smaller Th/Pb fractionation between garnet and cpx, compared with the large fractionation in U/Pb ( Table 2). The U-Pb ages are barely resolvable, and probably represent the lower limit obtainable for mantle derived garnet peridotites. These age relationships indicate that the minerals of the Ronda peridotites were in Pb isotopic equilibrium 20 Ma ago. As a result, the partitioning relationships for U, Th, and Pb between garnet and cpx are more well constrained than for olivine and orthopyroxene, and the garnet/cpx partition coefficients given in Table 3 are considered to represent a close approach to equilibrium. These results indicate that garnet is a significant host for U in the mantle, and to a lesser degree also for Th and Pb. This is reflected in the high U/Pb ratios and low Th/U ratios of these garnets compared with their corresponding clinopyroxenes. where Xmineral=weight fraction of the mineral in the bulk rock, and D i/ l is the solid/melt partition coefficient for element i in phase j. Substituting in the expressions: and the average garnet/cpx values from  ; these experiments were performed in air at 1 atm, and so U +6 is likely to be present in their charges . By consideration of equation (4), it is clear that the ratio DU/Dpb for the bulk rock increases with increasing garnet/cpx ratio. This is due not to an increasing compatibility of U, but a decreasing compatibility of Pb with increasing garnet/cpx ratios.
Within the uncertainty in the relevant partition coefficients of U and Pb, it is apparent that the ratios Du/Dpb and DIrh/Dpb may exceed unity. During melting of a garnet-bearing assemblage, the result of this effect would be to leave a residue with a higher U/Pb and Th/Pb ratios than before melting. In addition, the ratio I/D will be lower in a garnetbearing peridotite than in a garnet-free peridotite. Thus, the Th/U ratio in a partial melt of garnet peridotite should have higher Th/U than a melt of spinel peridotite; this is consistent with the generally higher Th/U ratios of OIB compared to MORB (ex. Tatsumoto, 1978).
Though a large degree of uncertainty still remains about the precise mineral/melt partition coefficients for U, Th, and Pb, it is clear that the retention of garnet in a residue of melting will leave that residue with higher U/Pb, Th/Pb, and lower Th/U than a garnet-free residue of melting. As a result, it is possible that a peridotite which is residual after partial melting in the garnet stability field may develop radiogenic Pb isotope ratios, even though it is a residue of melting. Figure 8 shows the 23 8 U/24Pb-206 Pbfl°'Pb data for the Ronda clinopyroxenes.

U-Th-Pb Budget of Mantle Peridotite
The data are not well correlated, but nonetheless show a broad positive trend. The cpx data scatter on both sides of a 3.1 Ga reference isochron, which corresponds to the 3.1 Ga Pb-Pb isochron in Fig. 6a. If the whole rock Ronda peridotites lie on the 3.1 Ga reference isochron, the cpx data indicate the possible presence of U and Pb (and Th) in the whole rock budget which is not contained in clinopyroxene; thus the clinopyroxene U/Pb ratio would not be representative of the whole rock U/Pb ratio. The cpx data from the garnet facies lie largely to the left of the isochron. This is consistent with the presence of garnet in these samples, and thus the bulk rock U/Pb ratios of the garnet-bearing samples would be shifted toward the isochron once the U-Pb budget of garnet is accounted for. However, a number of clinopyroxenes from spinel-and plagioclase-facies samples, as well as cpx from mafic layers, also lie to the left of the isochron, suggesting that some of the U (and Th) budget of these whole rocks may not reside in clinopyroxene. The studies of Zindler et al. (1983) and

2U/ 2 04Pb
Figure 8. U-Pb isochron diagram for clinopyroxenes from Ronda peridotites and mafic layers. The 3.1 Ga reference isochron corresponds to the 3.1 Ga isochron shown in Figure 6a. The data show a broad positive correlation, but do not define an isochron. Clinopyroxene data lie on both sides of the 3.1 Ga reference isochron; if the Ronda whole rock peridotites lie on a 3.1 Ga isochron, the cpx data indicate the possible presence of trace U (and Th) and Pb bearing phases in the peridotites.
rock could conceivably result in low U/Pb and Th/Pb ratios in constitutent cpx of garnetfree samples. Though this mineral was not observed in the samples studied here, small amounts of this phase may have escaped detection. Alternatively, if these samples represent residues of melting, or the products of crystallization from a maic melt, the low U/Pb and Th/Pb ratios may be the result of lower solid/melt partition coefficients for U and Th than for Pb.
Nearly all the plagioclase facies samples, as well as samples R238, R717, and R85-34 from the spinel facies, seem to have U/Pb, Th/Pb, and Ce/Pb ratios in clinopyroxene which are in excess of these ratios for the remaining samples (Figs. 5,8). This suggests that Pb may be partitioning into phases other than clinopyroxene in these samples. In the case of samples R25, R142, R145, R140, and R141, the low Sr/Nd ratios of the cpx indicates that Pb has been partitioned into plagioclase, leaving the constituent cpx with high U/Pb, Th/Pb, and Ce/Pb ratios. The remaining plagioclase facies samples (002R-404R) have normal Ce/Sr ratios and high Sr/Nd ratios, and plagioclase has not been observed in these rocks. These samples are LREE enriched, and thus U, Th, and the LREE may have been enriched relative to Pb in these samples. This could also account for the high Pb isotope ratios of these samples, which are from the east end plagioclase facies traverse ( Fig. 1). However, clinopyroxenes in peridotite xenoliths from San Carlos , which are plagioclase-free and dominantly LREE depleted, also have high  Carlos clinopyroxenes; this plot tends to "normalize" the effect of cpx equilibration with plagioclase, since both Pb and Sr partition into plagioclase. The data for the plagioclase facies samples lie systematically below the trend defined by the Ronda spinel-and garnetfacies samples and the San Carlos data; this suggests that the plagioclase/cpx partition coefficient for Sr may be higher than for Pb. Figure 10a shows that the U/Pb ratio in cpx is also a strong function of the Pb concentration in cpx. Figure 10b shows that those samples with high Ce/Pb also tend to have high U/Pb; this is also indicated by the San Carlos cpx data. In addition, though there is a good correlation between Sm/Nd and 143 Nd/ 144 Nd in the Ronda cpx data , the measured U/Pb ratios of the Ronda cpx are not correlated with high 2 06Pbfl/2Pb.
Taken together, these features of the cpx data suggest the possible influence of an additional Pb bearing phase in the Ronda peridotites (and also the San Carlos xenoliths).
Pb in the Ronda peridotites may have partitioned into a trace phase such as sulfide. Pb (ppb) Figure 9. A) Ce/Pb versus Pb for clinopyroxenes from Ronda peridotites and mafic layers. Cpx with Pb concentrations greater than about 70 ppb have Ce/Pb ratios near the oceanic basalt average of 25 . However, most of the data define a negative trend. Ce data for cpx from San Carlos xenoliths  were estimated by extrapolation of the REE pattern between Nd and Sm. B) Sr/Pb versus Pb in Ronda clinopyroxenes. The data, including data for cpx from San Carlos xenoliths, define a negative trend, suggesting that the bulk solid/melt partition coefficient of Pb is less than that of Sr. assuming 5% modal cpx, 0.4% of a sulfide phase with a Pb concentration of 10 ppm (Meijer and Rogers, 1990) in sample R238 would drop the whole rock Ce/Pb ratio to 51, which is well within the range of other cpx Ce/Pb ratios, and g would decrease to 7.75 (the single stage value indicated by the position of R238 near the geochron). Though it has not been firmly established that sulfide is a major host for Pb in the mantle, its role cannot be excluded. If sulfide is an important host for Pb in mantle peridotite, then the U/Pb, Th/Pb, and Ce/Pb ratios measured in clinopyroxene would not be representative of the whole rock. This is supported by the lack of a correlation between U/Pb and 2 06Pb/2 4 Pb for the cpx data. However, based on the fact that the 238 U/24Pb and Ce/Pb ratios measured in the Ronda cpx are reasonably close to values estimated for the mantle. , the fraction of the whole rock Pb budget which is "missing" from clinopyroxene probably amounts to no more than about 50% in the most extreme case.

Ce/Pb Ratios of the Ronda Peridotites
The Ce/Pb ratio of MORB and OIB appears to show relatively little variation around a value of 25 over a wide range of concentrations , suggesting that this value is representative of the present day upper mantle . Based on this observation,  have proposed that the apparent peridotite/melt partition coefficients for Ce and Pb are very similar. If true, this implies that the Ce/Pb ratio in residual mantle peridotites should also be around a value of 25. The above arguments suggest that the Ce/Pb ratios measured in cpx are not representative of the whole rock peridotite. If sulfide is an important Pb-bearing phase in mantle peridotite, then the Ce/Pb ratios of the Ronda clinopyroxenes will be systematically higher than the bulk rock peridotites. This will probably be most important for the samples which show low Pb concentrations in clinopyroxene. Figure 9a shows a plot of Ce/Pb versus Pb for the Ronda clinopyroxenes, as well as Ce/Pb estimates for cpx from San Carlos xenoliths studied by . The data at high Pb concentrations scatter about the oceanic basalt average. The negative correlation at low Pb concentrations may be the result of cpx equilibration with either plagioclase or sulfide, as mentioned above. If true, the bulk rock Ce/Pb ratios would be lower than the cpx Ce/Pb ratios. We cannot correct for this effect without knowledge of the relevant partitioning relationships for plagioclase and sulfide.
However, from Fig. 10b   , the Ronda data suggest that Ce and Pb concentrations in a partial melt are determined by two different phases (cpx for Ce, cpx and sulfide for Pb). The existing experimental partitioning data for Ce indicate a clinopyroxene/melt partition coefficient of about 0.15 (ex. . However,  measure a cpx/melt partition coefficient of 0.009-0.012 for Pb. This would seem to require an additional phase to buffer the Pb concentration in both residual peridotite and cumulate rocks in the mantle, possibly the aforementioned sulfide. Based on the observations that both Nd and Pb isotope ratios in MORB are generally higher than bulk silicate earth estimates (Tatsumoto, 1966), some process must be acting on the upper mantle to decouple U/Pb and Sm/Nd fractionations.  and  have pointed out that the continental crust has a lower Ce/Pb ratio than the mantle (Ce/Pb=9), and it has been suggested that the mechanisms which create the continental crust are responsible for this fractionation (e.g. ). This would seem to implicate the continental crust as a major reservoir of Pb, including unradiogenic Pb which may balance the radiogenic character of mantle Pb Reid et al., 1989). A strong transfer of Pb from the mantle to the crust would suggest that the Pb isotope evolution of the mantle may be more highly influenced by the processes of crustal growth and recycling than Sr and Nd isotope evolution.

Peridotite Sr-Nd-Pb Isotope Systematics
In general, among the samples from the spinel and garnet facies, 2 06Pb/ 20 Pb is positively correlated with 87 Sr/ 86 Sr (Fig. 6c). This feature is also present within the small scale sampling area in the garnet facies. The samples from the plagioclase facies traverse show little variation in 87 Sr/ 86 Sr, despite a large variation in 206 PbF2°Pb. The Sr-Pb isotope data are suggestive of mixing between a MORB-like component and HIMU (Fig.  6a). For 1 43 Nd/144Nd, the overall data, as well as the data from the garnet facies sampling area, show a broad negative correlation with 206 Pb/2PPb, but this correlation breaks down in the small scale sampling area within the plagioclase facies (Fig. 6d). In particular, many samples plot outside the range of oceanic basalts, with both high and low 143 Nd/144Nd for a given 2 06Pb/24Pb. The samples from the plagioclase traverse, with radiogenic 206 Pb/ 2 4 Pb, have lower 1 43 Nd/ 1 44Nd than HIMU; in addition, these peridotites have low with these samples being residues of melting. In particular, samples with high 143 Nd/ 144 Nd have very depleted REE patterns, but these samples have both high and low 206Pbf/ 2 4Pb; this is consistent with the similarity of the mineral/melt partition coefficients of U and Pb (Table 3), since the residue may have U/Pb higher or lower than before melting. The lack of a correlation between 1 43 Nd/144Nd and 2 06PblPb within the plagioclase facies traverse is probably related to the metasomatic event suggested by . In particular, the varying degrees of LREE enrichment of these samples (Fig. 4e-f) is consistent with metasomatism by percolating melts (e.g. . However, given the limited variability of these REE patterns, it is not possible to constrain the composition of this metasomatizing agent. Taken as a group, the samples from the garnet and spinel facies define a linear trend from low Pb isotope ratios near the geochron (R238) to very high 207 Pb2°4Pb ratios for a given 26Pb/04Pb, and scatter about a Pb-Pb isochron with an apparent age of 3.1 Ga ( Fig. 6a). Even if the 207 Pb/24Pb-2 06Pb/2PPb trend represents a mixing array, this age is indicative of the time needed to generate this degree of heterogeneity in 2 07PbflP4Pb. If this trend were due to contamination of the peridotite by a crustal component, then the samples with high 207 PbP/P4b ratios would be expected to have the slightly high 208 Pbf 204 Pb, high 87 Sr/ 8 6Sr and low 1 43 Nd/ 1 44Nd signature of continental crust, which is evidently not the case (Figs. 6c,d).
The apparent 3.1 Ga Pb-Pb age is in excess of the whole-rock isochron ages of 1.3 Ga (Sm-Nd, ) and 1.2 Ga (Re-Os, Reisberg et al, 1990) previously determined for Ronda peridotites. The evidence is strong that the Sm-Nd and Re-Os ages date a melting event Reisberg et al., 1990). The garnet and spinel facies peridotites, as a group, do not define a U-Pb or Th-Pb isochron, but it is difficult to determine the extent to which the clinopyroxene U/Pb and Th/Pb ratios are representative of the whole rock. This is certainly not the case for the garnet-bearing samples. Garnet contains significant amounts of U and Th, and the whole rock U/Pb and Th/Pb ratios depend strongly on the garnet/cpx ratio of these samples, which is difficult to determine given the heterogeneous distribution of garnet in hand specimen. Due to the uncertainty in the relationship between the bulk rock U/Pb and Th/Pb ratios to those ratios in cpx, no parent-daughter isochron relationships can be established on a massif wide basis, as was possible for the Sm-Nd and Re-Os systems.
However, the broad positive trend in Figure 8, defined largely by the different positions of the garnet-spinel facies data and the plagioclase facies data, is consistent with a 1.3 Ga age.
In addition,  have documented evidence for a metasomatic event about 200-300 Ma ago which was reflected in the Sr and Nd isotopic 51 compositions of samples from the eastern plagioclase-facies traverse (Fig. 1). This event probably was not responsible for creating the high 2 06,20 7 , 208 Pb/o4Pb and low 143 Nd/ 144 Nd signatures of the plagioclase traverse samples, because (1) the high 206 ,2 0 7, 208 Pb/ 204 Pb signature was likely already present 200-300 Ma ago (Fig. 8), and (2) the Sm-Nd isotopic systematics of sediment clinopyroxenes from the area of this traverse, as well as the weighted average of the Nd isotopic compositions of the traverse samples themselves, have 1 43 Nd/ 1 44Nd and 147 Sm/ 1 44Nd ratios less than bulk earth (LREE enriched), and also plot on the 1.3 Ga Sm-Nd isochron defined by samples from the rest of Ronda . This evidence indicates that the partial melting event at 1.3 Ga ago also created a low Sm/Nd, high U,Th/Pb section in the eastern end of the massif, and that the metasomatic event at 200-300 Ma ago resulted in the mixing event documented in the plagioclase facies traverse , as well as changes in Sm/Nd and U,Th/Pb ratios.

Peridotite-Mafic Layer Relationships
The isotopic compositions of the samples from the interlayered peridotite-mafic layer sections in Fig. 3 are all broadly similar, though signficant differences are present (Table 2). In particular, the similarity of the REE patterns of cpx from samples R140 (ML), R141 (ML), R142 (PD), and R145 (PD) indicate that some trace element exchange and equilibration has taken place. However, the 8 cm thick mafic layers R140 and R141 preserve distinct isotopic compositions, both of which are different from the thick peridotite layer R142 (Fig. 3). This indicates that isotopic heterogeneity at Ronda is present down to the centimeter scale, in agreement with Pb isotope results from Beni Bousera .
Relative to the peridotites, the mafic layers are more restricted in their isotopic compositions, especially in 2 06Pb/2PPb (Fig. 6). This is in contrast to the data of  for mafic layers from Beni Bousera, which show isotopic variability comparable to that of the peridotites. Since Beni Bousera and Ronda are thought to be parts of the same peridotite body, this is a somewhat surprising result. The number of mafic layers analyzed is small (7), and this may only be a fortuitous result. However, the Ronda garnet-bearing peridotites are very likely mixtures of garnet-bearing mafic layers and depleted wallrock peridotite, as suggested by  and Reisberg et al. (1990). This suggestion is supported by the generally high U, Th, and Pb concentrations in the garnet-facies peridotites. In detail, many of the Ronda clinopyroxenes, from all mineral facies, have Pb concentrations which are higher than cpx from San Carlos xenoliths ( Fig. 9); there also seems to be a bimodal distribution of Pb concentrations in cpx on either side of about 70 ppb (Fig. 5), which also corresponds to two different groups 52 based on Ce/Pb ratios (Fig. 9). Given the evidence for physical mixing of mafic layers into the host peridotite , it is suggested that the samples with cpx Pb concentrations in excess of about 70 ppb may have been derived from mixing of mafic layers into peridotite. If this is indeed the case, then the isotopic heterogeneity of the garnet facies samples reflects that of the pre-existing mafic layers, which argues for substantial mafic layer isotopic heterogeneity, in agreement with Pb isotope results from Beni Bousera . Indeed, the high concentrations of U, Th and Pb in the garnet facies cpx, compared to other analyses for residual peridotites  indicates that these peridotites have derived a large fraction of their trace elements from mafic layers. The higher trace element concentrations of the mafic layers represent an important source of components which may effect the isotopic and trace element systematics of the peridotites. Mafic layer clinopyroxenes have higher Ti and Zr and lower Cr compared those from peridotites (Table 1). It should also be noted that some mafic layer cpx have higher Cr than others. These high Ti peridotites (R142, R145) and high Cr mafic layers (R140, R141) are from the interlayered section of the plagioclase facies ( Fig. 2b), suggesting some exchange of trace elements between the peridotites and mafic layers. However, these interlayered samples display significant isotopic variability, indicating the preservation of isotopic heterogeneity on the scale of tens of centimeters (Fig. 2). The mechanism responsible for this interaction is difficult to pinpoint. Simple mixing can be ruled out, as this would create straight lines on element-element plots (not shown), with the affected samples lying directly between the compositions of the mafic layers and the peridotites. Diffusive interaction between peridotites and mafic layers may also be important , but a more detailed study is required to definitively answer this question. It is also possible that the peridotites may have interacted with a melt of some kind, either during crystallization of the layers, or from a partial melt of the layers.

Isotopic Evolution of Ronda
Two features of the U-Th-Pb data remain puzzling: the origin of the 3.1 Ga trend in Fig. 6a, and the lack of a strong 1.3 Ga signal in the Pb isotope data. The lack of a correlation between 1 43 Nd/144Nd and 2 06Pb/24Pb for the garnet and spinel facies samples ( Fig. 6d) indicates that the Pb isotope characteristics of Ronda were probably not determined, to a large extent, by depletion of U and Th relative to Pb (or vice versa) in a melting event at 1.3 Ga. In this context, two explanations exist to account for the 3.1 Ga Pb-Pb age and the 1.2-1.3 Ga Sm-Nd and Re-Os ages for Ronda, both of which are consistent with the data.

Ronda as Ancient MORB Source
An event at 3.1 Ga ago (partial melting?) created the present Pb isotope heterogeneity at Ronda, and the subsequent partial melting event at 1.3 Ga ago reset the Sm-Nd and Re-Os isochrons, but left the Pb-Pb isochron relationship intact. Thus the presently observable Pb isotopic heterogeneity at Ronda is an intrinsic feature of the peridotite. This evolution is shown in Fig. 8; extrapolation of the 3.1 Ga Ronda Pb-Pb isochron back to the geochron at 3.1 Ga ago indicates a first stage .t=7.87, possibly slightly less than the proposed bulk silicate earth =8.0 . To generate the present 207 Pb/204Pb isotope heterogeneity at Ronda requires a range of second-stage g=7.3-11.2, suggesting a slightly high U/Pb reservoir for the second stage. This scenario would appear to require that the event at 1.3 Ga ago resulted in an isotopic homogenization which was less efficient for Pb than for Nd and Os. However, the effect of isotopic homogenization on a Pb-Pb isochron is to move the points toward some average Pb isotopic composition on the isochron. Thus, if Pb isotopic homogenization is not perfectly efficient, the resulting Pb-Pb array will still retain a slope which indicates the initial age of the Pb isotope heterogeneity. In addition, this slope would be maintained through time if the U/Pb ratios of the points on the isochron were not drastically changed during the homogenization event. Under this scenario, there should also be a certain amount of 143 Nd/144Nd and 187 0s/ 186 0s heterogeneity at 1.3 Ga ago, which almost certainly can be accommodated within the errors on the initial ratios.
The initial 143 Nd/144Nd derived from the  Sm-Nd isochron indicates an £Nd of +6.0 for Ronda at 1.3 Ga ago. The initial 187 0s/ 186 0s calculated from the Reisberg et al. (1990) Re-Os isochron is 0.996+0.005 at 1.3 Ga ago, which would be depleted relative to bulk silicate earth (BSE) if BSE had a present-day 187 0s/ 186 0s of >1.08 . Together with the low 87 Sr/ 86 Sr of many of the Ronda samples, and the depleted Pb isotopic composition of R238, this evidence suggests that at least some parts of Ronda were already depleted at 1.3 Ga ago, and that the evolution from 1.3 Ga ago to the present represents a "third stage" in the isotopic evolution of Ronda since the formation of the earth.
If the time period of the "second stage" is taken to be 3.  Figure 11. Pb isotope evolution of the Ronda peridotite. Single stage growth curve from Canyon Diablo is for g=8.0 with tickmarks every 1 Ga. The Ronda 3.1 Ga isochron intersects the 1.45 Ga geochron (geochron 3.1 Ga ago) at a first stage g=7.87. Calculated second stage g ranges from 7.3-11.2 for the Ronda garnet and spinel peridotites. Additional events at 1.3 Ga ago (partial melting) and 300 Ma ago (metasomatism) potentially result in scatter about the 3.1 Ga isochron.

Pb/ Pb
55 system, a range of g (23 8 U/24Pb) from 7.3-11.2 is needed to create the observed heterogeneity in 207 Pb/2°4Pb (Fig. 8). Essentially, this would mean that, in the time period 3.1-1.3 Ga ago, Ronda would have had depleted 1 43 Nd/144Nd and 87 Sr/ 86 Sr, and enriched Pb isotopic compositions relative to bulk silicate earth. This is exactly the signature exhibited by present-day MORB. In support of this model, 208 Pb/26Pb is broadly correlated with ThAJ/U in most of the Ronda cpx ( Fig. 12a), recent metasomatism notwithstanding.

Ronda as Metasomatized Mantle
The partial melting event at 1.  Morris and Hart, 1983). In support of this model, 87 Sr/ 86 Sr is positively correlated with A7/4 within the garnet and spinel facies, and among the samples from the plagioclase facies and mafic layers. The isotopic characteristics of the Ronda garnet-bearing peridotites essentially reflect the isotopic characteristics of disaggregated garnet-bearing mafic layers, as discussed in Section 4. Thus the Ronda mafic layers could represent cumulates from magmas with isotopic characteristics similar to island arc volcanics. In this model, the Pb isotopic heterogeneity observed in the Ronda spinel and garnet peridotites would be an inherent property of the throughgoing magmas, because the high Pb concentrations of magmas relative to peridotite would cause the metasomatic Pb signature to completely dominate the peridotite. However, this would also be expected to be the case for the Sr and Nd isotope signatures of the garnet-bearing samples. In this case, the Sm-Nd isochron of  would not necessarily represent the melt depletion event recorded by the Re-Os isochron (Reisberg et al., 1990).

Conclusions
The picture of the U-Th-Pb system which emerges from this study is one of a complexity befitting highly incompatible elements. Large variations in the abundances of U, Th, and Pb are evident, and are consistent with varying degrees of mixing of incompatible element-rich mafic layers with variably depleted peridotite. Olivine and opx contain no U and Th, but may contain a small amount of Pb. Thus olivine may contribute a significant amount of Pb to the whole rock budget in clinopyroxene-poor peridotites. Garnets are characterized by low abundances of U (2.7-4.3 ppb), Th (1.4-5.2 ppb) and Pb (1.5-9.7 ppb), but have high g (28-122). These mineral/mineral partitioning results indicate that, of the major anhydrous silicate phases present in mantle peridotite, clinopyroxene and garnet are the dominant host phases for U, Th, and Pb. However, trace amounts of sulfide, not detected in this study, may exert an influence over the whole rock budget and partitioning relationships for Pb in mantle peridotites.
Garnet-cpx pairs from garnet-bearing samples display a range of ages from 17.3 Ma to 44.0 Ma, and are consistent with the Sm-Nd garnet-cpx ages determined by Zindler et al. (REF) for a Ronda garnet-clinopyroxenite (21.5±1.8 Ma), and by  for Ronda garnet peridotites (21.0+7.0 Ma to 24.5+7.3 Ma). These results indicate that mineral phases in the Ronda peridotites were in isotopic equilibrium 22 Ma ago. For the peridotites, large ranges in 206 Pb/24Pb (17.047-21.688), 207 Pb/2 04 ) and 208 Pb/2P4Pb (36.277-41.930) are evident, exceeding the range of Pb isotopic compositions reported for oceanic basalts. The garnet and spinel facies samples largely overlap in Pb isotopic composition, and the 207 Pb/ 2 4Pb-206 Pb/2 0 4 Pb data for these samples scatter about a Pb-Pb isochron with an age of 3.1 Ga. The high Pb isotope ratios of samples from the plagioclase facies traverse were probably created at about 1.3 Ga ago, when the massif was subject to a partial melting event. A subsequent event at about 200 Ma, which may have involved a small amount of local partial melting and melt percolation, resulted in metasomatism and further LREE enrichment in the eastern end of the plagioclase facies.
Based on the integrated isotopic data, the Ronda peridotite may represent either 1) a segment of MORB source mantle which was formed about 3 Ga ago, and incorporated into the subcontinental lithosphere at about 1.3 Ga; or 2) a segment of depleted mantle which was subject to metasomatism by a component similar in isotopic composition to island arc volcanics. In the first model, the Ronda mafic layers may have been formed during a melting event 1.3 Ga ago, or were formed around 3 Ga ago and partially re-equilibrated at 1.3 Ga ago. In the second model, the mafic layers probably represent crystal cumulates of melts derived both from the melting Ronda peridotites, and also from melts with island arc affinities.

Appendix-Analysis of U, Th, and Pb in Mineral Separates
Mineral separates of 17 to 200 mg were dissolved on a hotplate at 125 0 C for 5-10 days in 3 ml Savillex screw cap beakers in either 1) a 3:2 mixture of HF:HBr or 2) a mixed acid solution consisting of equal parts concentrated HNO 3 -6.2 N HCl-concentrated HF. A mixed spike containing 23 5 U, 230 Th and 205 Pb was added before dissolution. Pb was separated in 0.5 N HBr on 20 pl of Dowex 1 using a scaled down version of the technique of (Manhes et al., 1978), reserving the liquid for subsequent separation steps. It was found necessary to repeat the column separation for Pb using a separate, clean column in order to entirely eliminate Ca from the Pb fraction. The Pb fraction was evaporated to a small volume with 1-2 drops of 0.03 N H 3 PO 4 . After evaporation into H 3 PO 4 , the Pb fraction was evaporated repeatedly with concentrated HNO 3 in order to eliminate organics, which can interfere with 24Pb+ measurement during mass spectrometry.
At this point in the procedure, it was necessary to extract as much U and Th as possible from the fluorides which invariably form during dissolution in HF. Radiotracer studies have shown that U and especially Th partition strongly into Ca fluoride formed during the dissolution step (A. Zindler, pers. comm.). During dissolution, flourides form rapidly on the surfaces of mineral grains, and continuously replace the components which go into solution, resulting in fluoride pseudomorphs after the original mineral grains. The potential for sample-spike disequilibrium for U and Th may thus exist during dissolution, and it is important to make every effort to achieve dissolution of the fluoride residue. The fluoride residue was attacked with aqua regia at 150 0 C for several days, evaporated to dryness, and redissolved in 8 N HNO 3 . Roughly half the time, the residue went completely into solution (especially for smaller samples). The sample was centrifuged, and U and Th were separated together on AGl1X8 anion exchange resin in 8 N HNO 3 (saving the eluant for Sr and Nd separation), and eluted with 6.2 N HCl and 0.5 N HBr. 1-2 drops of 0.015 N H 2 SO 4 was added to the U+Th fraction, and the solution was evaporated down to a tiny drop for loading. The solution left from the U+Th step was dried down, redissolved in 6.2 N HCl several times, and finally dissolved in 2.5 N HC1. Subsequent procedures for the separation of Sr and Nd follow the procedures of Zindler, 1980). Blanks for the total procedure ranged from 9-45 pg Pb, <1-3 pg Th, <1-10 pg U, <200 pg Sr, and <30pg Nd and Sm. Reagents used during the separation procedures typically accounted for 75-100% of the measured Pb blank. The isotopic composition of the Pb blank was consistently MORB-like ( 2 06Pb/2PPb=18.5-19.5, 207 Pb/ 2°4 Pb=15.4-15.6, 208 Pb/2°4Pb=37-39), which resulted in minimal blank corrections for most analyses.
Pb was run on single Re filaments (0.001" x 0.030") using the silica gelphosphoric acid activation technique (Akishin et al., 1957;Cameron et al., 1969). The Pb fraction was heated on a hotplate, and 1-2 mg of silica gel was added. The solution was allowed to evaporate by about 20%, and then the entire solution was picked up and loaded.
Picking up the solution out of a hot beaker minimizes the amount of Pb left in the bottom of the beaker. The Pb solution was then loaded in as small an area as possible in the center of the filament, and dried at 1.0 amps. The filament current was then raised slowly to fume off the excess phosphoric acid (about 2.5-2.8 amps), then taken to dull red for 3 seconds.
The filament current was then decreased to about 2.2 amps, and the load was allowed to cook in air for 2-5 minutes. The filament must be closely watched during this period, as heating the Re filament in air at 2.2 amps can cause the filament to recrystallize and crack, and this step should be stopped if the filament appears to be recrystallizing. This heating step in air reduces the amount of "low temperature Pb" observed during mass spectrometry, and results in a more stable, more intense signal compared with runs for which this was not done. Due to the very small amounts of Pb analyzed (150 pg to 20 ng), data were collected using an electron multiplier operated in analog mode at a gain of 2x104.
Early in the Pb runs, a "low temperature" fraction of Pb was always observed at filament currents <2.0 amps, which was characterized by rapidly growing or dying signals and a persistent interference on 2 04Pb+, resulting in very low 207 Pb/ 2 04Pb and 2 06Pb/204Pb ratios. In addition, interferences were typically found at masses 205 and 203, which probably correspond to 203 , 205 T1+. These interferences were always found at filament currents of <2.0 amps (1x30 mil Re), which corresponds to approximately 1000 0 C filament temperature, and sometimes as high as 2.2 amps for nanogram amounts of Pb. As a result, isotopic composition data was only taken above 2.1-2.2 amps. Data for 205 Pb for isotope dilution measurements was always taken after the data for Pb isotopic composition, in order to allow TI + to burn off, which was always the case (as determined by measuring the 203/204 ratio). Typical ion currents for 208 Pb+ were 0.5-3x10-12 A for 1 ng of Pb. A correction factor of 0.375 %/amu was employed based on repeated analysis of NBS 981 common Pb, using the values of . Precision for most runs is less then 0.1% on all ratios, and the reproducibility of NBS981 runs (300-2000 pg) is 0.07%/amu (Table Al). Reproducibility of duplicate samples is also generally on the order of 0.07%/amu.
For the loading of U and Th, a small amount of water was added to the sample in the beaker, and warmed on a hotplate. The reason for evaporating U and Th in H 2 SO 4 is that Ca sulfates are quite insoluble, while U and Th sulfates are soluble in water. Thus, by evaporating the U+Th fraction down into H 2 SO 4 , potential contaminants are made insoluble, and are not loaded if U and Th are picked up in water. U and Th were loaded together on single Re filaments with colloidal graphite, and also run using the electron multiplier. Colloidal graphite should be chosen with care, as nearly all brands have substantial U blanks (alternatively, U could be run as an oxide with silica gel and phosphoric acid). In addition, the zone refined Re filament sometimes had a small Th blank, which was generally eliminated by outgassing the Re filaments at 5.5-6.0 amps (about 20 minutes), and checking each filament for Th before loading. A small amount of Ca was typically observed during the U-Th runs, which usually burned off after 10-20 minutes at 3.0 amps. U + was typically run at 3.4-4.0 amps, and Th + run at 4.0-5.0 amps.
A correction factor of 0.4%/amu was applied to the U and Th data based on repeated analysis of SRM 960 U. Isotope dilution measurements of U, Th and Pb are believed to be accurate to about 5%, and this error is reported except for concentration data for olivine, opx, and garnet, where uncertainties approach 10%.
Constraints on the Nature of Melting and Melt Migration in Mantle Plumes: A Trace Element Study of Mantle Xenoliths from the Islands of Savaii and Tubuai

Introduction
The study of peridotites derived from the mantle is the most direct way to investigate the geochemical processes at work in the deep interior of the earth. Samples of mantle peridotite occur as tectonically emplaced bodies ("orogenic peridotites") and also as xenoliths carried to the surface by volcanic eruptions. Compared with orogenic peridotites, mantle xenoliths are generally less modified by retrograde metamorphism and crustal contamination; however, their small size and discrete nature eliminate any spatial relationships between xenoliths which may have existed before entrainment and eruption.
Modification by the volcanic host rock can also effect the texture, mineralogy, and chemistry of the xenolith.
The origins of mantle xenolith samples from oceanic islands are generally more well constrained than their more common counterparts found in continental volcanics.
Xenoliths in continental alkali basalts and kimberlites are typically samples which have been part of the subcontinental lithosphere for long periods of time, in excess of 3 Ga in some cases (Richardson et al., 1985). These samples have often been subject to many episodes of metamorphism and metasomatism during their residence in the subcontinental lithosphere. Xenoliths from oceanic islands will be either 1) igneous inclusions which have crystallized from mantle melts (either MORB or OIB magmas), 2) pieces of the mantle which have been accreated to the oceanic lithosphere, either at a mid-ocean ridge or by conductive cooling of the plate, or 3) entrained samples of the convecting mantle. The geochemical characteristics observed in OIB-hosted xenoliths are thus 1) results of events, usually associated with volcanic activity, which have taken place in a period of time which is limited by the age of the oceanic lithosphere beneath the individual island, or 2) characteristics present in the mantle source of the volcanics, or both. In these respects, OIB-hosted xenoliths represent the subset of mantle samples which are most likely to contain geochemical information about the convecting mantle. Mantle derived xenoliths are often texturally and chemically heterogeneous on the scale of a single specimen (e.g. Cox et al., 1987). These samples often show evidence of processes which are largely averaged together during magma genesis, and are thus either unobservable or have only subtle effects on the chemistry of magmas. An example of such a process is melt migration and percolation, the chemical effects of which have been observed in peridotite samples Bodinier et al., 1990; but are not obvious in the geochemistry of mantle derived magmas (Hofmann, 1984). The isotopic heterogeneity of oceanic island basalts requires the existence in the convecting mantle of geochemically distinct reservoirs, with quasi-independent chemical histories over time periods up to several billion years (e.g. . Isotopic and trace element studies of OIBs have provided much information on the chemistry of the source regions of these volcanics (e.g. , but often our knowledge of the mantle source geochemistry is limited by the extent of our knowledge (or ignorance) of the melting process. In this context, the study of xenoliths from oceanic islands holds great potential for placing constraints on the origins of chemically distinct parts of the mantle, with the additional ability to target those islands with unique isotopic signatures (provided the xenoliths exist).
With this strategy, an investigation of mantle derived xenoliths from the islands of Savaii (Western Samoa) and Tubuai (Austral Islands) is presented. Basalts from Savaii are characterized by high 87 Sr/ 8 7 Sr and high 207 Pb/ 204 Pb , and lie close to the EMIl isotopic endmember . Tubuai volcanics are characterized by very high Pb and Os isotope ratios ; Chapter 4), and lie close to the HIMU endmember . The petrographic and geochemical data reveal similarities and differences in the mantle beneath these two islands with very different isotopic signatures. This data provides information on the nature of melting and the efficiency of melt extraction in the hotspot mantle sources of these islands.

Sample Locations
The island of Savaii is located on the western end of the Samoa Islands chain, in the western Pacific Ocean (Fig. 1). The ages of Samoan shield lavas display an age progressive trend toward the southeast end of the chain Natland and Turner, 1985), consistent with a hotspot origin . However, the exposed volcanics on Savaii are largely post-shield alkali basalts (<2 Ma), with only a small exposure of shield lavas (4-6 Ma) on the northeast side of the island. Ultramafic xenoliths were sampled from several sites on the island, with the largest number of samples coming from a tuff cone which serves as a mine for road mettle (SAV 1 locality).
The island of Tubuai is located in the Austral Island chain in the south Pacific Ocean (Fig. 2). The ages of the Cook-Austral Islands follow a hotspot trend of decreasing age toward the southeast from Mangaia (20 Ma) to historic eruptions of Macdonald seamount Turner and Jarrard, 1982;  and picrite with occasional exposures of phonolitic plugs. The exposure of the western volcano consists of a chain of small hills forming an arcuate structure which may be the remains of a small caldera (Brousse et al., 1980). The exposed rocks are dominantly of a silica-undersaturated basalt (SiO2-=41.35%, Nenorm=29%), which has very high alkali contents (Na20=6.22%, K 2 0=1.62%) and MgO=7.65% (Mg#=.52), and is referred to as a "mafic phonolite" . Locally, this rock contains abundant olivine xenocrysts and peridotite microxenoliths (up to 1 cm). Larger xenoliths (1-6 cm) were collected from various exposures.

Textures and Petrography
To this point, a systematic petrographic study of the Savaii and Tubuai xenoliths has not been pursued. As a result, the extent to which the trace element characteristics of individual samples relates to their petrographic identities cannot be ascertained. However, some very broad generalizations are possible based on examination of hand specimens and a limited number of thin sections.
Most of the samples from Savaii were erupted in a tuffaceous flow, and have experienced limited interaction with the host basalt. The xenoliths from Tubuai were collected from massive boulders of basalt; the xenoliths show varying degrees of interaction with the host basalt. Some samples (ex. SAV 1-1, SA 3-11) have small veinlets running through the sample, either as well crystallized basalt or glass, which can be traced to the host basalt. Other samples show incongruent dissolution of pyroxene at the xenolith margins. The xenoliths have also experienced varying degrees of chemical weathering in the tropical environment; however, serpentinization of the xenoliths is minimal (typically less than 1%), and fresh olivine is preserved in all of the samples analyzed here.
The xenoliths from both islands show a range of textures. Several xenoliths with protogranular textures are present (SAV 1-27, SA 3-9, SA 3-11), with large olivine grains up to 5 mm. Most samples display porphyroclastic textures, with orthopyroxenes displaying a range of sizes up to 2-3 mm. In general, the Tubuai samples seem to have a smaller average olivine grain size than the Savaii samples. No consistent correlation of texture with trace element character is apparent, though most samples with depleted REE patterns have protogranular textures.
The xenoliths from Savaii and Tubuai are both characterized by low modal abundance of clinopyroxene, in most cases less than 5%, classifying these samples as harzburgites. One notable exception is TBA 1-9, which is a wehrlite (roughly 40% cpx, 60% olivine). In no case is the distribution of clinopyroxene uniform in these peridotites.
Instead, the clinopyroxene is concentrated as small grains into patches or "stringers", often in conjunction with small orthopyroxene crystals. Clinopyroxene color is also slightly variable; LREE-depleted clinopyroxenes are generally a dark green, whereas clinopyroxenes very strongly enriched in the LREE (ex. SAV 1-1, TBA 4-11) are often a light "apple green" color. Often these LREE enriched samples contain olivine which is characterized by extensive systems of annealed cracks, making the olivines appear cloudywhite in hand specimen. These olivines contain inclusions of glass and/or fluid along these annealed cracks. In general, from the examination of hand specimens, the Savaii xenoliths commonly contain substantial modal abundances of orthopyroxene, up to 40% in some clinopyroxene-free samples which have not been examined here. In those samples without clinopyroxene, the orthopyroxenes are commonly of a grey-green color. Some xenoliths from Savaii (SAV 1-3, SAV 1-19, SA 3-11) also contain symplectite intergrowths of spinel+opx_+cpx. Symplectites of spinel+opx are also commonly found in the cpx-free xenoliths from Savaii. No symplectites have been found thus far in the Tubuai xenoliths.

Analytical Procedures
For some samples, fragments of polished thin sections were gold coated for ion microprobe analysis. For samples without corresponding thin sections, mineral grains were handpicked and mounted in epoxy, polished, and gold coated. This was necessary in those cases where clinopyroxenes or symplectites were not present in the thin sections.
Trace elements (Sc, Ti, V, Cr, Sr, Zr) and rare earth elements (La, Ce, Nd, Sm, Eu, Dy, Er, Yb) in individual phases were analyzed in situ by secondary ionization mass spectrometry (SIMS) using the Cameca IMS 3f ion microprobe at the Woods Hole Oceanographic Institution. For most trace element analyses, a primary beam of O-ions with a current of approximately 0.2 na was focussed to a spot size of 8-15 mm. For REE analyses, and for Sr and Zr analyses below 1 ppm, a 1-2 na primary beam was used, focussed to a spot size of approximately 20-30 mm. Positive secondary ions were collected and counted by an electron multiplier, and molecular interferences were excluded by energy filtering (10V energy window, -90V offset for trace elements, -35V to -60V offset for REE elements, . Concentrations for clinopyroxenes were determined from empirical working curves using a set of well determined standards.
Reproducibility of the trace element concentrations is generally on the order of 10%-30% for the data reported here, with the exception of some low level REE measurements approaching the detection limit, where uncertainties may be as high as 50%. Analyses with estimated errors in excess of 50% are not reported. Each reported analysis in Tables 1 and  Table 3. Isotopic Data for Savaii and Tubuai xenoliths. Uncertainties are + 0.004% on 8 7 Sr/86Sr and 14 3 Nd/1 44 Nd, 0.3% on 187 0s/ 186 0Os, and 0.1%/amu on Pb isotope ratios. Uncertainties for U-Th-Pb concentrations is estimated at 1-3%. Figure 3 (a-s). Chondrite normalized trace element data for clinopyroxenes in peridotite xenoliths from the island of Savaii, Western Samoa. Each trace element pattern represents the analysis of a single grain. Data are normalized using the chondrite data of Anders and Grevesse (1989).  I  I  I  I  I  I  I  I  I  I  I  I  I   During REE analyses, it was common to measure large positive anomalies in Eu and smaller positive anomalies in Er. This is caused by the interference of barium oxides on the masses of interest ( 135 Ba 1 60 on 15 1 Eu; 1 35 Ba1 6 02 on 1 67 Er), which cannot be eliminated by energy filtering at -60V offset. The presence of Ba during the REE analysis of clinopyroxenes is correlated with cracks and cloudy areas in the mineral grains, and is not present (above about 1 ppm Ba) in clear, inclusion free areas. The Ba oxide interferences were eliminated by either moving to a different spot on the grain or employing the REE program with Ba oxide correction (on Eu only) during analysis. As a result, for some analyses, Eu and/or Er may have larger errors, or may be eliminated from the reported data.

Results
Trace element data for the Savaii xenoliths is given in Table 1 and plotted in Figurela-s; data for Tubuai xenolith clinopyroxenes is given in Table 2 and plotted in  (Table 1); however, Ti and Zr show varying degrees of depletion with respect to the REE (Fig. 1). In general, the patterns appear to show varying amounts of LREE enrichment starting from LREE depleted patterns. The clinopyroxene analyses are classified into three groups based on REE pattern (Table 1) Isotopic data for olivine and clinovyroxene separates from SAV 1-1, and a clinopyroxene separate from TBA 4-11 are given in Table 3. The clinopyroxenes from these two xenoliths have Group 3 trace element patterns, with very high LREE and very low Ti concentrations. The TBA 4-11 cpx is characterized by 87 Sr/ 86 Sr and Pb isotope ratios which fall within the range of basaltic lavas from Tubuai (REFS, Chapter 4).
However, the cpx separate from SAV 1-1 is characterized by very high 87 Sr/ 8 6 Sr, which is well outside the range of 87 Sr/ 86 Sr measured for Samoa basalts (highest 87 Sr/ 86 Sr is .7075, . The 206 Pb/ 204 Pb and 208 Pb/ 204 Pb ratios for this sample is typical of lavas from Savaii, and the 207 Pb/24Pb is near the highest values measured for Savaii lavas (see Chapter 4). An olivine separate was analysed from this sample in order to determine the isotopic composition of enclosed fluid and melt inclusions. The Pb isotope ratios are identical to the clinopyroxene within error (Table 3), and the 87 Sr/ 86 Sr is similar to, but slightly lower than, the extreme value for the SAV 1-1 cpx.

Origin of the Depleted (Group 1) Signatures
The Group 1 depleted clinopyroxenes are shown in have negative Ti anomalies. The strongly depleted patterns with positive Zr and negative Ti anomalies are signatures which are characteristic of garnet, though the REE concentrations in these cpx are lower than typical mantle-derived garnets. Some Tubuai Group 1 patterns have negative anomalies in both Ti and Zr, and bear some similarities to cpx from abyssal peridotites dredges from fracture zones near hotspots (Bouvet, Discovery II) . LREE concentrations are variable, and suggest the earliest stages of a metasomatic enrichment process. However, in some cases (ex. SAV 1-27) the concentrations of the LREE (but not Zr) approach the detection limit of the ion probe analysis, in which case these concentrations would be upper limits.
The Savaii Group 1 cpx patterns are distinctly different from both the abyssal peridotite and Tubuai Group 1 patterns. The Savaii Group 1 cpx are characterized by low Yb concentrations and very fractionated HREE, with (Yb/Dy)n up to 10. These samples also display large positive Zr anomalies, with slightly negative or non-existent Ti anomalies. Though the Savaii cpx have Nd and Sm concentrations an order of magnitude lower than abyssal peridotites, the Zr concentrations are similar. These patterns are also suggestive of residual garnet, though the HREE concentrations in the Savaii cpx are somewhat lower than in the Tubuai cpx.
Most of these trace element signatures are suggestive of origins as residues of melting with variable amounts of garnet. Due to the extreme fractionations of some trace elements with very similar solid/melt partition coefficients (i.e. Yb and Dy), the Savaii and Tubuai cpx patterns are modelled as residues of fractional melting. This has been successfully done for abyssal peridotite cpx by Johnson et al. (1990). The equations of Shaw (1970) for non-modal fractional melting are used, and are cast into a form which describes the trace element concentrations in both the bulk solid and clinopyroxene as a function of the degree of melting: 1 PF The initial concentrations in the bulk solid are assumed to be 2.5 times Cl chondrite for all trace elements. For the Savaii xenoliths, this assumption is justified by nearchondritic 143 Nd/ 1 44Nd (.51264) measured for some Samoan lavas (e.g. ; Chapter 4). However, some lavas from Samoa, and all basalts from Tubuai are characterized by depleted 14 3 Nd/ 144 Nd signatures, and so an assumption of a depleted REE signature for the initial solid composition would be more appropriate in these cases.
The most depleted 14 3 Nd/ 1 44Nd signatures in the Samoa and Tubuai lavas could be created in a 1-3 Ga old source which had experienced 1-5% melting, and so the absolute degrees of melting calculated from the present model may be overestimates by about 1-5%; however, this has no bearing on the conclusions since the emphasis here is on the amount of melting in the garnet lherzolite stability field relative to the spinel lherzolite stability field.
The initial phase proportions in the solid are given in Table 4, and are appropriate for pyrolite (Ringwood, 1979) in the garnet lherzolite (GL) and spinel lherzolite (SL) stability fields. Also given in Table 4 are the melt modes for various peridotite mineralogies. These coefficients describe the proportions of phases which enter the melt.
The term "garnet harzburgite" (GHz) is used here to refer to the 3-phase assemblage olivine+opx+garnet. When a mineral phase is exhausted, or when the mineralogy is changed (i.e. gt --> cpx+opx+sp) during the melting calculation, the bulk partition coefficients are recalculated according to the calculated phase proportions, and the calculation continued.
All of the trace element patterns are modelled by starting melting in the GL field, with subsequent further melting in the SL field. This requires the breakdown of garnet to cpx+opx+spinel by the following reaction: Assuming that MgTs is partitioned into cpx and opx in the ratio 2:1, the above two mineral reactions may be combined to give: (1-X)Mg 2 SiO 4 + Ca. 6 Mg 2 . 4 A1 2 Si 3 0 1 2 --> (1.4-X)Mg 2 Si 2 0 6 (X gAl 2 SiO 6 (olivine) (garnet) (opx+MgTs) + (0.6)CaMgSi 2 0 6 (2XMgAl 2 SiO 6 3X (cpx+MgTs) The variable X determines the amount of spinel which is used to make MgTs, and could be chosen to have any value between zero (no Al in pyroxenes) and unity (all spinel as MgTs). A value of 0.5 results in a clinopyroxene with about 40% wollastonite, which is typical of many mantle derived clinopyroxenes. With X--0.5, the above reaction in terms of weight fractions is: In addition, solid solution exists between clinopyroxene and orthopyroxene. In peridotitic bulk compositions, the effect of this solid solution with increasing temperature and pressure is to increase the modal abundance of cpx at the expense of opx: Since the extent of opx-cpx solid solution is almost entirely a function of temperature, this reaction cannot be accurately modelled without a detailed temperature history for a parcel of melting peridotite. In modelling the Tubuai trace element patterns, it was not necessary to take pyroxene solid solution into account. For the Savaii modelling, a constant value of 8 wt% opx solution into cpx is assumed so that cpx is not exhausted during melting in the spinel lherzolite field. The "reaction modes" for these reactions are given in Table 4. The mineral/melt partition coefficients used in the modelling are given in Table 5, and the partitioning patterns are shown in Figure 6. Clinopyroxene/liquid values are chosen from the experimental literature (e.g. , and are similar to values reported by Johnson et al. (1990) and Hart and Dunn (1992). The Cpx/liquid pattern is characterized by a pronounced decrease in values for the LREE relative to the HREE, and a significantly lower value for D(Zr) compared with D(Nd) and D(Sm). The value of D(Ti) is slightly less than for the adjacent REE.
Garnet/liquid values are an average of experimental literature data (ex. Nicholls and Harris, 1980) and values calculated from garnet/cpx partition coefficients measured from Ronda (Chapter 2) and from garnet peridotite xenoliths from Patagonia (Salters, 1989). The garnet/melt partitioning pattern is characterized by a positive anomaly for D(Zr) and a negative anomaly for D(Ti).
Mineral/melt partition coefficients for olivine, orthopyroxene, and spinel are taken from mineral/mineral partition coefficients reported by Stosch (1982) and McDonough et al. (1992) combined with the above cpx/melt Ds, and from the data of McKay (1986), , Fujimaki et al. (1984), and Dunn (1987); the values are the same as those used by . Olivine, opx, and spinel are all characterized by D(Ti) and D(Zr) values much higher than for adjacent REE. The olivine and opx REE partition coefficient patterns are characterized by a strong fractionation of LREE from HREE, and the HREE (Dy, Er, Yb) from each other. These partition coefficients are assumed to be constant throughout melting. In fact, mineral/melt partition coefficients for the various phases are functions of pressure (P), temperature (T), and the composition of individual phases. For example, at P-T conditions above the pyroxene solvus, a single pigeonitic pyroxene is the stable pyroxene phase (Lindsley and Andersen, 1983). Since this phase has a different crystal structure than typical orthoand clinopyroxenes, it will likely have different mineral/melt partition coefficients than either opx or cpx. The same effect may also apply to garnet, as pyroxene solid solution into garnet increases with increasing P and T (Takahashi, 1986). Since the La Ce Nd Zr Sm Eu Gd Ti Dy Er Yb Figure 6. Mineral/melt partition coefficient patterns for olivine, orthopyroxene (opx), clinopyroxene (cpx), spinel, and garnet. The partitioning patterns for garnet, opx, and olivine all have steep negative slopes for the HREE (Dy, Er, Yb) and large anomalies for Zr (relative to Sm) and Ti (relative to Dy). The partitioning pattern for cpx has small negative anomalies for Zr and Ti. The changing proportions of these minerals during melting results in variable fractionation of Zr and Ti from the REE.
relevant mineral/melt partition coefficients are presently unknown, no attempt is made to account for these effects. The solid/melt partition coefficient pattern for a given bulk rock will depend on the proportions of the various minerals. For example, the bulk rock partition coefficient pattern of pyrolite will be different in the GL facies than in the SL facies. Melting in the GL field, followed by garnet breakdown, will yield a clinopyroxene with a trace element pattern quite different from a cpx from a residue of melting in the SL field. Depending on how much melting takes place in the GL and SL stability fields, a variety of trace element patterns can be produced, with variable absolute concentrations, degrees of LREE depletions, and either positive or negative Zr anomalies.

Tubuai Xenoliths (Group 1)
The modelled trace element patterns for the Tubuai Group 1 pyroxenes (heavy lines) are shown in Fig. 7a-h along with the measured patterns. Since most of the measured clinopyroxenes show clear evidence of incipient LREE enrichment, the main goal was to try and fit the absolute and relative concentrations of Zr, Ti, and the HREE Dy, Er, and Yb. Critical melting, in which some fraction of liquid remains in the residue throughout melting (Maaloe, 1982), would conceivably result in a more efficient retention of the LREE in the residue; however, this phenomena would be largely indistinguishable from incipient LREE enrichment through metasomatism, which clearly effects most of these xenoliths. All of the trace element patterns are modelled by starting melting in the GL field, breaking down garnet, and continuing melting in the SL field. The total degree of melting modelled for the Tubuai samples ranges from 16.8% (TBA 4-6) to 27.5% (TBA 5-1). In the above melting model, the degree of HREE fractionation (i.e. Yb/Dy ratio), the Ti/Dy ratio, and the Zr/Sm ratio are sensitive to the amount of melting in the GL field. For example, sample TBA 4-8, with a negative Zr anomaly, is modelled by 9% melting in the GL field followed by 13% melting in the SL field (Fig. 7d). Sample TBA 1-7 is modelled with a larger relative amount of melting in the GL field (15% GL melting, 11.5% SL melting) due to the positive Zr anomaly and high Yb/Dy ratio (Fig. 7f). The absolute concentrations of the HREE and, to a lesser degree Ti, are sensitive to the amount of melting in the SL field. Since the cpx/melt partitioning pattern is relatively smooth for the elements Eu-Yb, melting in the SL field (under about 10%) has only minor effects on the trace element pattern for Eu-Yb, but has a significant effect on the absolute trace element concentrations. For example, samples TBA 4-6 ( Fig. 7a) and TBA 4-8 (FIG. 7d), with pseudo-parallel patterns, are both modelled by 9% melting in the GL field, but different amounts of melting in the SL field, due to their different HREE concentrations. In all cases, the models result in a poor fit to the LREE concentrations, but Zr concentrations are usually accurately modelled. A notable exception is the trace element pattern for TBA 5-1 ( Fig. 7g), which has a garnet-like pattern, but a very high Zr/Sm ratio which cannot be modelled with any combination of melting in the two stability fields.

Savaii Xenoliths (Group 1)
The modelled trace element patterns for the Savaii Group 1 clinopyroxenes are plotted with the measured data in Fig. 8a-e. In general, the higher Yb/Dy ratios of the Savaii samples require a higher degree of melting in the GL field than the Tubuai samples.
In fact, the only way that the melting model can fit many of the Savaii Group 1 patterns is to melt in the GL stability field to, and in some cases beyond, the point at which clinopyroxene is exhausted from the residue (cpx-out), in this case 20.6% melting, leaving a residue of olivine+opx+garnet. The exact degree of melting at which the cpx-out point is reached is dependent upon the initial GL modes and the GL melt mode (Table 4).
However, the degree of Yb/Dy fractionation requires melting to the cpx-out point, no matter the absolute degree. Because the clinopyroxene/melt partition coefficients for Dy, Er and Yb are essentially the same (Table 5), melting to the cpx-out point in the GL stability field is required in order for the garnet/melt partitioning pattern to exert sufficient influence on the trace element pattern of the residue. The high Yb/Dy ratios and negative Ti anomalies of the Savaii Group 1 clinopyroxenes requires residual garnet to dominate the solid/melt partitioning during melting.
The low HREE concentrations in the Savaii clinopyroxenes also require substantial degrees of melting in the SL field, after melting in the GL field and garnet breakdown to opx+cpx+spinel ( Fig. 8a-e). In order to match the observed HREE concentrations in the Savaii cpx, it was required to assume 8 wt% solution of opx into cpx, so that melting did not proceed to the cpx-out point in the SL field before the HREE concentrations were matched. The modelling was generally successful, with the exception of cpx from sample SA 3-11, which is characterized by a very high Yb/Dy ratio, very low HREE concentrations, and less than 9 ppm of Ti measured in the cpx. In order to fit these characteristics with the assumed partition coefficients, a very high degree of melting is needed (42.2%), accommodated by assuming 13% solution of opx into cpx (which may be excessive). In all of these cases, the mineral modes which are calculated from the model are characterized by very low modal abundances of cpx, in most all cases less than 2%. This is consistent with the general paucity of clinopyroxene observed in the Savaii Group 1 xenoliths. For the Savaii clinopyroxenes, the estimated total degree of melting for individual patterns ranges from 33% to 42.2% (Fig. 8a-e). subsequently reacted out at lower pressure to form clinopyroxene. One possible candidate phase is pigeonitic pyroxene, which is the result of mutual solubilities of clino-and orthopyroxene as a function of temperature and pressure (Lindsley and Andersen, 1983).
To date there have been no studies of trace element partitioning between high-pressure pigeonite and basaltic melts. Only the data of Takahashi (1986) allow some estimation of partitioning of Ti between high-P pigeonite and melt. Keeping in mind the complexities of deriving "near equilibrium" partitioning data from very high T and P experimental charges (Walker and Agee, 1989), the mineral and melt compositions from run #53 of Takahashi (1986) suggest a value of 0.1 for D(Ti) between pyroxene and melt. This value is between the opx/melt and cpx/melt values in Table 5. This may be the result of either the composition/crystal structure of high-P pigeonite, or possibly a lower value for D(Ti) at higher temperature (e.g. Nicholls and Harris, 1980). In either case, this may suggest lower values for tetravalent cations (i.e. Ti 4 + and Zr 4+ ) in high-pressure pigeonite, which is in the opposite direction required to model the Zr concentrations in the Savaii clinopyroxenes.
Another possible candidate phase is majorite garnet, which is the result of the increasing solubility of pyroxene into garnet (Takahashi, 1986). The trace element partitioning data of Kato et al. (1988) suggest values of 0.6 for D(Zr) and 0.2 for D(Sm) between majorite and ultrabasic liquid in a pyrolite starting composition at 16 GPa. The resulting ratio D(Zr)/D(Sm) for majorite/melt (3.0) is higher than the same ratio for garnet/melt in Table 5

Origin of the LREE Enriched (Group 2 and 3) Samples
The variable nature of the LREE enrichment in the Group 2 clinopyroxenes from both Tubuai and Savaii strongly resemble REE patterns which result from chromatographic-type melt migration processes acting on a LREE depleted mantle composition . This process is typically modelled clinopyroxenes were calculated using the cpx/melt partition coefficients in Table 5, and are plotted in Fig 9. In Fig. 9a, some of these hypothetical melts show good agreement with the trace element patterns in alkali basalts from Tubuai and Samoa , which indicates the suitability of alkali basalt as the percolating melt in some cases. However, the REE concentrations, LREE enrichments, and Ti and Zr depletions of some of the hypothetical melts are distinctly different from the Tubuai and Samoa basalts. In particular, the model melts in equilibrium with the Group 3B clinopyroxenes from samples listed in Fig. 9b have higher REE concentrations, higher LREE/HREE ratios, and much larger negative Ti and Zr anomalies than typical oceanic island basalts. From Fig. 9b, it is obvious that these hypothetical melts have trace element With some observational constraints on the compositions of the migrating melts, we now turn to the matrix composition. A progressive enrichment of the LREE, Zr, and Ti with "reaction progress" is evident from the Group 2 trace element patterns, typified by the sequence of patterns measured in the clinopyroxenes from sample SAV 1-46 (Fig. ln). Starting from the "depleted" Group 1 pattern (cpx 1), progressive enrichment in the LREE are observed with the concentrations of Zr, Ti, Dy, Er, and Yb remaining constant (cpx 3,5  (Fig. 10), such as would be the case if the matrix consisted dominantly of olivine+opx (see Table 5). This is also consistent with the generally small amount of , clinopyroxene in the observed modes for the Savaii and Tubaui xenoliths. Any melt percolating through a matrix with this partitioning pattern will develop negative anomalies in Zr and Ti, the magnitudes of which will increase with distance from the melt source as Zr and Ti are further fractionated from the REE.
In order to demonstrate the ability of the porous flow melt percolation process to reproduce the characteristics of the Group 2 clinopyroxene patterns, melt percolation was modelled according to the numerical method outlined by  (see their Appendix A). In this version of the model, a melt of constant composition is percolated through a matrix of peridotite. The melt is assumed to percolate through the matrix with no reactions taking place, only trace element exchange between the melt and matrix. In reality, some reaction between melt and matrix might be expected to occur, such as the pyroxene dissolution reaction modelled by . However, the considerable uncertainty in the phase equilibria of the above hypothetical melts, and the pressure and temperature at which the percolation takes place, make predicting such a reaction rather speculative. Simple percolation with trace element exchange is likely to model the most important features of the melt migration process in the present case. Trace element diffusion in the melt and matrix phases is taken into account by assuming a single diffusion coefficient for all elements in the matrix (10-13 cm 2 /s) and in the melt (10 -7 cm 2 /s). The effect of modelling diffusion in the solid matrix is to disperse the "fronts" of trace elements in the melt, thereby smoothing the concentration variations in the melt . Two melt trace element compositions are used in the modelling, given in Table 6: 1) SA 3-11 glass veins, which are similar in composition to typical alkali basalt, and 2) the melt calculated to be in equilibrium with SAV 1-28 cpx, similar in its trace element composition to carbonatites (Nelson et al., 1988). In all cases, the matrix mineralogy is that calculated from the polybaric melting model for SAV 1-27 cpx (Fig. 10), and the matrix trace element composition is that in equilibrium with SAV 1-27 cpx (Fig. lh). partitioning pattern (Fig. 10). Despite the ease with which the REE can be fractionated from Zr and Ti in this process (Fig. 11), the combination of extremely high LREE concentrations and extremely low Ti concentrations in some samples (SAV 1-1, SAV 1-28, TBA 4-11, TBA 5-4) require that the very high LREE and very low Zr and Ti concentrations be characteristics of the input melt (ex. Fig. 9b). Figure 12 shows the obvious fact that extreme LREE enrichment with concomitant Zr and Ti depletion can be accomplished by percolation of a carbonatitic melt (e.g. see Fig. 4i). In addition, these samples very commonly contain substantial amounts of Ba concentrated in inclusions, cracks, and grain boundaries. Although this Ba is not present in the cpx crystal structure, the measured intensity of Ba during ion microprobe analysis would be equivalent to 5-40 ppm (compared with <1 ppm in typical LREE enriched cpx,   Table 6. Trace element concentrations (ppm) of melts used in the percolation model. SA 3-11 veins column is the measured composition of glass veins and patches in SA 3-11 xenolith. SAV 1-28 "melt" is the hypothetical melt in equilibrium with SAV 1-28 cpx, calculated from the cpx/melt partition coefficients given in Table 5.  . Model "carbonatite" is the hypothetical melt in equilibrium with SAV 1-28 clinopyroxene, and the matrix is the same as in Fig. 11. Trace element patterns in clinopyroxene calculated at a distance of 10 meters from point of melt input. Melt velocity is 10 cm/yr, porosity is 0.1%, and tc=10 years. A lithospheric origin for the Tubuai xenoliths is supported by the 1870s/1860s ratios of two xenoliths from this island ( Table 3). As shown in Fig. 13, TBA 1-7, with a depleted garnet-like trace element pattern, and TBA 4-11, with a carbonatitic pattern, both have 187 0s/ 186 0s ratios within the range of estimates of depleted mantle (e.g. , and distinctly lower than 187 0s/ 186 0s measurements of basalts from Tubuai Chapter 4). Though the Pb isotopic composition of TBA 4-11 is within the range of Tubuai basalts, it is very likely that this is a metasomatic signature, as outlined above. Based on this low 187 0s/ 186 0s relative to the Tubuai basalts, it would appear that the carbonatite melt which resulted in the TBA 4-11 trace element signature may have had a low Os concentration or low 187 0s/ 186 0s (possibly due to percolation); in any case, this melt was ineffective in imprinting the high 187 0s/ 186 0s Tubuai signature on this xenolith.
The 187 (s)/ 186 Os ratios of two xenoliths from Savaii (SAV 1-27, depleted garnet-like pattern; SAV 1-1, carbonatitic pattern) are within the range of 1870s/186Os measurements of Savaii basalts  Chapter 4); however, they are also within the range of depleted mantle estimates, so ruling out a lithospheric origin for these xenoliths remains problematic. It is interesting to note, however, that the depleted xenolith SAV 1-27 has a very low 187 0s/ 186 0s of 1.018, which is near the lowest 187 0s/ 186 0s ratio so far measured in a Savaii basalt (1.026, Chapter 4). In any case, the the extremetly high degrees of melting calculated for the Savaii xenoliths suggests a mantle plume origin for these xenoliths.
It appears that fractional melting was an important melting process in the Samoan mantle plume and, by analogy, possibly other hotspots as well. This conclusion is supported by the coupled fractionations of Sm/Nd and Lu/Hf in oceanic basalts ). In addition, the xenolith cpx trace element patterns require that melting took place in the presence of garnet. The role of garnet in the generation of hotspot magmas has been simultaneously supported by trace element evidence (ex. Feigenson, 1986;Frey and Roden, 1987), and refuted from experimental petrological studies which have failed to find olivine-opx-cpx-garnet multiple saturation in proposed primary magma compositions (ex. Green and Ringwood, 1967;Eggins, 1992). The process of fractional melting requires that erupted melts be some aggregate of instantaneous melts, probably generated at a range of pressures and temperatures. As pointed out by Eggins (1992), this fact may preclude the existence of equilibrium with a garnet lherzolite mineral assemblage. Fractional melting in mantle plumes is consistent with the constraints available from experimental studies on primary magma compositions, trace element studies of hotspot basalts, and the trace element systematics of oceanic island peridotite xenoliths. If instead some of the LREEdepleted xenoliths are fragments of oceanic lithosphere formed during MORB genesis, then the trace element data presented here provide unequivocal evidence for the role of garnet in MORB genesis, in agreement with .
The model of melt percolation through harzburgite developed in the previous section was shown to be very efficient at creating depletions in Zr and Ti, relative to Sm and Dy, as previously demonstrated by Keleman et al. (1990). In addition to interphase partitioning as advocated by McDonough et al. (1991), this percolation phenomena may provide an explanation for the widespread presence of Ti and Zr depletions in peridotite clinopyroxenes (Salters and Shimizu, 1988). This is likely to be an important phenomena in creating Zr and Ti depletions especially in xenolith cpx, since the fragments of peridotite entrained in erupting magmas originate from the wallrocks of magmatic conduits, and are thus very likely to have experienced exchange or reaction with a magma. This may explain the general dominance of LREE enriched over LREE depleted xenolith samples , as well as LREE depleted over LREE enriched peridotites in peridotite massifs (ex. , and strongly suggests that peridotite xenoliths are inherently not   Figure 14. A) Sr-Nd and B) Sr-Pb isotope plots of cpx separates from Samoa and Tubuai xenoliths, relative to fields for Samoa and Tubuai basalts, and other OIBs. The data for TBA 4-11 lies within the field of Tubuai basalts, whereas the data for SAV 1-1 lie on an extension of the Samoa basalt array to much higher 7 Sr/8 Sr and lower 143 Nd/ 1 " Nd. The high 87 Sr/6 Sr, low 4 3 Nd/'" Nd, and high 207 Pb/ 206 Pb are broadly similar to modem oceanic sediments  The trace element characteristics of the Group 3b samples SAV 1-12, SAV 3-3 #1, and SAV 1-36 #4 demonstrates the suitability of Tubuai and Samoa alkali basalts as the percolating melts which generated many of the Group 2 trace element patterns. However, the clinopyroxenes listed in Fig. 9b indicate the presence of a melt with a trace element composition very similar to carbonatite melt (Nelson et al., 1988). There are basically two origins for carbonatite magma: 1) immiscible exsolution of carbonatite magma from CO2 rich nephelinite at pressures of 2-25 kilobars (Baker and Wyllie, 1990); and 2) small degree partial melt of carbonated peridotite (Wallace and Green, 1988). In addition, a small degree partial melt of carbonated peridotite will evolve toward nephelenitic composition with increasing degree of melting, resulting in a compositional continuum, probably in terms of trace as well as major elements, between carbonatite melt and nephelinite. Such a carbonate rich melt could also create the trace element patterns of the Group 3b clinopyroxenes. The isotopic compositions of two Group 3b clinopyroxenes (TBA 4-11, SAV 1-1, Irrespective of the mechanism of origin of the carbonatitic melts, it is clear that the isotopically enriched endmember components beneath both Tubuai and Samoa are volatile (CO2) rich. It is important to ascertain the provenance of this volatile-rich mantle, whether it is a widespread component in the upper mantle, or whether it is restricted to the Tubuai and Samoa mantle plumes. The low concentrations of CO2, H 2 0, and CH 4 in mid-ocean ridge basalts (Moore, 1970;Byers et al., 1986;Michael, 1988) suggests a depletion of volatiles in the upper mantle sources of MORB relative to the higher volatile concentrations in plume-related basalts (Moore and Schilling, 1973;Byers et al., 1985). The presence of a carbonatitic component in the mantle sources of both Tubuai and Savaii argues against a direct relationship between this component and the trace element characteristics which have resulted in the different endmember isotopic compositions of these islands, since these endmember isotope signatures require very different parent/daughter ratios. This indicates that, although the Tubuai and Samoa plume mantles are volatile rich, the carbonatitic signatures are the result of magma generation processes operative in these hotspots.
The presence of volatiles in these hotspots has important implications for melting in mantle plumes, as discussed for Hawaii by . The mantle at the plume axis (about 15000C) will cross the solidus of peridotite+CO2+H20 at a depth of approximately 350 km (Boettcher et al., 1980;Olafsson and Eggler, 1983;Falloon and Green, 1989), generating a small degree partial melt which is rich in CO2, and may approach a carbonatitic composition (Wallace and Green, 1988). With increasing degrees of fractional melting, as the volatile component is segregated from the melting zone, the solidus of peridotite will shift toward the anhydrous peridotite solidus, requiring further decompression before larger melt fractions are generated. The result is a large region of the mantle plume which is generating small melt fractions, and a much smaller region of the plume which is above the anhydrous peridotite solidus, generating larger melt fractions, with the compositions of the erupted melt products strongly dependent on how the melts are aggregated. The ultimate origins for the volatiles in the Tubuai and Samoa mantle plumes may be in subducted materials recycled into the asthenosphere, and incorporated in upwelling mantle plumes.

Conclusions
Clinopyroxenes in peridotite xenoliths from the islands of Savaii and Tubuai display a large degree of trace element heterogeneity, both between and within single xenolith hand specimens. Trace element modelling of the subset of clinopyroxenes with depleted signatures indicates that these samples have experienced large degrees of polybaric fractional melting (18%-42%) within the stability fields of garnet lherzolite and spinel lherzolite. In particular, the extremely fractionated trace element patterns of the Savaii depleted clinopyroxenes requires that these peridotites melted to the point of clinopyroxene exhaustion while in the garnet stability field, leaving a residue of olivine+opx+garnet, which then experienced further melting in the spinel lherzolite field after breakdown of garnet to pyroxene and spinel. These characteristics have thus far not been found in abyssal peridotites, and thus a mantle plume origin may be indicated for these xenolith samples, as well as other LREE enriched xenoliths with clinopyroxene HREE and Ti concentrations similar to the depleted (Group 1) signatures. The high degrees of melting calculated for these samples is in apparent conflict with the low degrees of melting suggested by the trace element modelling of oceanic basalts (ex. Feigenson, 1986;Frey and Roden, 1987). In addition, the requirement of melting in the garnet stability field conflicts with the lack of experimental evidence for equilibrium of primary magma compositions with garnet lherzolite (Green and Ringwood, 1967;Eggins, 1992). However, both of these apparent conflicts can be reconciled with the xenolith data, because fractional melting requires that the erupted basaltic melts are aggregates (mixtures) of many small melt fractions.
The variable degrees of LREE enrichment in most of the Savaii and Tubuai xenoliths is consistent with the migration of basaltic melts through harzburgite. The abundance of LREE enriched xenoliths, and their relative scarcity in abyssal peridotites (REF) indicates that melt extraction is less efficient from mantle plumes than from the mid-

Introduction
The Re-Os isotope system has received considerable attention from the geochemical community over the past 10 years, following the pioneering work of Luck et al., (1980). The 3-decay of 187 Re to 186 Os produces measurable variations in the abundance of 187 Os in samples of natural osmium. The very different behaviors of Re and Os during basaltic melt generation, as well as their siderophile and chalcophile characters, provide information quite different from the other parent-daughter systems (Rb-Sr, Sm-Nd, Lu-Hf, U-Th-Pb).
The Re-Os system has been used as a unique tracer in studies of crustal and mantle geochemistry (Palmer et al., 1988;Walker et al., 1988;Esser, 1990, Martin, 1991, the geochemistry of ore deposits Lambert et al., 1989;Martin, 1989;Hattori et al., 1991), and as a geochronometer for dating ores  and terrestrial rocks (Walker et al., 1988;Ravizza et al., 1989;, as well as providing an estimate for the age of the galaxy (Luck et al., 1983).
Re-Os studies have demonstrated that both oceanic and continental crustal materials have much higher Re/Os ratios than peridotites (Morgan et al., 1981;Esser, 1990;Martin, 1991). Re concentrations in crustal materials are typically 10-100 times higher than peridotites, while Os concentrations are 10-10,000 times lower than peridotites. Thus Re is thought to be moderately incompatible, and Os highly compatible, during melt generation. As a result of such high Re/Os ratios, crustal materials also have much higher 187 0s/ 186 0s ratios than peridotites ( 187 0s/ 186 0s = 3 to >100 for crust, 187 Os/ 186 0s = <0.90 to 1.10 for peridotites: Esser, 1990;Luck et al., 1991;Pearson et al., 1991;. The high Re concentrations and high Re/Os ratios of crustal materials, relative to mantle peridotite, make the Re-Os system a potentially powerful tracer for examining crustal recycling in the mantle.
The isotopic signatures of some oceanic islands have been interpreted as being derived from crustal material mixed into the mantle sources of these islands (Hofmann et al., 1980;Hofmann et al., 1982). Specifically, the EMII signature of high 87 Sr/ 86 Sr and high 207 Pb/ 204 Pb ratios  has been attributed to the recycling of sediments in the mantle . In addition, the high Pb isotope ratios which characterize the HIMU mantle component  have been attributed to subducted oceanic crust (Hofmann et al., 1980;. The trace element signatures of HIMU have also been attributed to recycled oceanic lithosphere , and a number of other oceanic island isotope signatures have also been attributed to this process .
In order to constrain theories of crustal recycling in the mantle, the Re-Os and Sr-Nd-Pb isotope systematics have been investigated in a suite of oceanic island basalts from the south Pacific Ocean. The combined Os, Sr, Nd, and Pb isotope results demonstrate that recycling of oceanic crust is responsible for some of the isotopic heterogeneity observed in the oceanic mantle and place constraints on the composition and age of the recycled crust in the mantle sources of these basalts.

Geologic Background
The southern Pacific Ocean is home to many linear island chains of volcanic origin.
Previous studies have demonstrated that the age of volcanism decreases monotonically toward the east-southeast end of several of these island chains Dalrymple et al., 1975;Turner et al., 1982), often with active volcanism at the extreme easterly end (Hekinian et al., 1991), supporting a hotspot origin for these features   ., 1976)). However, the islands from Mangaia east to Macdonald display a monotonic age progression consistent with the hotspot theory . Another possible exception is the Samoan chain, in which the lavas of the shield building phase are of progressively younger age to the east-southeast Natland et al., 1985), yet subsequent volcanism has taken place over a 600 km length of the chain within the last 1 Ma, mostly at the northwest end (Natland, 1980).
In contrast to Hawaii (Macdonald et al., 1964), geochemical studies have demonstrated that volcanism in the south Pacific is dominantly alkalic, with rare examples of tholeiitic volcanism (Duncan et al., 1986). The distinct stages of volcanic activity recognized in the Hawaiian chain are observed at some islands in the south Pacific (Samoa, Marquesas) (Duncan et al., 1986; but not others (Cook-Australs) . Trace element and isotopic studies (Liotard et al., 1986;Dupuy et al., 1987;Dupuy et al., 1988; have demonstrated that a large degree of geochemical variability is present in the mantle beneath the south Pacific Ocean, and has been recognized in samples as old as 120 Ma (Staudigel et al., 1991). This variability is manifested in geochemical differences between island chains, as well as extreme variability within single islands (Duncan et al., 1986;). In addition, examples of all of the oceanic mantle endmembers as defined by Zindler and Hart  are found in the south Pacific (DMM-East Pacific Rise ; EMI-Pitcairn ; EMII-Samoa, Tahaa ; HIMU-Mangaia, Tubuai ), as well as islands with elevated 3 He/ 4 He (Samoa, McDonald Seamount, Rapa ). The oceanic mantle in this restricted part of the world is strikingly rich in geochemical diversity.

Sample Selection
The basalt samples analyzed in this study were collected in the fall of 1990 specifically for Re-Os analysis. Analyzed samples are from the islands of Savaii (Western Samoa), Rarotonga and Mangaia (Cook Islands), Rurutu and Tubuai (Austral Islands) and Tahaa (Society Islands). The samples were chosen to include islands with known extreme isotopic compositions for 87 Sr/ 86 Sr (Savaii, Tahaa) and Pb isotopes (Tubuai, Mangaia) in order to search for a crustal signature in these islands.
Due to the high Re/Os ratios measured, the ages of the various islands examined in this study are important, in that samples from the older islands require corrections for radiogenic ingrowth since eruption. Though none of the samples have been directly dated, some constraints on their ages exist from field relations. The samples from Savaii are all young (<1 Ma) shield-capping flows, and two are from historic eruptions. The samples from Rarotonga are from the Te Manga group, dated at 1.2-2.3 Ma (Turner et al., 1982).
Reported ages from Tahaa range from 1.1 Ma to 3.4 Ma (Gisbert, 1989). The ages of the samples from Rurutu are not well constrained; the range of possible ages is 0.88-12.8 Ma . For Tubuai, reported ages range from 5.7 Ma to 10 Ma (Bellon et al., 1980). The oldest island sampled is Mangaia, with reported ages in the range of 16 to 20 Ma (Dalrymple et al., 1975;Turner et al., 1982). Large amounts of each sample (several kg) were collected, and an emphasis was placed on obtaining fresh samples; in the case of Mangaia, this was possible only by collecting stream cobbles, due to the extent of weathering of the few volcanic outcrops. When possible, several samples rich in olivine and pyroxene phenocrysts were chosen from each island in order to analyze samples with high Os concentrations and low Re/Os ratios, in an attempt to minimize uncertainties in the age corrections. Analytical procedures are given in the appendix.

Overview of Re-Os Systematics
Due to the geochemical characteristics of the two elements, the Re-Os isotopic system possesses some unique features which distinguish it from other radiogenic isotopic systems. During partial melting of mantle peridotite, Re behaves as a moderately incompatible element, whereas Os is strongly concentrated in the residue (Morgan, 1986).
As a result, mantle-derived melts are characterized by high Re concentrations and high Re/Os ratios relative to the residues of melting. Segregation of the melt leaves a residue with a lower Re/Os ratio than before melting. The behavior of Os is in contrast to Sr, Nd and Pb, which are partitioned into the magma during melting. The result is a much more extreme parent/daughter fractionation in the Re-Os system than in the other isotopic systems.
Due to its high Re/Os ratio, continental crust develops very high 187 0s/ 186 0s with time. In a study of continental river sediments and glacial loess deposits, Esser (Esser, 1990) measured 1870s/1860s ratios of 5.6 to 13.4 for these sediments, which act as integrators of large areas of continental crust. Though the crust is markedly heterogeneous in Re/Os and 187 0s/ 186 Os ratios, Esser has suggested a 187 0s/ 186 Os ratio of 10.5 for average continental crust, as well as average Re (400 ppt) and Os (50 ppt) concentrations (Esser, 1990). This is consistent with the existing measurements of continental crustal material (Morgan et al., 1967;. In addition to their different behaviors during melting, both Re and Os are chalcophile and strongly siderophile, and thus their geochemical behavior may be dominated by trace metallic or sulfide phases. As a result of this, it is likely that both Re and Os were partitioned strongly into the core early in earth history. The relative abundances of the highly siderophile elements in the mantle are approximately chondritic (Jagoutz et al., 1979;Mitchell et al., 1981;Morgan et al., 1981). Also, the chondritenormalized abundances of these elements in the mantle (about 10-2) are thought to be too high to reflect equilibrium with either a metallic or sulfur-bearing core. It has been suggested that the mantle budget of these elements was provided by accretion of chondritic material subsequent to core formation (Jagoutz et al., 1979;Morgan, 1985;Morgan, 1986); however, disequilibrium effects, incomplete core segregation, or variable metal/silicate and sulfide/silicate partition coefficients may also account for these abundances (Morgan et al., 1981). The Os isotopic evolution of the earth through geologic time is currently an issue with considerable uncertainty. Due to the possibility of Re/Os fractionation during accretion and core formation, the Os isotope evolution of the silicate earth may be different from that of the whole earth. Analyses of group IIAB and IIIAB iron meteorites (Horan et al., 1992;Morgan et al., 1992) indicates an initial 187 0s/ 18 60s of 0.794±.010. The measured present day 187 0s/ 186 0s ratios of chondritic meteorites range from 1.00 to 1.16 (Luck et al., 1983;, with an average of 1.07. Though an early study of osmiridiums of known age  suggested that the upper mantle followed a Re-Os evolution with a present day 187 0s/ 186 0s of 1.04, subsequent osmiridium studies Hattori et al., 1991) have demonstrated significant Os isotopic heterogeneity within and between localities, precluding the identification of a well constrained evolution curve. Luck and Allegre  have subsequently refined their present-day bulk silicate earth estimate to 187 0s/ 186 0s = 1.05-1.06 based on analyses of ophiolite peridotites.  have suggested a present-day value of 1870s/1860s = 1.10 for the bulk silicate earth based on analyses of abyssal peridotites and a crust-mantle mass balance. A similar value has been suggested by Martin (1991) for the mantle source of Hawaii based on analyses of basalts with elevated 3 He/ 4 He. Present-day measured 187 0s/ 186 0s ratios for peridotite xenoliths from South Africa and Siberia Pearson et al., 1991) lie in the range of <0.90 to 1.07, clearly demonstrating the existence of ancient, low Re/Os mantle in the subcontinental lithosphere.  measured 187 0s/ 186 0s ratios from 0.977 to 1.120 in peridotite samples from the Ronda ultramafic complex. A strong negative correlation of 187 0s/ 186 0s with Mg# in the peridotites suggests that a 1 87 0s/1 86 Os of 1.06-1.08 may be representative of undifferentiated mantle, similar to the ordinary chondrite average of 1.07. In detail, however, the Os isotope evolution of the earth's mantle is only broadly constrained.

Results
The Sr, Nd, U, Th and Pb concentrations, and Sr, Nd and Pb isotope results are given in Table 1. The concentrations of these elements are similar to those typically reported for alkali basalts (ex. ). 238 U/2 04 Pb (m) ratios vary from 18-61 and Th/U ratios range from 3.14-4.98. Both ratios are high relative to mid-ocean ridge basalts Cohen et al., 1980;Condomines et al., 1981;Cohen et al., 1982;Jochum et al., 1983;Newman et al., 1983;Goldstein et al., 1991); differences in source chemistry and melting processes are both likely to account for this. The Sr-Nd-Pb isotope ratios given in Table 1 agree well with previously reported data for these islands . The islands of Savaii and Tahaa are characterized by very high 87 Sr/ 86 Sr and high 207 Pb/ 20 4 Pb, and approach the EMII enriched mantle endmember . The values reported here are slightly lower than the most extreme 87 Sr/ 86 Sr ratios reported from Tutuila, American Samoa Farley et al., 1989 ratios represent the combined uncertainties on sample ages, 1 87 Re/ 1 8 6 0s (7%), and analytical reproducibility on (1 8 7 0s/1 8 6 Os)m (03%). Data averages are taken for samples with replicate analyses. Ages are estimated from sample locations and published ages for these islands Bellon et al., 1980;Turner et al., 1982;Natland et al., 1985;Gisbert, 1989). Phenocryst abundances are estimated from visual inspection of the hand specimens.
of the range of previously reported data from this island McDonough et al., 1991). The Re-Os data are given in Table 2 and plotted in Figs. 1 and 2. Also plotted in Figure 1 are Re and Os concentration data for basalts and komatiites from Gorgona Island , komatiites from Munro township (Walker et al., 1988) and basalts from Hawaii (Martin, 1991). Re concentrations in the south Pacific basalts range from 100 to 1621 ppt (parts per trillion, 10-12 g/g), and Os concentrations vary from 26 to 750 ppt.
The Os concentrations are systematically lower than Os concentrations in komatiites (Walker et al., 1988;. 187 Re/ 186 0s varies from 5.34 to 650, and exhibits a clear negative correlation with Os concentration (Fig. lb). The Re and Os concentration data in Table 2 suggest a clustering of Os concentrations into three groups (<:100ppt, 100-400 ppt, 400 ppt). 187 0s/ 186 0s ratios for the various islands are also reported in Table 2. Measured 187 Re/ 186 0s ratios in some of the samples were high enough to require age corrections on 187 0s/ 186 0s. Initial 187 0s/ 186 0s ratios were calculated using the middle of the age ranges listed in Table 2, and the age corrected 187 0s/ 186 0s ratios are plotted with the 87 Sr/ 86 Sr, 143 Nd/ 144 Nd, and 2 06Pb/ 204 Pb data in Fig. 2, along with 187 0s/ 186 0s data from Hawaii, and Iceland reported by Martin (Martin, 1991). Initial 187 0s/ 186 0s ratios for Samoa vary from 1.0261-1.0739, while 187 0s/ 186 Os ranges from 1.0567-1.0861 for Tahaa and 1.0419-1.0737 for Rarotonga. The higher values are between the two 1870s/1860s estimates for the bulk silicate earth . In order to evaluate the data relative to depleted upper mantle, also displayed in Fig. 2 are whole rock 187 0s/ 186 0s analyses of peridotites with 8 7 Sr/ 86 Sr, 14 3 Nd/1 44 Nd, and 2 06Pb/ 204 Pb similar to MORB, as determined from analyses of clinopyroxene separates . In this context, it should be noted that the peridotite with 187 0s/ 186 0s of 1.10 is a garnet-rich sample from Ronda which is likely a disaggregated mafic layer . Excluding this sample, the MORB-like peridotites have 187 0s/ 186 0s around 1.04-1.05, which is low relative to both bulk silicate earth estimates.  . The data from Rurutu, Tubaui and Mangaia suggest a correlation between 187 Os/ 186 0s and 206 Pb/ 204 Pb.

Re and Os concentrations
From Table 2, it is clear that samples with high abundances of olivine+clinopyroxene phenocrysts have higher Os concentrations and lower 187 Re/ 186 0s ratios than aphyric samples. The Re-Os concentration systematics in komatiites (Walker et al., 1988; also suggest the involvement of a low Re/Os phase in which Os is compatible. Preliminary Re and Os partitioning data reported by Watson et al   With one exception, Re concentrations in these basalts are systematically lower than Re concentrations from Hawaiian tholeiites (Martin, 1991)

and tholeiites from Gorgona
Island . Some of the lowest Re concentrations are probably due to dilution of the melt with phenocrysts (ex. MGA-B-47). The systematically lower Re contents in the basalts studied here may reflect either differences in the generation of tholeiites and alkali basalts, or differences in source composition .
However, if Re is incompatible during partial melting of peridotite, Re concentrations in alkali basalts should be higher than in tholeiites. The higher Re concentrations of tholeiites might indicate the involvement of a mantle phase which remains in the residue at small degrees of melting, yet might be exhausted during the relatively higher degrees of melting involved in tholeiite generation. With the exception of sample RAR-B-9 from Rarotonga,  Morgan, 1986), the average Re concentrations of the basalts in this study suggest an apparent partition coefficient (peridotite/melt) near unity during the generation of alkali basalts. This is consistent with the negative trend in Fig. Ic; if the Re/Nd ratio is pedominantly controlled by partial melting and fractional crystallization, Fig. lc indicates that Re was more compatible than Nd during these processes.

18 7 0s/ 186 0s Systematics of EMIl Islands
Despite their extreme 87 Sr/ 86 Sr and elevated 207 Pb/ 2 04Pb, the Samoa and Tahaa samples are not distinctive in their 187 0s/ 186 0s ratios, falling within the range of 187 0s/ 186 0s for abyssal peridotites (Martin, 1991;Snow, 1991), "normal" ophiolite peridotites  and MORB-like peridotites . The high 87 Sr/ 86 Sr and elevated 207 Pb/ 20 4 Pb of the Samoa and Tahaa samples may have their origins in a source containing a component similar to modern sediments, as advocated previously for Samoa . If sediment is indeed involved in the origin of the Samoan mantle source, the amount of sediment must be small, not more than a few percent, in order to fit the observed Nd and Hf data for Samoa (White et al., 1984). Mixing of such a small amount of sediment into the mantle would have only a small effect on the 187 0s/ 186 0s ratios, due to the low Os concentration of continental crustal material (Esser, 1990). Mixing of a depleted mantle ( 87 Sr/ 86 Sr-.703, 143 Nd/ 144 Nd= .51290, MORB-like Pb, 187 0s/ 186 0s=1.02-1.05), with 1-2% modern sediment, could reproduce the Samoan data. The relative concentrations of Pb, Sr, Nd and Os in most clastic sediments and peridotite (ratio of ppm sediment/ppm peridotite) decrease in the order Pb-Sr-Nd-Os. Thus, in a sediment/peridotite mixture with a small fraction of sediment, the Pb isotopes would be closest to the sediment component, followed by 87 Sr/ 86 Sr, then 143 Nd/ 144 Nd and 1 76 Hf/1 77 Hf, and finally 187 0s/ 186 0s would be only slightly changed from the peridotite value, if at all. This is essentially the order of deviation of the EMII isotope ratios from depleted mantle values. Some type of metasomatism, which has not strongly effected the Re-Os system, could also be invoked to explain the Samoa and Tahaa data. The present Os isotope data, as well as Nd and Hf isotope data for EMIl basalts, indicate that the mantle source of Samoa and Tahaa is nearly chondritic to slightly depleted in Re/Os, Sm/Nd and Lu/Hf. A detailed Re-Os investigation of the EMII islands, with many more samples than reported here, would be needed in order to evaluate the presence of a possible trend consistent with a sedimentary component in these islands.   (Martin, 1991), the range of data for abyssal peridotites (AP) (Martin, 1991;Snow, 1991), and peridotites with Sr, Nd, and Pb isotope ratios similar to MORB (Walker et al., 1989; AI1991). Error bars on the 1 7 0s/ 86 0s ratios represent the combmined  (Church et al., 1975;Cohen et al., 1980;Cohen et al., 1982)  In addition, if this process were important, it would be expected to have an even larger influence on the 187 0s/ 186 0s ratios of the lavas from Savaii, which rests on seafloor with an age in excess of 100 Ma. This is in conflict with the low 187 0s/ 186 0s ratios thus far observed in the Samoa data. The peridotitic part of the MORB lithosphere likely has low 187 0s/ 186 0s ratios, similar to abyssal peridotites (Martin, 1991;Snow, 1991) and "normal" ophiolite peridotites . While assimilation of this material may be important in some of the variation in the low 187 0s/ 186 0s samples, it cannot be the source of the high 187 0s/ 186 0s signatures of the HIMU basalts. Given the above arguments, we can eliminate crustal contamination as a process to generate the observed HIMU Os isotope signatures. Thus the high 187 0s/ 186 0s ratios are indicative of the Os isotopic composition of the mantle sources of the Rurutu, Tubuai and Mangaia basalts.

Separation of a Metal or Sulfide Phase
Since both Os and Pb are chalcophile elements, it is useful to consider the possibility that the high 187 0s/ 186 0s, high 206Pb/ 20 4 Pb signature is the result of removal of Os and Pb relative to Re and U by the separation of a sulfide phase from some portion of the earth's mantle (Vollmer, 1977;Vidal et al., 1978). This has probably taken place early in the earth's history to form the core. The hypothesis of continuous extraction of siderophile and chalcophile elements from the mantle to the core through geologic time has been investigated by , who measured the abundance ratios of siderophile and chalcophile elements to lithophile elements of similar incompatibility (ex. Mo/Pr and W/Ba). If the radiogenic Pb signature is the result of a metal-sulfide segregation process, resulting in a high U/Pb ratio, then this signature should be coupled with a low Mo/Pr or low W/Ba ratio. The near constancy of these ratios (within a factor of 4) in oceanic basalts, irrespective of isotopic composition, indicates that the high 206 Pb/ 20 4 Pb signature is not the result of fractionation of a metal-sulfide phase from the mantle . Such a process would also be expected to create large variations in the Re/Nd ratio, but the Re/Nd ratios of the HIMU basalts are not systematically unique in Fig. 1c. In addition, without knowledge of the relevant partition coefficients at mantle pressures and temperatures, it is not clear how such a process would affect the Re/Os ratio, since both elements are chalcophile and siderophile elements. While sulfide or metal fractionation of up to 0.1% is possible within the data of Newsom et. al., this small amount is probably not enough to generate the factor of 2-5 increase in the U/Pb ratio, relative to bulk silicate earth, required by the Pb isotope signature of HIMU.

Mantle Metasomatism
The 187Os/1860s ratios of the Rurutu, Tubuai, and Mangaia basalts are distinctly higher than measurements for mantle peridotites and other oceanic basalts. In order to evaluate mantle metasomatism as a process for raising the 1870s/186Os of the HIMU basalts, it is instructive to compare the HIMU Os data with 187 0s/ 186 Os measurements of metasomatized peridotites. The measurements of Walker et al ) on xenoliths from the Kaapvaal craton and Pearson et al (Pearson et al., 1991) on South African and Siberian xenoliths from kimberlites all have 187 0s/ 186 0s less than 1.08. These xenoliths include some extensively metasomatized and LREE-enriched samples, some with incredibly high 87 Sr/8 6 Sr and low 14 3 Nd/ 144 Nd, yet the metasomatism apparently did not result in increased Re/Os and 187 0s/ 186 0s ratios (notwithstanding Re contamination from the kimberlite host ). The Ronda plagioclase facies peridotites analyzed by Reisberg et al  are also LREE-enriched, with low 143 Nd/ 144 Nd and very radiogenic 2 06Pb/2 04 Pb (Bourdon et al., 1990). These peridotites had the lowest Re/Os and 187 0s/ 186 0s of all the Ronda samples, again suggesting that the Re/Os system was resistant to the metasomatism which resulted in enriched signatures in other isotope systems . Though a Re-Os characterization of mantle metasomatism is far from complete, it appears that the metasomatic enrichment processes reflected in these peridotite samples are incapable of generating high 187 0s/ 186 0s signatures. Given that the measured 187 0s/ 186 0s ratios of the HIMU basalts are higher than any peridotite values, we can tentatively rule out metasomatism as a mechanism for producing the high 1 87 0s/ 186 0s in these basalts.

Crustal Recycling
It is clear that the Rurutu, Tubuai and Mangaia 187 Os/ 1 86Os systematics require a source with a high time-integrated Re/Os ratio. The only geologic materials thus far recognized to have high Re/Os are magmas, insofar as oceanic and continental crust are the products of melting. Layers of mafic bulk compositions found in the Ronda ultramafic complex, with 187 0s/ 186 0Os ratios of 1.71 to 47.9 , are probably also the products of melting, either as trapped melts , cumulates from mafic magmas , or ancient, subducted oceanic crust . While there is no Pb isotope data for the Ronda mafic samples, Hamelin and Allegre  have measured the Pb isotopic composition of peridotites and mafic layers from several orogenic peridotite massifs. Though substantial heterogeneity exists in the mafic layer data, the Pb isotopic compositions of a few pyroxenites from the Beni Bousera massif approach HIMU values, as do some mafic layers from Ronda (Hart unpublished data). However, it is not known if these mafic rocks have elevated 187 0s/ 186 Os, or if there is a positive correlation between 1870s/186Os and Pb isotopic composition. In addition, the elevated 1870s/186Os of the Ronda mafic layers were created while the massif was isolated in the subcontinental lithosphere over the last 1.3 Ga . These layers, ranging in thickness from several cm to several meters, likely would not survive the diffusion and mixing processes operating in the convecting mantle (Hofmann et al., 1978), where the HIMU source must reside.
Ancient, subducted oceanic crust may provide a suitable high Re/Os, high 187 0s/ 186 0Os reservoir in the convecting mantle. The oceanic crust, with its several kilometers of thickness, would be more resistant to diffusive and convective mixing than meter scale veins or layers. Due to the high Re concentration and low Os concentration of tholeiitic basaltic crust relative to mantle peridotite, the main effect of recycling oceanic crust is to create areas of locally higher Re concentrations. It is unlikely that the Os in the HIMU magmas was derived entirely from ancient oceanic crust, as this material would probably have much higher 187 0s/18 6 Os ratios than observed. Only a moderately high mantle Re/Os ratio (about 10-20) is needed to raise the 187 0s/ 186 0s from depleted mantle values (about 1.05) to the HIMU 187 0s/ 186 0s values (about 1.25) in a few billion years.
This suggests that the time integrated Re/Os ratio of the HIMU source is the result of mixing high Re/Os crust with low Re/Os peridotite. We can quantitatively model this mixing if we have constraints on the timing of the recycling process. If the HIMU source is a mixture of recycled oceanic crust and mantle peridotite, then the U-Th-Pb evolution of the mixture is totally dominated by the recycled crust, even at low fractions of crust, due to the very low concentrations of these elements in peridotites Galer et al., 1989, Hauri unpublished data). As a result of this, the Pb isotopic composition of the HIMU source is essentially that of the crustal component, and constraints on the age, U/Pb and Th/U ratios emerge from inversion of the Pb-Pb systematics. The working assumptions are; 1) the depleted MORB mantle (DMM) is assumed to be a second stage reservoir, with a maximum age of 3.0 Ga, derived from the bulk silicate earth (present-day bulk silicate earth values of 87 Sr/ 86 Sr-.7047 (Allegre et al., 1983), 143 Nd/ 1 44Nd=.512638 (DePaolo et al., 1976), 1 76 Hf/1 77 Hf=.282880 (Salters et al., 1990), 187 0s/ 186 0s=1.07, chondrite average, );(present day DMM taken from most depleted MORB points for 87 Sr/ 86 Sr (.70220), 143 Nd/ 1 44Nd (.51330) and 176 Hf/ 177 Hf (.28355), and 187 0s/ 186 0s= 1.00); 2) the MORB crust is assumed to be derived from the depleted MORB mantle (DMM) at any time <3.0 Ga ago with initial isotope ratios equivalent to either DMM, or BSE (i.e. a very young DMM); 3) the evolution of the MORB crust from the time of its generation to the present day isotopic composition of HIMU ( 87 Sr/ 86 Sr=.7028, 14 3 Nd/ 14 4 Nd=.512850, 176 Hf/ 177 Hf=.282900, 1870s/1860s=1.25) is approximated by a single evolution curve.
For the 20 7 Pb-206 Pb system, these assumptions imply that the intersection of any third stage isochron (representing HIMU) with any second-stage isochron (representing DMM) must lie within the present-day MORB field. These assumptions result in the boundary conditions displayed in Fig. 3. N-MORB data are MORB analyses with 87 Sr/ 86 Sr<.703 ( (Mahoney et al., 1989;Dosso et al., 1991) and data sources summarized in ) and Mangaia data are from ,  and this study. Given the above assumptions, the bounding isochrons shown in Fig. 3a are absolute limits on the age of the crustal component in the HIMU source, and indicate an age of 770-2100 Ma. Calculated third stage 238 U/ 2 0 4 Pb ratios range from 19.7-40. Using these ages, the Th/U ratios calculated from the bounds in Fig.   3b range from 1.42-3.56.
A) The bounding isochrons delineate the upper and lower limits on the age of the recycled oceanic crust in teh HIMU source (see text). B) Bounding lines showing the limiting Th/U ratios of the recycled oceanic crust in the HIMU source.

Age of Recycled Crust (Ga)
Age of Recycled Crust (Ga) Figure 4. Results of the inversion of the Mangaia isotope data for parent/daughter ratios in the recycled crustal component. The curves represent the parent/daughter ratios calculated for recycled crust of various ages, assuming initial isotopic compositions corresponding to either depleted MORB mantle (DMM) or bulk silicate earth (BSE). The vertical lines are limits on the age of the recycled crust from the Pb isotope inversion (see text, Table 3 and Fig. 3).  Table 3. Calculated parent/daughter ratio results in subducted oceanic crust compared with isotope dilution measurements in fresh MORBs, an altered MORB composite , and average N-MORB of Hofmann . Averages of the MORB data are given in parentheses. The model parent/daughter ratios are those needed in order for subducted oceanic crust to evolve from either depleted MORB mantle or bulk silicate earth to the composition of the HIMU endmember in 770-2100 Ma (see text). MORB data sources: Rb/Sr and Sm/Nd (White et al., 1978;Mahoney et al., 1989;Dosso et al., 1991), Lu/Hf (Patchett et al., 1980;Patchett, 1983;, U-Pb Cohen et al., 1980;Cohen et al., 1982), Th/U Cohen et al., 1980;Condomines et al., 1981;Cohen et al., 1982;Jochum et al., 1983;Newman et al., 1983;Goldstein et al., 1991), Th/Pb (Church et al., 1975). crustal Re concentrations of 500-3000 ppt, the calculated 187 Re/ 1 86Os ratios constrain the amount of crust in the HIMU source to be 15%-78%. These calculated percentages of crust are quite sensitive to the crustal Re concentration and peridotite Os concentration, and are only illustrative. The lower age limit (770 Ma) requires the highest 187 Re/ 186 0s and largest amount of crust, whereas the upper age limit (2100 Ma) requires the lower 187 Re/ 186 0s and a smaller amount of crust in the HIMU source. Even at 15% crust, the Sr, Nd and Hf evolution of the HIMU source is determined largely by the crustal component, and in a similar fashion, we can place limits on the range of possible Rb/Sr, Sm/Nd and Lu/Hf ratios in the crustal component (Figs. 4b-d). Table 3 summarizes the results of the inversion along with the ranges for these trace element ratios measured by isotope dilution for fresh MORB glasses (Church et al., 1975;White et al., 1978;Cohen et al., 1980;Patchett et al., 1980;Condomines et al., 1981;Cohen et al., 1982;Jochum et al., 1983;Newman et al., 1983;Patchett, 1983;Mahoney et al., 1989;Dosso et al., 1991;Goldstein et al., 1991), and compared with estimates of average N-MORB  and altered MORB . The limits on these ratios calculated from the inversion are remarkable for their similarity to the range of values measured in fresh mid-ocean ridge basalts. This result was also found by Chauvel et al., (1992) from modelling of the trace element and isotopic characteristics of HIMU basalts. If the mantle sources of Rurutu, Tubuai and Mangaia contain subducted oceanic crust, this is a surprising result, considering the large additions of U, Rb and seawater Sr to the upper crust during alteration .
In detail, the Rb/Sr, U/Pb and Th/Pb ratios are slightly higher than the averages of the MORB results. The deviations of the Rb/Sr and U/Pb ratios are in the direction of those for altered MORB crust   (Table 3), but Th/Pb and Th/UJ are higher than expected for altered crust. Given that the MORB crust is obviously affected by low temperature alteration, the similarity of the model parent/daughter ratios to fresh MORB may be used to suggest that; 1) the low temperature alteration signature may be largely removed during passage through the subduction zone, and/or; 2) the altered portion of the MORB crust makes up only a small part of the total crustal budget for the elements in Table  3. These calculations serve to demonstrate the suitability of subducted oceanic crust as a component in the generation of the HIMU reservoir.
The inversion results imply that the role of mass transfer during subduction zone processing was largely to remove the alteration signature from the subducting slab, at least for the elements examined here. In detail, however, the inversion results for U/Pb and Th/Pb are high relative to the N-MORB average of Hofmann , though the Th/U constraints are consistent. If the N-MORB averages are representative of the composition of the basalt which is being subducted (i.e. small contributions from more enriched MORB and OIB), then the inversion results suggest a depletion of Pb relative to U and Th in the recycled oceanic crust. Chauvel et al., (1992) have proposed that Pb is leached from basaltic crust during hydrothermal alteration and deposited at the ridge in metalliferous sediments. This Pb is probably transfered to the continental crust during subduction and arc magmatism (O'Nions et al., 1979), and may be concentrated in a low U/Pb lower crust , possibly during plagioclase and amphibole fractionation from arc magmas.

Constraints on Melt Percolation
The high 187Os/186Os of the Tubuai and Mangaia basalts also serves as a tracer for evaluating the interaction of these magmas with the depleted upper mantle, which probably has 187 0s/ 186 0s in the range of 1.00-1.08. Due to the high Os concentration of mantle peridotite relative to basalts, the 187 0s/ 186 0s ratio of a given magma is quite sensitive to assimilation of peridotite with a different 187 Os/ 186 0s ratio. For example, assimilation of 10% of a peridotite (3000 ppt Os) with 187 0s/ 186 0s of 1.05 into a magma (300 ppt Os) with 187 0s/ 186 0s of 1.25 will lower the 187 0s/ 186 0s of the magma to 1.15. Magmawallrock reaction  or melt percolation (McKenzie, 1984; through peridotite with low 187 Os/ 186 0s should also have a significant effect on the 187 0s/ 186 Os of the magma. In the case of percolation of melt through peridotite, it is well known that each element moves at some fraction of the melt velocity which is proportional to the element's bulk solid/melt partition coefficient (McKenzie, 1984;. Because Os is a compatible element, the bulk peridotite/melt partition coefficient for Os is much higher than for Sr, Nd, Hf and Pb. As a result, for any reasonable melt velocity, the incompatible elements Sr, Nd, Hf and Pb will move much faster than Os, and the fronts of these elements will be almost entirely separated from that of Os after only a few hundred meters of percolation.
The effect on the isotopic composition of the melt is such that the Sr, Nd, Hf and Pb isotopic compositions will reflect the source material, whereas the Os isotopic composition will reflect that of the matrix through which the melt is moving. The only way to prevent this fractionation of the compatible elements from the incompatible elements is to move the magma through the matrix fast enough to prevent significant exchange of compatible elements with the matrix peridotite. This essentially implies the existence of a channel or fracture network which can transport the magma from the source region within the plume to the surface, ultimately to be erupted. The high 187 0s/ 186 0s ratios for the HIMU basalts, and the consistent covariation of the isotope ratios of the two elements with the largest difference in peridotite/melt partition coefficients (Os and Pb), requires that interaction with low 187 0s/ 186 0s mantle had a negligible effect on the isotopic composition of the basalts erupted on Rurutu, Tubuai and Mangaia.

Global Isotope Systematics
With the presently available Re-Os data, it is now possible to delineate much of the global Sr-Nd-Pb-Os isotopic variability in the oceanic mantle (Fig. 2). The position of the depleted mantle is estimated from 187 0s/1 86 0s measurements of abyssal peridotites (Martin, 1991;Snow, 1991) and other peridotites with MORB-like Sr, Nd and Pb isotopes . Estimates of the positions of the various endmembers defined by Zindler and Hart  are shown in Figs. 2a-c. Notwithstanding the lack of MORB 187 Os/ 186 0s data, it is likely that the MORB source is characterized by 187 0s/ 186 0s 1.08, and DMM may have 187 0s/ 186 0s as low as the lowest measured 187 0s/ 186 0s for abyssal peridotites of 1.0032 (Martin, 1991). The position of EMI is unknown due to the lack of Re-Os data for this endmember, though Sr, Nd and Pb isotope affinities with the subcontinental mantle may suggest a low 187 0s/ 186 Os signature for EMI (<1.00?). The 187 0s/ 186 0s data for Samoa and Tahaa suggests that the EMII endmember is characterized by 187 0s/1860s ratios which lie between estimates of depleted mantle (about 1.00) and bulk silicate earth (about 1.08), consistent with the EMII 143 Nd/ 144 Nd and 176 Hf/ 177 Hf signatures (Patchett et al., 1980;. The homogeneity of the Tubuai and Mangaia 187 0s/ 186 Os data suggests that a value of about 1.25 is representative of the Os isotopic composition of HIMU. Martin (Martin, 1991) has proposed that a mantle source exists with high 3 He/ 4 He and 1 87 0s/ 186 0Os of around 1.10, based on Re-Os analyses of basalts from Hawaii and Iceland.
The only island in the present study with documented high 3 He/ 4 He is Savaii, Western Samoa , with 187 0s/ 186 0s of 1.0261 to 1.0739. These results suggest that the proposed high 3 He/ 4 He endmember , recently recognized in the Sr-Nd-Pb isotope data and termed FOZO by Hart et al  may be characterized by a range of 187 0s/1 86 Os within the range of estimates of depleted mantle.
The identification of the HIMU isotopic signature (high 187 Os/ 1 860Os, high 206 Pb/ 20 4 Pb, low 87 Sr/ 86 Sr) with recycled oceanic crust has important implications for mixing relationships in the earth's mantle. The earth presently has 37,000 km of subduction zones, and if we extrapolate the present subduction velocity of 80 km/Ma (Reymer et al., 1984) back through time, this suggests that the total volume of oceanic crust subducted in 3 Ga is roughly 7% of the total volume of the mantle (or 10% since 4.55 Ga). This contrasts with the relative rarity of the extreme HIMU signature, which has only been observed in the Cook-Austral Islands, St. Helena (Chaffey et al., 1988) and two seamounts in the western Pacific Ocean (Staudigel et al., 1991). This suggests that the extremely high Pb isotopic compositions represent only the most well preserved (i.e. least well mixed), and possibly the oldest, subducted crust. The slightly higher 207Pb/ 20 4Pb signature of St. Helena, relative to the Cook-Austral Islands trend, also suggests that St. Helena represents a separate source than that for Tubuai and Mangaia, with a slightly different history. Realistically, there is likely to be a continuum of Pb isotopic compositions between DMM and HIMU which would correspond to either younger, or more well mixed, recycled oceanic crust. Depending on the individual histories, there could also be a variety of 1870s/1860s isotopic compositions in these parts of the mantle.
There may also be a recycled oceanic crustal signature in the data for N-MORB.
From Fig. 3, it is obvious that there are many MORBs with 87 Sr/86Sr less than .70300 that also have radiogenic Pb isotopic compositions (Ito et al., 1987;Dosso et al., 1991). If the MORB mantle is the depleted mantle complement of the continental crust, then it should be very depleted in highly incompatible elements such as U, Th, and Pb. As a result, it will be more susceptible to having its Pb isotopic signature dominated by a recycled component. In this context, "less depleted" MORB mantle might lie closer to the geochron, whereas "more depleted" MORB mantle, prone to contamination by a recycled oceanic crustal component, would tend to lie farther to the right of the geochron. If in fact a large fraction of the mantle exists with Pb isotopic compositions near the geochron, but susceptible to contamination with recycled oceanic crust due to very low Pb concentrations, then this may provide an explanation for the enigmatic "Pb paradox", especially in MORBs. More 1 87 Os/1 86 0s data is needed to test these ideas, on both MORBs and OIBs with a variety of Pb isotopic compositions.

Conclusions
The Re-Os isotope systematics in a group of oceanic island basalts from the south Pacific Ocean have been examined in order to constrain theories of crustal recycling in the mantle. The highly variable Os concentrations in the lavas are controlled by a low Re/Os phase (or phases) in which Os is compatible, possibly olivine, chromite, and/or sulfides.
These Os concentration variations determine the Re/Os ratios of the erupted basalts.

Appendix: Analytical Procedures
Hand samples were split into large pieces using a hydraulic carbon-steel splitter, and these pieces were broken down using a tungsten carbide jaw crusher. The crushed fragments were rinsed with distilled water, dried, and reduced to powder in an agate shatterbox. For the analysis of Pb, Sr, and Nd isotopes and trace element concentrations, 50 mg of powder was spiked with 84 Sr, 150 Nd, 235 U, 230 Th, and 2 05Pb, and dissolved in a mixture of HNO 3 , HCI and HF on a hotplate at a surface temperature of 125 'C for several days in a closed 7 ml Savillex screw cap beaker. Pb was separated first in 0.5 N HBr on a column of 20gl of AG1x8 (200-400 mesh) and purified by repeating the column step. The eluants from the Pb chemistry were evaporated to dryness and redissolved in 8 N HNO 3 . U and Th were separated together in 8 N HNO 3 on column of 100 ll of AG1x8 (200-400 mesh) and eluted with 6.2 N HCI and 0.5 N HBr. The liquid from the U-Th step was taken to dryness and dissolved in 2.5 N HC1. Subsequent procedures for the separation of alkalies, Sr and REE are given by , and separation of Sm and Nd follows the procedure of Richard et al , modified by Zindler et. al. . Mass spectrometry of Pb, Sr and Nd was performed on the Woods Hole VG354 5-collector mass spectrometer. Pb was run using the silica gel-phosphoric acid technique on single Re filaments in the static mode using 5 Faraday cups, and the data is corrected for fractionation relative to the NBS 981 values given by Todt et al . Reproducibility of the Pb runs is 0.02% per amu based on repeat runs of NBS 981.
Sr was run on single W filaments with a Ta oxide activator (Birck, 1986) in a 3-step dynamic mode with 5 Faraday cups. The 87 Sr/ 86 Sr data are normalized to a value of .71022 for NBS 987, and repeat analyses of this standard indicate a reproducibility of 0.0045%. Nd was loaded on the Ta side filament of a Ta-Re double filament assembly, and was run in a 3-step dynamic mode with 5 Faraday cups. 14 3 Nd/ 144 Nd was normalized to a value of .511860 for the LaJolla Nd standard, and repeat analysis of this standard indicate a reproducibility of 0.0040%. U and Th were analyzed on the NIMA-B mass spectrometer at Woods Hole. U and Th were loaded together on a single Re filament with colloidal graphite and analyzed using the electron multiplier, and were corrected for fractionation based on repeat analyses of SRM 500 U. Trace element concentrations (except Re and Os) are accurate to better than 1%. Analytical blanks are given in Table 1 and are insignificant for all analyses reported here.
Analysis of Re and Os Isotopes by Oxygen-Enhanced N-TIMS Re and Os Separation. All the acids and H 2 0 used in the separation of Re and Os were purified by subboiling distillation in Vycor glass, quartz or Teflon. For analysis of Re, 1-5 grams of rock powder was weighed out, spiked with 185 Re, and dissolved in a 10:1 mixture of HF and HNO 3 in a 60 ml closed Savillex PFA Teflon screw cap vessel. The sample was agitated in an ultrasonic bath for 15 minutes, then set on a hot plate at a surface temperature of 100 oC for several days. The sample was opened, evaporated to dryness, and dissolved in several milliliters of 0.2 N HNO 3 . The liquid was centrifuged and loaded onto a column of 1 ml of AG1X8 anion exchange resin (200-400 mesh). The sample was washed with 0.2 N HNO 3 , 0.2 N HC1, and 0.2 N HNO 3 , and Re eluted with 8 N HNO 3 . The sample Re was taken to dryness at a surface temperature of 75 'C. This procedure was then repeated with a smaller column (20 pl resin).
For Os analysis, Os was preconcentrated from the rock matrix by nickel sulfide fire assay (Hoffman et al., 1978). Prior to the fire assay, 30-100 grams of rock powder were weighed into a Coors glazed ceramic crucible, spiked with 190 0s , and then, after the spike had dried, mixed with a glass rod in order to distribute the spike evenly through the powder. The flux consisted of a mixture of 20 g borax, 10 g Na 2 CO 3 , 4 g Ni powder, and 2 g sulfur. The flux was added to the sample powder and homogenized with a glass rod. The sample was fused at 1000 'C for 1.5 to 3 hours (blanks were fused for 1 hour). During the fusion, the platinum-group elements are concentrated in the immiscible NiS bead which segregates at the bottom of the crucible (Hoffman et al., 1978). For fusions with high sample/flux ratios, typically the NiS formed several small beads. After cooling, the NiS beads were extracted by crushing the crucible and its contents and picking out the beads.
The NiS bead was dissolved in 6.2 N HCI on a hotplate at a surface temperature of 150-200 'C under a nitrogen flow. After cooling, the solution was filtered through a 0.45 p.m Millipore cellulose filter. The Os was concentrated in the residue left on the filter paper. The distillation and collection of Os as the volatile OsO4 (b.p. 100 (C) is similar to the procedure described by Luck . The sample Os is distilled from a solution of CrO 3 (VI) in 4 N H 2 SO 4 and collected in concentrated HBr chilled in an ice water bath. The HBr solution was then transferred to a 15 ml Savillex PFA Teflon screw cap beaker, capped tightly, and heated in an oven at 100 'C overnight to allow the reduction of OsO4 by HBr to go to completion. The beaker was then opened and evaporated on a hotplate at 75 0 C to a volume of less than 1 pl for the purification step.
Purification. The sample Os was purified by ion exchange using single resin beads . The Os sample in HBr was taken to a <1 pl volume, and 8 pl of water containing a single bead of Chelex 20 resin (20 mesh) was added, resulting in a solution of <1 N HBr. The beaker was mounted on the edge of a disc rotating at 30 r.p.m., rotated for 1 hour, allowed to sit for 1 hour, and the bead transferred to a clean 3 ml beaker. The bead was rinsed with 100 pl of 0.5 N HBr and the sample Os was eluted by adding 30 pl of concentrated HBr and agitating in an ultrasonic bath for 30 minutes. The resin bead was discarded and the solution evaporated at 75 'C to <1 p.l for loading.
For the overall separation and purification, the Re yield is about 80-90%, while the Os yield varied from 50-90%. Measured blanks averaged 35 pg for Re (including filament blank) and 40 pg Os for the full procedures. The analytical blank had a measured 187 0s/ 186 0s of 6.60. The Re and Os data in Table 3 are corrected for these analytical blanks. Mass Spectrometry. The negatively charged oxides of Re (ReO 4 -) and Os (OsO 3 -) are produced by the oxidation of the sample Re and Os by barium oxide on the surface of a Pt filament (Creaser et al., 1991;Volkening et al., 1991). Barium nitrate was prepared by dissolving BaCO 3 in dilute nitric acid and repeated dissolution and precipitation from concentrated HNO 3 . This serves to convert all the Ba to Ba(NO 3 ) 2 and also to oxidize and eliminate organics. The final precipitate is dissolved in water to yield a solution with a concentration of 5000 mg/g of Ba(NO 3 ) 2 .
Filaments for mass spectrometry consist of 1x20 mil zone refined 99.95% Pt ribbon (H. Cross).
This ribbon contains small amounts of Re, presumably as contamination from the manufacturing of Re products. This is a potential problem due to the possible isobaric interference of 187 Re 1 60 3 -on 187 Os 1 60 3during mass spectrometry. Several different techniques to clean Re from the Pt ribbon were tried, including cleaning in concentrated HNO 3 , cleaning in H202, fluxing with sodium carbonate, and heating in air, none of which were successful. However, based on standard runs, the isobaric interference of 187 Re 1 60 3 -on 187Os 1603-was not observed during our measurements of Os, even for filaments which were not cleaned using the above methods.
Pt filaments are outgassed at 1000 'C for 20 minutes under a vacuum of <10 -7 torr. The sample Re is dissolved in 1 p.l of 0.1 N HNO 3 and is mixed with 1-3 gg of Ba(NO 3 ) 2 which is then loaded onto the filament and dried at 0.5 amps. It is important to minimize the area of the loads of Re, Os and Ba(NO 3 ) 2 , so as to minimize the Re oxide signal from the filament and thus the potential for isobaric interference. Repeated analyses of Re spike indicate an average filament Re blank of 0.38 pg for two different batches of Pt filament, with a range from 0.2-0.52 pg.
However, occasionally high Re levels were observed during some Os runs, which may be related to local concentrations of Re contamination on the Pt ribbon.
For Os samples, the Os in <1 ml HBr is loaded onto the center of the filament and dried down gently at 0.5 amps. The Os is then reduced to the metal on the filament by heating to 600 'C under a vacuum of <10-6 torr for 3-12 hours. In addition to reducing the sample Os, this serves to burn off any volatile contaminants which may be carried over from the sample distillation. Then 1-3 mg of Ba(NO 3 ) 2 is loaded directly on top of the Os and dried at 0.5 amps. At this stage, the Os sample is ready for mass spectrometry.
Re and Os isotope ratio measurements were made on the NIMA-B 9-inch, 600 sector thermal ionization mass spectrometer at the Woods Hole Oceanographic Institution. Ions are accelerated through a potential of 4800 V and collected by a Johnston 15 stage discreet dynode electron multiplier operated in the analog mode at a gain of 24000.
For Re analysis the filament was immediately raised to about 700 'C, which is just below running temperature. As soon as ReO 4 -peaks were observed, the filament temperature was raised rapidly so as to result in the maximum signal intensity in the shortest possible time. This was typically at a temperature of 750-800 'C as measured by optical pyrometry. Ion currents for several hundred picograms of Re were on the order of 10 -13 to 10-12 amps. Intensities were measured at masses 249 ( 185 Re 1 60 4 -), 251 ( 187 Re 1 60 4 -) and 252.5 (zero), and 251/249 was usually measured to better than 0.1%. The sample Re, loaded from nitric acid, is already in its most oxidized form (Re 2 O 7 ), and it is likely that the formation of ReO 4-occurs at different temperatures and with different efficiencies for the sample Re (Re 2 0 7 ) and the filament Re (Re metal). This procedure for measuring Re is that which minimizes the contribution of Re from the filament, as determined by repeated measurements of Re spike.
Os runs without oxygen suffered from poor ion yields, typically less than 1%, and isobaric interference from 187 Re 1 60 3 -was severe. Without oxygen, OsO 2-and OsO 4 -species were also observed, though at low intensity. The presence of oxygen gas has two effects. The first effect is to enhance the oxide speciation of Re and Os to ReO 4-and OsO 3-by reducing the level of the subordinate oxides to background levels. The second effect is to improve the overall ionization efficiency for ReO 4 -and OsO3-, resulting in higher signal intensities and higher ion yields. Under optimum conditions of temperature and oxygen pressure, the potentially serious interference of 1 87 Rel60 3-on 187 0s 160 3-is eliminated within the resolution of our measurements. However, this interference can become substantial at higher temperatures and/or non-optimal oxygen pressures. Ionization efficiencies for Os range from >4% to 14%, with no apparent systematic variations with sample size. The average ionization efficiency of about 10% is more than a factor of two higher than reported by Creaser et al (Creaser et al., 1991) and far in excess of Os ionization yields reported for other methods (Luck, 1982;Fehn et al., 1986;Russ et al., 1987), allowing the measurement of very small amounts of pure Os. Considering the overall transmission of the mass spectrometer (30-50%), this suggests that at much as 40% of the Os may be forming negatively charged oxide ions. The measured 187 Os/ 186 Os ratios for the standard runs are reproducible to better than 0.15% over five orders of magnitude in sample size (excluding the 800 fg run).

Introduction
Since the earliest recognition that the earth's mantle was isotopically heterogeneous (Faure and Hurley, 1963;Gast et al., 1964), studies have attempted to elucidate the origins of these variations in the context of physical models of the earth (Armstrong, 1968;Allegre et al., 1980;Anderson, 1982). With the advent of plate tectonic models (e.g. Vine, 1972) and theories of buoyancy driven fluid flow applied to the earth Oxburgh and Turcotte, 1968), it was recognized that the mantle could behave as a convecting, viscous fluid over geologic time scales. Numerous subsequent studies in various disciplines have attempted to clarify the complexities of mantle convection, using methods of observation (Anderson, 1967;Jordan, 1977;Dziewonski and Anderson, 1981), experiment (Goetze and Kohlstedt, 1973;Whitehead and Parsons, 1978;Lees et al., 1983), and theory (Parmentier et al., 1976;Yuen and Peltier, 1980;Richter and McKenzie, 1981).
Recent years have seen increased efforts at integrating the information available from the geophysical, geochemical, and fluid dynamic approaches (Allegre, 1982;Richter et al., 1982;Davies, 1984;. Studies which have combined geochemical observations with geophysical data (Hart, 1984) and fluid dynamic models (Davies, 1984) have resulted in a better understanding of the processes by which chemical heterogeneities may be created, maintained, and modified in a dynamic earth. However, a great deal remains to be discovered about about the ultimate origins of the geochemical signatures observed in studies of mantle derived rocks.
This study attempts to relate aspects of viscous flow in thermally buoyant mantle plumes with geochemical observations of volcanic rocks from oceanic islands. The existence of buoyant plumes in the mantle are robust features of any fluid mechanical description of the interior of the earth, and provide a compelling mechanism for the creation of age-progressive volcanic island chains .

Boundary Layer Plume Model
This study examines the vertical, steady-state boundary layer flow around a point source of heat in axisymmetric coordinates (Fig. 1). In this analyses, only the plume conduit is examined; the plume source, and the ultimate fate of the plume material at the top of the conduit, are not specified, nor are they required for the examination of the conduit.
Due to the relative magnitudes of temperature and velocity gradients in the vertical direction compared to the radial direction, boundary layer theory (Schlichting, 1968) provides a good framework in which to describe flow in thermal plumes. The fluid is assumed to be incompressible, with the exception of thermal buoyancy (Boussinesq approximation), and viscous dissipation is ignored. In addition, the vertical momentum equation is assumed to represent a balance between buoyancy and the radial component of the shear stress in the vertical direction (Yuen and Schubert, 1976). The equations governing the conservation of mass, energy, and momentum are: where P is the non-hydrostatic pressure, (U,V) are the horizontal and vertical velocities, (R,Z) are the radial and axial coordinates, T is temperature, t is the shear stress tensor, r is density, k is thermal diffusivity, a is the coefficient of thermal expansion, and AT is the excess plume temperature. For the boundary layer approximation, it is assumed that the flow is slow, so that the non-hydrostatic pressure term in (2) can be ignored, and that vertical gradients in temperature and velocity are small compared with the radial gradients.
With these approximations, the conservation equations reduce to: "-zr= (goFAT )(7 where n is the power law creep exponent, .to is a pre-exponential factor (viscosity), FAT describes the temperature dependence of the rheology, and the strain rate is approximated by the vertical velocity gradient in the radial direction (Yuen and Schubert, 1976). The linear, Newtonian power law (n=1) is valid in the limit of low deviatoric stress, where diffusion creep is the relevant deformation mechanism (Weertman and Weertman, 1975).
Deformation by the mechanism of dislocation creep is described by a non-Newtonian power law (n>1). Experimental deformation studies, though conducted at strain rates several orders of magnitude above typical tectonic values, have measured non-Newtonian rheologies for olivine, indicating a value for n of 2-5 (Goetze and Kohlstedt, 1973).
The standard Arrhenius relationship for the temperature dependence of viscosity has a functional form which is incompatible with the form of the conservation equations, and thus cannot be used. Instead, the temperature dependence of the rheology is given by an empirical relationship: which will be abbreviated by: In this parameterized temperature dependence term, the number of successive exponentials, as well as the constants A and C, can be fit to an Arrhenius function for viscosity for any activation energy (Goetze and Kohlstedt, 1973;Stocker and Ashby, 1973), and is a function of AT relative to the ambient temperature of the fluid (1300 IC in this case). In this relationship,the dependence of viscosity on pressure is ignored.
The boundary layer equations are non-dimensionalized according to: where ATBL is the difference between the ambient fluid temperature (1300 0 C) and the axial temperature of the plume at its base (z= 1). The length scale h is a free parameter which is undetermined. The equations are solved by substitution of a stream function AV based on a similarity variable, such that: The similarity transformation is: where T 1 is the similarity variable, s is the similarity exponent, and A is the stream function. After substitution of the similarity variables, the momentum equation becomes: In order for the similarity solution to be valid, 1T must be the only independent variable, and thus the term This Rayleigh number should not be confused, or compared, with the equivalent parameter used in studies of fluid layer convection, due to the different length scales used (see below). For the constant viscosity case (C=0) with a linear rheology (n= 1), these equations reduce to the point source equations of (Brand and Lahey, 1967;Liu and Chase, 1991).
The transformed momentum and energy equations are coupled ordinary differential equations in one variable, and are integrated with a fourth order Runge-Kutta-Fehlberg algorithm using the shooting method. In this method of integration, the nonlinear properties of the governing equations are fully preserved, which is important for describing the flow in a fluid with a variable viscosity. The equations were solved subject to the boundary conditions: 6(oo)=0 (27) Equation (25) indicates a stress free condition at the plume axis. Equation (23) specifies zero temperature gradient at the plume axis; eqs. (26) and (27) indicate that the excess temperature and vertical velocity vanish far from the plume. The boundary conditions far from the plume were satisfied at rj=5, which in the dimensional results discussed below, corresponds to a distance of roughly 10,000-30,000 km from the plume centerline; carrying the integration out to larger values of T1 results in only minor changes in the dimensional results (i.e. about <1% increase in centerline vertical velocity for Ti=10). The results are dimensionalized by assuming the base of the plume starts at z=1. Thus, height above the base of the plume (z*) is related to the coordinate system through a virtual origin, where the virtual origin (z--0) is located a distance h below the base of the plume: z=(z*+h)/h pre-exponential factor (n=1) 1 kg m-1 s-1 90,3 pre-exponential factor (n=3) 3.25x10-10 kg 3 M-3 S-5 p fluid density 3300 kg m-3 g gravitational acceleration 9.81 m S -2 0X coefficient of thermal expansion 1.45x10-5 oC-1 it thermal diffusivity 2.5x10-6 m 2 s-1 Dimensional quantities can be calculated from the non-dimensional results by the following expressions: The length scale h is a critical parameter in converting the results of the numerical integration into dimensional information. Yuen and Schubert (1976)  The percent entrainment goes as R 2 , and thus the actual value of %E depends only on the relative values of z* (depth of the fluid layer) and h. For a fixed layer depth z*, the value of h determines the distance of that layer from the point source, and determines the curvature of the plume boundary with height ( Fig. 1). If h is large, then the plume radius and the axial temperature change little with height, and thus entrainment is small. For small h, the plume radius and axial temperature vary more with height, and entrainment is larger.
In the present study, the emphasis is not on absolute amounts of entrainment, but on describing the processes which enhance or diminish entrainment. For the results presented below, the value of h was varied from 1000-5000 km, and ATBL varied from 250-1000 0 C. The results of the numerical experiments described below show, however, that the processes which govern the entrainment of ambient fluid are largely independent of the actual value of h. Thus the results are of general interest in describing the entrainment process in viscous fluids. The differences in the flow regime for linear (Newtonian) and non-linear (non-Newtonian) rheologies will be examined, assuming that thermal expansion, thermal diffusivity, and viscosity (at constant temperature) do not vary with depth. In this case, the plume conserves buoyancy along its length. The values of the various physical constants used are given in Table 1. In a later section, the effect of the variation of go, a, and K with depth on the growth of the plume boundary will be discussed.

Linear and Non-Newtonian Rheologies
Figures 2 and 3 show quantitative results for two integrations of the model, with linear (n=1) and non-Newtonian (n=3) rheologies, both with a creep activation energy of 523 kJ/mol, which is appropriate for olivine (Goetze and Kohlstedt, 1973). The value of h used is 2700 km, which is essentially the assumed depth of the fluid layer (allowing 100 km each for upper (lithosphere) and lower (CMB) boundary layers). These results were calculated at a height of 2700 km above the base of the plume. Figure 2 shows that the effect of the non-Newtonian rheology is to narrow the radial velocity and temperature profiles. In both cases, the vertical velocity profile extends to much larger radii than the temperature profile. This is due to viscous coupling of the ambient fluid to the flow in the plume conduit. This effect is easily recognizable by considering the fluid's Prandtl number, which is the ratio of the kinematic viscosity to the thermal diffusivity:

192
(35) For the earth's mantle, this number is on the order of 1024. The kinematic viscosity can be thought of as a momentum diffusivity, and for the mantle we can see that the diffusion of momentum, or force, is much faster than the diffusion of heat, and thus the different scale lengths of the velocity and temperature boundary layers. This feature is characteristic of high Prandtl number fluids.
In addition, the vertical velocity profile for the non-Newtonian plume displays a region around the plume axis, out to about 10 km, with a very low velocity gradient. This part of the plume is surrounded by a region in which the velocity drops off very rapidly, and finally the velocity decays exponentially to zero. This "plug flow" is a robust characteristic of nonlinear rheologies (Parmentier et al., 1976). In the Newtonian plume, the velocity gradients are not as localized, and instead the profile displays a more gradual decay as a function of radius.
The reason for this difference in velocity field can be seen from Figure 2c. In the linear case, the viscosity depends only on temperature, and so the radial viscosity profile mirrors the temperature (Fig. 2b). In the non-Newtonian case, the viscosity at the plume center increases to infinity toward the plume axis (Fig. 2c). This is due to the inverse dependence of viscosity on strain rate, which drops to zero at the plume axis. This high viscosity at the plume axis makes this material very rigid and difficult to deform, resulting in the low axial velocity gradient shown in Fig. 2a. Farther from the axis, the effects of decreasing temperature (Fig. 2b) and increasing shear stress (Fig. 2d) on viscosity work against each other, and so the viscosity reaches a minimum value. Far from the plume center, the viscosity in the non-Newtonian case remains low due to the finite shear stress in the ambient fluid. This lower viscosity in the ambient fluid for the non-Newtonian case allows the shear stress to be relieved closer to the plume center, thus narrowing the velocity field relative to the linear case. The higher vertical velocities in the non-Newtonian plume also result in a lower radial pressure in the conduit, further narrowing the velocity profile. It is important to note that these characteristics of the non-Newtonian plume do not depend on the activation energy of the dislocation creep process. In the regions of the plume where the non-Newtonian viscosity deviates most from the linear case, the strain rate dependence dominates over the temperature dependence. At the plume center, the strain rate drops to zero, and thus the viscosity must tend toward infinity, no matter the temperature dependence. Far from the plume, the temperature has decayed to zero, yet the strain rate is still finite, resulting in a lower viscosity compared with the linear case. By increasing the activation energy, and thus the temperature dependence of the viscosity, the main effect would be to shift the location of the viscosity minimum toward the plume axis. This would narrow the region of "plug flow" at the center of the plume, but would not eliminate it entirely.
In reality, the viscosity exactly at the plume axis in the non-Newtonian case will not be infinitely high. At the axis, shear stress and strain rates are low, and so the deformation mechanism will be diffusion creep, which is linear (n= 1). However, the transition to dislocation creep (non-Newtonian) takes place at shear stresses of 10-2 to 10-1 MPa (Turcotte and Schubert, 1982), which would be established only a few meters from the plume axis (Fig. 3b). At this distance from the axis, strain rates are still negligible in the linear case (Fig. 2a). This analysis indicates that the "plug flow" exhibited by the non-Newtonian rheology is a persistent feature which is independent of the temperature dependence of viscosity.

2 Mechanism of Thermal Entrainment
Equation (34) shows that the radius of the plume conduit, defined as the point at which the axial excess temperature decays to 1%, increases as a function of height above the plume source. The increase in radius goes as the 1/2 power in the linear case, and as the 2/3 power for n=3. The growth of this boundary layer is due to the entrainment of ambient fluid into the plume flow. Heat diffuses outward into the ambient fluid, and this heat increases the buoyancy of the fluid near the plume, and also lowers its viscosity. As a result, this material gains additional vertical velocity, and becomes part of the plume flow.
The process is aided by a slow flow of ambient material toward the plume conduit, which balances the mass of entrained fluid flowing up the conduit.
In order to illustrate the fluid flow during this process, streamlines were calculated for the above non-Newtonian plume, and are plotted in Figure 3. These streamlines are the paths of fluid flow for the calculated model, and it can be seen that ambient fluid crosses the plume boundary, which increases with height. In this case, the plume boundary was defined as the point at which the excess temperature dropped to 1% of the axial value, and so defines the horizontal limit of the excess temperature of the plume. In this particular case, the plume radius increases by about 40% through the depth of the fluid layer (Fig. 3).
In addition to this entrainment process, a significant redistribution of fluid occurs within the plume conduit For example, in Fig. 3a, fluid which starts out at the plume boundary (R=50 km) near the base of the system flows toward the center of the conduit, and is located 20 km from the axis near the top of the system. This indicates that fluid which is entrained at the plume boundary continues to move toward the center of the plume due to a small, but finite horizontal velocity component, which vanishes at the plume axis. Although this laminar entrainment process does not result in intimate mixing of the plume and ambient fluids on a small scale, significant juxtaposition and translation of different parcels of fluid, due to shear within the conduit, does occur during this process. Figure 3b shows the evolution with time of a layer of 75 km thickness (heavy horizontal line) which is located at the base of the plume. The fluid at the plume axis rises much faster than fluid at the periphery, and so this layer is deformed due to the differential velocities along different streamlines. In addition, as noted above, the fluid at the edge of the plume near its base moves slowly toward the plume axis. The directions of motion indicated by the streamlines show that the original plume source material is effectively compressed toward the plume center with increasing height. The streamline indicated by the black dots (Fig. 3b) delineates the boundary between the original source fluid (inside) and the entrained fluid (outside). The streamlines in Fig. 3 demonstrate that the fluid which is ultimately entrained into the conduit originates at the lowest levels of the system. Because the conduit radius increases as z -s, and the velocity goes as z 2s+ 1, the plume mass flux (UR 2 ) increases linearly with height (z). However, due to the shape of the streamlines, this increase in mass flux does not representatively sample the full depth of the fluid, but instead pulls fluid up from the base of the system. In the present example, even the fluid which is finally entrained at a height of 2700 km, at the very top of the fluid layer, originated from a depth of greater than 1500 km. This the why the radius of the plume increases as z -1 / 2 (n=1) and z-2 / 3 (n=3); this curvature reflects the increase in the mass flux due to entrainment at the lowest levels.

Parameterization of the Laminar Entrainment Process
The plume Rayleigh number defined in equation (21) is a measure of the strength of the plume, which increases with increasing DT and increasing h. Another measure of the plume strength is the buoyancy flux (Sleep, 1990), which is defined as: with ATBL. This figure shows that Ra and B are well correlated, and that the variation of B with h for a constant ATBL essentially mirrors the effect of increasing ATBL.
The mechanism of thermal laminar entrainment is essentially determined by the balance between the outward conduction of heat and the horizontal convergence of fluid toward the conduit. This balance can be conveniently expressed through the Nusselt number, which describes the relative magnitudes of heat transport by advection and conduction (Turcotte and Schubert, 1982). For the case of the plume conduit, this parameter is defined as: where R is the radius of the plume boundary (as defined above), V is the horizontal velocity at the plume boundary, and K is the thermal diffusivity. A smaller relative value for Nu indicates that diffusion of heat is strong compared with the advective flux of heat.
Since it is the lateral diffusion of heat which drives the entrainment of ambient fluid into the plume, a lower value of Nu should imply more entrainment. A larger value of Nu indicates that the horizontal convergence of fluid toward the conduit limits the outward diffusive flux of heat, reducing the entrainment of ambient fluid. Nusselt numbers were calculated for the non-Newtonian results; however, the Newtonian integrations were of insufficient accuracy to calculate a precise value for Nu (due to the inaccuracy of the horizontal velocity), and these results are not shown. The plume Nusselt numbers are plotted against Ra in Fig. 4b. For the non-Newtonian rheology, the variation of Nu with h again essentially mirrors the effect of temperature; in fact, a single curve could be fit to these data. A similar result is indicated by Fig. 4c, where Nu is plotted against buoyancy flux. The numerical results indicate that the effect of increasing Ra is to decrease the plume radius by increasing the horizontal velocity of fluid which is converging toward the conduit. Balanced against this increased convergence of fluid is the higher vertical velocity of the fluid, which effectively decreases the amount of time for heat to conduct away from a given volume of fluid. The net result of these competing effects is that entrainment decreases with increasing Nu, as shown in Fig. 4d. This is the expected result; at higher Nu, the greater horizontal advection of fluid toward the conduit decreases the lateral extent to which heat can diffuse, and so entrainment is less. Qualitatively, these results demonstrate that stronger, more intense plumes will suffer less fractional entrainment than smaller, weaker plumes.

Variable ax, yo, and IC
Recent studies of the seismic equation of state (Anderson, 1987) and laboratory experiments on mantle compositions (Chopelas and Boehler, 1989) have demonstrated that the physical properties go, C and KI vary significantly with density, and thus with depth in the earth. Chopelas and Boehler (1989) discovered experimentally that the coefficient of thermal expansion of olivine decreases with increasing density according to: where o and Po are the values for the uppermost mantle. This results in a decrease of the coefficient of thermal expansion by a factor of about 20 down to the base of the mantle. In addition, based on the theoretical dynamics of crystal lattice structure with increasing pressure, Anderson (1987) has proposed that thermal conductivity decreases with density according to: Alternatively, Osako and Ito (1991) have measured the thermal conductivity of MgSiO 3 perovskite at high pressures, and propose that thermal conductivity increases with depth by at least a factor of four through the depth of the mantle, which can be expressed as: Laboratory studies of the rheology of olivine have also shown that the viscosity of the mantle should increase with depth (Stocker and Ashby, 1973). In the present model, the fluid is incompressible, and so fluid density does not vary with depth. However, we can qualitatively study the effect of these density-variable parameters by making them functions of depth (z). For a value of h-=4030 km, the dimensionless height z across the full depth of the mantle varies by the same amount as the normalized density po/p, such that: For different values of h, the exponent on the quantitiy (0.6 z) can be changed to match the density increase through the depth of the mantle. Since thermal diffusivity has been assumed to be constant in eq. (10), its depth dependence cannot be modelled here.
However, esing eq. (40) as a proxy for density allows thermal expansion and viscosity to be expressed as functions of depth: where the exponents a and b describe the dependence of the coefficient of thermal expansion and viscosity with depth relative to reference values specified at the top of the system. By substituting (41-42) into equation (21), the Rayleigh number becomes: To obtain a solution, the similarity exponent (eq. 17) becomes: This different expression for the similarity exponent (s) has a profound effect on the nature of the plume flow and the shape of the plume conduit as a function of height, and thus for the nature of entrainment. The effects of these depth dependent properties will be illustrated for the Newtonian case; the effects would be similar for the nonlinear rheology. Thus the fluid velocities and the shape of the plume boundary will be quite different from the constant property case, depending on the values of a and b. In addition, Ra will be a function of z (relative to Raref), and so the plume strength will vary with height. The effects of depth dependent (X and p.to will be discussed separately for a Newtonian rheology. The effects of the depth-dependent variables would be similar in the non-Newtonian case.

Variable thermal expansion
The effect of increasing thermal expansion with height should be to increase the buoyancy, at constant temperature, of a given parcel of fluid, resulting in an increase in the vertical velocity with height. Figure 5 shows that this is indeed the effect. At higher values of a, the plume boundary is seen to make a transition from growth with height to a radius which decreases with height. Figure 5 shows that the vertical velocity increases with height due to the increasing buoyancy, and that Ra also increases with height. The narrowing of the plume boundary with height indicates that entrainment is minimal in the upper levels of the fluid layer, and that most of the fluid is entrained from the base of the system. Figure 6 shows the effect of a viscosity increase with depth (decrease with height, Eq. 43) on the shape of the plume boundary. In these diagrams, the exponents -6, -10, -14, and -22 result in an increase in viscosity with depth by factors of 21, 165, 1276, and 9846 respectively across the depth of the fluid layer (2700 km). The effect of increasing viscosity with depth is to change the flow such that the plume radius decreases with height. From Figure 6, the effect of decreasing viscosity with height (increasing viscosity with depth) is to cause the vertical velocity to increase with height in the plume. This is the expected result; since viscosity provides the resistance to the buoyancy force, the vertical 204

Variable thermal diffusivity
Although a depth-dependent thermal diffusivity cannot be quantitatively modelled here, we can qualitatively estimate its effect on plume flow and entrainment. Since the lateral conduction of heat is the main driving force for entrainment, the effect of thermal diffusivity which decreases with depth (increases with height above the base of the mantle) should be to promote more entrainment in the upper levels of the system. This suggests that thermal diffusivity which increases with height (analogous to the suggestion of Anderson, 1987; Eq. 39a) causes the plume boundary to expand outward in the upper part of the fluid. However, a thermal diffusivity which decreases with height (analogous to the measurements of Osako and Ito, 1991;Eq. 39b), has the effect of enhancing the entrainment of lower mantle material relative to upper mantle material, since that is the regios where thermal conductivity would be highest

Constraints from Boundary Layer Theory
In attempting to extrapolate the results of experiment or theory to the earth's mantle, one must always be aware of the various assumptions upon which the models rest. While recent experimental studies have presented a qualitative picture of mantle plumes, an increased understanding of the nature of fluid flow in these features requires better knowledge of the physical properties of the earth at depth, and more detailed modelling of the various features associated with mantle plumes which may be unique to the earth. The assumption of incompressibility in the present model requires that the effects of adiabatic cooling be ignored. In addition, viscous heating has been neglected, an effect which would produce heat in the regions of highest shear. However, the effects of adiabatic cooling and viscous heating tend to counteract each other (Zhao and Yuen, 1987), and so these approximations are not likely to significantly change the results presented here. In addition, though this model has incorporated experimentally constrained physical properties of olivine, extrapolation of these quantities to higher pressure phases may not be warranted. However, the physical phenomena which have been shown to drive entrainment in this study will probably also be the same processes which govern entrainment in mantle plumes, irrespective of the precise deformation processes operative in higher pressure phases. The most important question to be addressed is whether entrainment actually occurs in mantle plumes. As previously stated, the accuracy of the dimensional results of this model are only as good as the accuracy of the assumptions and physical parameters. However, we may make some broad inferences from Fig. 2. Both of the plumes depicted in Figure 2 are characterized by high vertical velocities, compared with plate velocities and velocities calculated for plumes in a constant-viscosity mantle (Parmentier et al., 1975).
For the non-Newtonian axial velocity of 7 meters/year, this indicates that plume material from the base of the mantle would reach the surface in roughly 400,000 years. While this modelled velocity may seem excessive, it should be noted that, even with this high velocity, the plume radius has increased by 40% through the full depth of the mantle, and the calculated entrainment is 47%. If actual mantle plume velocities are lower, then this implies a lower Rayleigh number for the plume, and consequently more entrainment. This indicates that entrainment should be a process of some significance in mantle plumes.
The primary constraint derived from the present analysis is the location of origin of the fluid which is entrained. For physical properties which are constant with depth, and a viscosity which depends on temperature and shear stress, the fluid which is entrained into a thermally buoyant plume originates from near the base of the plume, and entrainment of fluid from the upper levels of the system is minor. The effect of increasing viscosity with depth results in less entrainment of fluid in the upper levels, due to the increase of the vertical velocity of the plume. This effect is also enhanced by a coefficient of thermal expansion which increases with plume height. The direction of the depth dependence of these two parameters (decreasing thermal expansion, increasing viscosity) are rather firmly established. Whether thermal conductivity increases or decreases with depth in the earth is more controversial (Anderson, 1987;Osako and Ito, 1991). However, from Figs. 5 and 6, it is clear that the two strongest effects are increasing viscosity and decreasing thermal expansion with depth. Together, these effects indicate that the ambient mantle which is entrained into mantle plumes should originate dominantly from the lower mantle, and that entrainment of upper mantle material into thermal plumes should be minimal.
An interesting characteristic of the non-Newtonian rheology is the existence of "plug flow" in the thermal plume conduit (Fig. 2), due to the high viscosity of the fluid at the plume axis. If such a rheology is applicable to the whole of the mantle, then this rheology provides a mechanism for transporting fluid through the full depth of the fluid layer without significant shear mixing and dilution, as suggested by Fig. 3b and Figure 7. Two dimensional projections of the Sr-Nd-206Pb/204Pb isotope data for oceanic island basalts, from . The data are fully enclosed by a tetrahedron, with the corners corresponding to the DMM-HIMU-EMI-EMII endmembers described by .

HII
The arrangement of the data arrays shows a fan-shaped pattern converging toward the middle of the tetrahedron (FOZO), indicating a common component to hotspots from around the world which is distinct from N-type MORB. MORB data from 14°N on the mid-Atlantic ridge plot near FOZO (Dosso et al, 1990 previously not been recognized in the heavy isotope data, leading some to suggest that 3 He/ 4 He has been decoupled from the heavy isotope systems ). However, stratigraphically controlled studies incorporating 3 He/ 4 He and heavy isotope systems systems Kurz and Kammer, 1991), as well as the evidence presented here, demonstrate consistent covariation between He isotopes and those of Sr, Nd, and Pb, and show that this component is a common to a number of hotspots from around the world. This high 3 He/ 4 He endmember has been termed FOZO by .
Using this data to constrain entrainment processes in mantle plumes is a complex issue. This requires knowledge about the interaction of the plume flow with the moving lithosphere , as well as detailed information on the pathways of magma segregation and mixing processes. However, one constraint that is immediately clear from Fig. 7 is that, with the exception of ridge centered hotspots, neither DMM nor typical N-MORB sources are components in any of the mixing arrays shown in Fig. 7; this point is emphasized by the increasing 3 He/ 4 He ratios of some of these arrays approaching FOZO. This lack of mixing with MORB mantle is consistent with the prediction from entrainment theory that entrainment of the uppermost mantle should be insignificant in mantle plumes. This absence of upper mantle entrainment would seem to be inconsistent with the model for entrainment in an inclined plume conduit Griffiths and Campbell, 1991); the sharpness of the bend in the Hawaii-Emperor Seamount chain essentially requires that the inclination of the plume conduit take place in the uppermost mantle ). However, with the possible exception of lithospheric components in some post-shield volcanics (Chen and Frey, 1985), no evidence for MORB source components exists in the isotope data for the Hawaiian Islands.
An exception to the absence of MORB source in the OIB ararys is that ridgecentered hotspots often show evidence of mixing with the uppermost mantle; Iceland and the Galapagos Islands are classic examples (Schilling, 1973;Hart et al., 1973;Sun et al., 1975;White et al., 1992). It is likely that these plumes have incorporated ambient MORB mantle due to the superposition of the sub-ridge mantle flow on the upwelling plume flow. In addition to these islands, the MORB data of Dosso et al. (1990) from 14N on the Mid-Atlantic Ridge have exceptionally high 2 06pb/204Pb, but have 87 Sr/ 86 Sr<.7030. This region of the MAR also exhibits other geochemical anomalies such as LREE enrichment (Dosso et al., 1990), but it is not anomalously shallow, and no abvious expression of a hotspot exists. Whether this and other mid-ocean ridge anomalies represent nascent plumes, or an expression of a heterogeneous MORB source, is a classic problem (e.g. see Allegre et al., 1984). However, the general absence of typical N-MORB mantle as a component in these arrays remains valid.
In the context of the present results, if FOZO does in fact have high 3 He/4He, then it may be suggested that an origin for plumes from a thermal boundary layer at 670 km depth can be discounted. If such plumes existed, they would be expected to entrain upper mantle, and so show some mixing toward MORB, which is clearly not observed in Fig. 7 (with the exception of ridge-centered hotspots). If FOZO is associated with a boundary layer at 670 km (instead of core-mantle boundary), then plumes with FOZO as a component should still show mixing toward MORB, since it is the downward motion of the upper mantle which would replenish material in a 670 km thermal boundary layer. Even if the boundary layer were made up entirely of subducted oceanic crust, such sinking cold plumes should still entrain upper mantle material due to the lateral conduction of "coldness", in much the same manner as hot plumes entrain ambient mantle. In addition, experimental studies of layered convection (Richter and McKenzie, 1981;Olson, 1984) have shown significant disruption of a density-stratified boundary due to viscous coupling between the layers. Thus the location of FOZO in the mantle above 670 km is deemed unlikely due to the absence of a high 3 He/ 4 He signature in N-type MORB. Since it is unlikely that an origin for mantle plumes in a 670 km boundary layer can be reconciled with the presence of a high 3 He/ 4 He FOZO, this provides support for convection across the 670 km discontinuity, and probably throughout the entire mantle.
The arrays shown in Fig. 7 essentially connect the isotopic composition of FOZO with variable isotopic compositions characterized by more enriched signatures in 87 Sr/ 86 Sr, 1 43 Nd/ 144 Nd, and 206 Pb/ 204 Pb. In addition, the enriched mantle compositions are often not pure EMI (Walvis, Pitcairn), EMII (Societies, Samoa), or HIMU (Macdonald), but often seem to be compositions along the binary joins of the EMI-EMHI-HIMU triangle (Kerguelen EMI-EMII; Azores EMII-HIMU; Cameroon Line EMI-HIMU). As noted by Hart et al. (1986), this may be evidence for mixing events which have taken place previous to the mixing toward FOZO. Alternatively, the most isotopically enriched ends of these arrays may have developed through time in reservoirs with the specific Rb/Sr, Sm/Nd, and U/Pb ratios needed to generate these various isotopic signatures, instead of being specific mixtures of isotopically homogeneous endmembers. For example, the Azores may not be a mixture of EMII and HIMU, but instead might be a distict reservoir characterized by relatively high Rb/Sr, Sm/Nd, and U/Pb. This view is supported by the absence of linear arrays which trend parallel to the joins of the EMI-EMII-HIMU triangle (Fig. 7). In this scenario, it is still possible that intermediate enriched compositions are due to mixing between components prior to long-term isolation and isotopic evolution, such as a high Rb/Sr component and a high U/Pb component (both with high Sm/Nd) for the Azores. Alternatively, since the parent-daughter characteristics of EMI, EMII, and HIMU are likely associated with specific processes which fractionate Rb/Sr, Sm/Nd, and U/Pb in the required directions, the enriched ends of the arrays in Fig. 7 which are intermediate between EMI-EMII-HIMU may result from the superposition to varying degrees of these processes. These issues remain unanswered, and the analysis presented here is consistent with all of these possibilities.
The binary nature of these arrays begs the question as to which components are present in the plume source, and which components are entrained. In this respect, 3 He/He is an excellent tracer. Due to the lack of high 3 He/ t He signatures in MORB, high 3 He t He indicates a source which is distinct from the uppermost mantle. Based on the evidence from entrainment theory, this would seem to implicate a lower mantle origin for the high 3 He/ 4 He component. However, the location of FOZO in the lower mantle does not provide an answer to whether FOZO is plume source, or entrained mantle. For example, plumes are often proposed to originate from a thermal boundary layer at the core-mantle boundary (Stacey and Loper, 1983). This requires that the thermal boundary layer be replenished to replace the mantle which was lost to mantle plumes. The core-mantle boundary layer (CMBL) is essentially replenished by the downward motion of the lowermost mantle toward the core. Thus, if FOZO is present in the lower mantle, then it must also be present in the CMBL.
Two endmember scenarios are possible which would be consistent with the isotope data and the results from entrainment theory: 1) The enriched components (EMI, EMIl, HIMU, and intermediate compositions) are located in the CMBL, and FOZO represents entrained lower mantle.
Evidence for the presence of both FOZO and pure endmember components exists in the isotope data for Samoa (EMII), Pitcairn (EMI) , and the Macdonald hotspot chain (HIMU), indicating that all three enriched endmember components must be available for mixing with FOZO in the lower mantle. To make the CMBL and the lower mantle isotopically distinct would require some process which transports material in a relatively pure state through the mantle to the CMBL, whereupon it is incorporated into mantle plumes. The model presented here, and the numerical mantle convection modelling of (Malevsky et al., 1991) indicate that subduction in a fluid with a non-Newtonian rheology may be just such a mechanism. The behavior of plumes with both positive and negative buoyancy is similar to the flow depicted in Fig. 2a, though with an inverted temperature profile. In a fluid with a stress dependent rheology, subducted slabs could sink through the mantle with minimal, though possibly still significant, mixing with ambient mantle; because the pressure at the head of the descending plume induces shear in the fluid ahead of it, this allows the slab to sink through the mantle surrounded by a sheath of low viscosity mantle. The identification of the HIMU signature at Tubuai and Mangaia with recycled oceanic crust (described in Chapter 4), coupled with evidence for a high 3 He 4 He signature at Macdonald seamount, provides support for this scenario.
2) FOZO represents the source mantle for plumes in the CMBL, and enriched components are entrained from the lower mantle.
This would suggest that recycled crustal materials may not be able to sink all the way to the CMBL. If the lower mantle rheology were Newtonian, and exhibited a significant increase in viscosity with depth, this would provide increasing resistance to subduction with depth. Instead, the recycled crust may not sink through the mantle fast enough to accumulate in large amounts at the CMB, and would instead be swept up in the background convective flow within most of the mantle, to be available for entrainment into mantle plumes.
The entrainment theory presented above indicates that the strongest plumes will be least entrained (Fig. 4), and thus the strongest plumes would contain the lowest fraction of entrained (EMI-EMII-HIMU) components. Basalts from Koolau (Roden et al., 1984) have enriched isotopic compositions which approach the EMI endmember, which contradicts the prediction that Hawaii should be the least entrained plume. However, the expression of plume isotopic signatures in erupted lavas is critically dependent on the melting and melt segregation process, and so this is not a fatal blow to this scenario.
Evidence in favor of this model comes from the high 3 He/ 4 He values measured at Hawaii and Iceland, two plumes with high buoyancy fluxes (Sleep, 1990). The 3 He/ 4 He measurements on basalts from Loihi and the neovolcanic zones of Iceland  are the highest values yet reported for oceanic islands, and provide support for the idea that the strongest (i.e. least diluted) plume signature should be observed at the strongest plumes. In addition, the streamlines in Fig. 3 indicate that the entrained mantle should occupy a region at the periphery of the plume. The well documented geochemical gradients along the Reykjanes Ridge leading up to Iceland (Hart et al., 1973;Schilling, 1973;Sun et al., 1975; demonstrate mixing between the Iceland plume and upper mantle MORB source. The region of highest melt production, highest 3 He/ 4 He values, and location of the maxima of the Icelandic thermal anomaly indicate that the Iceland plume is centered beneath the island 214 DMM Hotspot HIMU Figure 8. Two-dimensional projection of Sr-Nd-206Pb/204Pb isotope data for OIB, as in Fig. 8. Diagram show the fields for several island chains in the Pacific Ocean. Data for the youngest volcanoes in each chain lie toward the middle of the tetrahedron in the region of convergence. Of these islands, Loihi (20-33 Ra), Mehetia (11.8 Ra), Rapa (11 Ra), and Macdonald Seamnount (9 Ra) have documented high 3He/4He ratios. He data from , Staudacher and Allegre (1989), and Desonie et al. (1991).
proper (Sleep, 1990). The location of the Reykjanes Ridge at the edge of the Iceland swell provides support for the location of entrained (MORB source) material at the periphery of the plume. The scale of the "anomalous" geochemical signature along the Reykjanes Ridge (>400 km) indicates that this feature is not simply a result of melt generation/segregation processes acting on a smaller feature.
In addition to the evidence described above, the presence of a strong FOZO signature in some island chains (all from the Pacific) seems to be connected with the most recent shield building volcanism within the chain. Loihi Seamount (Hawaii), Macdonald Seamount (Macdonald), Manu'a Islands (Samoa), and Mehetia Seamount (Society) all lie at the FOZO end of the data arrays (Fig. 8). Most of these young volcanos (Loihi, Mehetia, Macdonald) are characterized by 3 He/4He > 9 Ra (Staudacher and Allergre, 1989;Desonie et al., 1991). In addition, the highest 3 He/ 4 He data from Iceland comes from the southeastern neovolcanic zone, which became active only 1.5 Ma ago  and is the youngest of the three rift zones on Iceland. If the mantle at the plume axis is at the highest temperature, and is rising at the highest velocity, then melt production will be greatest at the axis of the plume, and these melts may be the dominant melt products at nascent volcanic features. This idea may be supported by the 3 He/ 4 He data from Loihi, in which the highest 3 He/ 4 He ratios come from tholeiitic basalts (26-35 Ra), and a basanite records the lowest Loihi value (20 Ra) . At Samoa, however,  have measured 3 He/ 4 He values of 8-25 Ra within a single exposure of shield flows from the island of Tutuila, which indicates the complexity of this problem. In actuality, the two scenarios presented above, both of which place FOZO and the enriched components in the lower mantle, are not mutually exclusive. It is likely that the truth lies somewhere in between. For example, the isotopic composition of the basalts along the Macdonald hotspot chain change abruptly from endmember HIMU compositions (Mangaia, Rurutu, Tubuai, 20-6 Ma) to compositions near the center of the tetrahedron (Rapa, Macdonald Seamount, 6 Ma-present) (Fig. 7). The ages of volcanics from the islands of Tubuai and Rapa overlap between 6-7 Ma, indicating that these two islands, in the same island chain, were simultaneously erupting basalts with very different isotopic compositions. This seems to require an abrupt change in the isotopic composition of the mantle being supplied by the plume.
In reality, it is likely that the mantle in the boundary layer source of most mantle plumes is probably already heterogeneous, and whether a plume carries endmember components or FOZO mantle may instead depend on the local concentrations of these materials in the lower mantle. The necessity of maintaining isotopically distinct upper and lower mantles does not require layered convection, but may the the result of different time 216 scales of mixing for the upper and lower mantles. In this case, it is possible that this difference in isotopic composition may be the time integrated signature of a lower mantle with a distinct major element composition. Mineral/melt partitioning data for the various parent/daughter systems in ultra-high pressure phases would be enormously important for testing this issue.

Conclusions
The 10-20% melting in the spinel lherzolite stability field. Due to the extremely high total degrees of melting experienced by these samples (33-42%) compared with abyssal peridotites (10-20%), as well as the high degree of melting in the garnet lherzolite stability field, suggests a mantle plume origin for at least the Savaii xenoliths. Though peridotite xenoliths are usually considered to be fragments of the lithosphere, a plume origin is entirely consistent with fluid dynamic modelling which predicts advective thinning of the lithosphere by upwelling plume mantle . If, however, these xenoliths are fragments of the lithosphere which is residual after MORB melting, then the Group 1 trace element patterns provide unequivocal evidence for the participation of garnet during MORB genesis. A large majority of the xenolith clinopyroxenes from both Savaii and Tubuai are LREE enriched to varying degrees, and many samples display significant intergrain trace element heterogeneity. This highly variable yet systematic heterogeneity was the result of metasomatism by percolating melts undergoing chromatographic trace element fractionation. The unsupported 143Nd/144Nd of the TBA 4-11 xenolith (i.e. high 143Nd/144Nd coupled with low Sm/Nd) indicates that this metasomatism was recent, and most likely associated with the melting events which formed the respective islands. The trace element compositions of some LREE enriched clinopyroxenes are consistent with the percolating melt being typical oceanic island basalt. The clinopyroxenes with the highest LREE concentrations from both islands, which also have very low Ti and Zr concentrations and large amounts of grain-boundary hosted Ba, require that the percolating melt in these cases had the trace element signature of carbonatite melt. The extreme isotopic compositions of SAV 1-1 relative to Samoan basalts (Chapter 3, Fig. 14) indicates that these melts were not erupted in their pure form, but were mixed with melts of less enriched isotopic compositions; this is consistent with the fractional melting hypothesis for mantle plumes advanced in Chapter 3. The LREE-enriched xenoliths examined here have essentially served at "traps" for collecting small melt fractions which would not otherwise reach the surface. These "carbonatitic" signatures indicate the presence of volatile-rich, isotopically extreme components in the mantle beneath Tubuai and Savaii, possibly due to crustal recycling; the Sr-Nd-Pb isotopic composition of SAV 1-1 bears a notable resemblance to modem oceanic sediments . These data indicate that the melt generation/segregation process in hotspots takes some average of the composition of the plume mantle; exactly how this averaging taps different parts of the plume requires detailed knowledge of the physics of magma extraction. In regard to this, the dominance of LREE-enriched over LREE-depleted xenoliths, and the scarcity of LREEenriched signatures in abyssal peridotites, indicates that melt extraction is less efficient from hotspots than from the sub-ridge mantle.
The Re-Os isotope systematics of oceanic island basalts from Rarotonga, Savaii, Tahaa, Rurutu, Tubuai, and Mangaia were examined (Chapter 4) in order to place further constraints on the composition of isotopically extreme mantle, using the information available from the study of a parent-daughter system whose elements have unique geochemical behaviors compared with other isotope tracers. The Savaii and Tahaa samples, with high 87 Sr/ 86 Sr and 207Pb/204Pb ratios (EMII), as well as basalts from Rarotonga, have 1870s/186Os ratios of 1.026-1.086, within the range of estimates of bulk silicate earth and depleted upper mantle. Though recycled sediment may be required to generate the most extreme Sr-Nd-Pb isotopic compositions observed at Samoa, is process will have a fairly minor effect on the Re/Os systematics of the sediment-peridotite mixture, due to the low Re and Os concentrations of oceanic sediments (Ravizza, pers. comm.).
The basalts from Rurutu, Tubuai, and Mangaia (Macdonald hotspot), characterized by high Pb isotope ratios (HIMU), have 187 0s/ 186 0s ratios of 1.117-1.248, higher than any estimates for bulk silicate earth, and higher than Os isotope ratios of metasomatized peridotites. Though the Ronda mafic layers are characterized by high 1870s/1860s ratios , their possible analogs in the convecting mantle cannot function as the HIMU source. Mafic layers will contribute almost all of the Pb to a melt of a peridotitemafic layer mixture, and so they must have high 2 06Pb/204Pb. But almost all of the Os in the melt will be contributed by the peridotite, not by the mafic layers (which have low Os concentrations). The result of mixing melts of mafic layers and melts of peridotite would define a strongly curved hyperbola, with most melts having low 187 0s/ 186 0s and high 206Pb/24Pb. The high 187 0s/ 186 0s ratios indicate the presence of recycled oceanic crust in the mantle sources of Rurutu, Tubuai, and Mangaia, which would be more resistant to convective dispersion than the meter-scale Ronda mafic layers. The Re/Os ratios calculated for the HIMU mantle source require substantial amounts of crustal material to be recycled into the mantle; since the subduction of MORB is by far the largest return of crust to the mantle, this is the most likely source for the HIMU signature. Furthermore, the mixing of the Macdonald hotspot array toward FOZO (Chapter 5, Fig. 7), and the carbonatitic 100-  (1988). The plume is isotopically zoned, with "plume mantle" at the center and "entrained mantle" at the periphery. The plume crosses the volatile-bearing peridotite solidus at 350-400 km depth and begins to generate volatile-rich, small degree partial melts, some of which may have compositions similar to carbonatite. The melting plume is characterized by a large volume of mantle which is generating small degree, incompatible element-rich melts and a smaller volume of mantle above the anhydrous peridotite solidus generating higher degree melts. The compositions of erupted basalts depends strongly on how these various melts are mixed and segregated. Significant uncertainty remains in the distribution of plume mantle, entrained mantle, and lithosphere beneath hotspot volcanos; such information can come only from detailed fluid dynamic modelling of plume-lithosphere interaction employing an experimentally constrained peridotite rheology.
229 signatures present in the Tubuai xenoliths (Chapter 3, Fig. 4), indicates that oceanic crust and volatiles are recycled into the lower mantle. The homogeneity of the Sr-Nd-Pb-Os isotopic data for Tubuai and Mangaia indicate that melt percolation through low-187 0s/ 186 0s mantle, observed to occur in xenoliths from Tubuai (Chapter 3, Fig. 13), had little effect on the composition of the erupted magmas. The combined Os-Pb isotope systematics are a very sensitive indicator of melt percolation by porous flow; since Os is a compatible element and Pb is highly incompatible, porous flow through depleted mantle will be most obvious, and most hyperbolic, in the 187 0s/ 186 0s -2 0 6 Pb/20 4 Pb signature. The evidence of melt percolation in the Tubuai between "source" and "entrained" mantle, but instead results in a concentric zoning about the plume axis, with source mantle at the center and entrained mantle at the periphery. In this scenario, the binary mixing arrays in Fig. 7 of Chapter 5 are not due to the mixing of distinct volumes of mantle, but are the expression of magma mixing during fractional 230 melting and melt extraction in the individual plumes. The similarity of Sr/Pb, Sr/Nd, and Nd/Pb ratios in OIBs may then provide an alternative explanation for the quasi-linearity of the binary arrays. Such a scenario is depicted in Fig. 2, which is adapted from . A concentrically zoned, volatile-bearing plume will be characterized by a large volume which is between the volatile-bearing and anhydrous peridotite solidi, and which is generating incompatible and volatile element rich, small degree partial melts. At the axis of the plume is a smaller region above the anhydrous peridotite solidus which is generating higher degree melts. The way in which these melt fractions of diverse compositions are mixed together depends strongly on the physics of fracture formation in a two-phase, viscous, non-Newtonian medium. One observation which may be pertinent to this case is the common association of replacive dunites with shear zones in the Josephine peridotite (Keleman, pers. comm.). If in fact melts are localized along shear zones, then this may provide a mechanism for mixing of melts from the concentric zones of the plume; in Figs. 2 and 3 from Chapter 5, it is apparent that the region of greatest shear in a plume is located near the boundary between "source" and "entrained" mantle.
The combined fluid dynamic and isotopic results indicate that both FOZO and enriched mantle components (EMI, EMII, HIMU, and intermediate compositions) must be available for transport into the lower mantle; thus the origin of the HIMU signature in recycled oceanic crust requires mass exchange between the upper and lower mantle. In addition, the absence of a MORB source (=upper mantle) signature in off-ridge hotspots, coupled with high 3 He/ 4 He in FOZO and the low 3 He/ 4 He of MORB, suggests that mantle plumes do not originate from a thermal boundary layer at 670 km, and thus that convection must penetrate the full depth of the mantle. However, the MORB source and FOZO, associated with the upper and lower mantle, respectively, are still isotopically distinct, though there may be some overlap in Sr, Nd, Pb, and Os isotopic compositions. The preservation of isotopically different upper and lower mantles does not require layered convection, but may be the result of a longer residence time for the mantle below 670 km than the upper mantle, possibly the result of an increasing mean viscosity with depth.