Olivia E Anderson
email: anderson03@ucsb.edu

M G Jackson

E F Rose-Koga

J P Marske

M E Peterson

A A Price

B L Byerly

A A Reinhard

Testing the Recycled Gabbro Hypothesis for the Origin of "Ghost Plagioclase" Melt Signatures Using 87 Sr/ 86 Sr of Individual Olivine-Hosted Melt Inclusions from Hawai'i

Hawaiian melt inclusions are variable in 87 Sr/ 86 Sr, but are within the 87 Sr/ 86 Sr range of the lavas from their host volcano.

• Mauna Loa melt inclusions with high (Sr/Ce)N (ghost plagioclase) signatures have the same 87 Sr/ 86 Sr as inclusions with normal (Sr/Ce)N.

• Diffusive interaction between rising melt and Hawaiian gabbros can produce the ghost plagioclase signature in Mauna Loa melt inclusions.

Introduction

Melt inclusions, encapsulated within growing magmatic phenocrysts at depth, provide "snapshots" of melt evolution that may not be preserved in whole rock compositions. One geochemical signature found in melt inclusions is high Sr concentrations relative to trace elements of similar incompatibility (such as Ce, Nd, and Sm). The magnitude of the Sr anomaly can be quantified with the ratio (Sr/Ce)N (where N signifies normalization to primitive mantle; [START_REF] Mcdonough | The composition of the Earth[END_REF]. Melt inclusions with high (Sr/Ce)N ratios are significant because the Sr anomaly found within these inclusions suggest plagioclase was involved in melt petrogenesis. However, plagioclase accumulation, or assimilation, is not always obvious in the major element chemistry of these melt inclusions [START_REF] Danyushevsky | Crustal origin for coupled 'ultra-depleted' and 'plagioclase' signatures in MORB olivine-hosted melt inclusions: evidence from the Siqueiros Transform Fault, East Pacific Rise[END_REF][START_REF] Danyushevsky | Melt inclusions in primitive olivine phenocrysts: the role of localized reaction processes in the origin of anomalous compositions[END_REF][START_REF] Gurenko | Enriched and depleted primitive melts included in olivine from Icelandic tholeiites: origin by continuous melting of a single mantle column[END_REF][START_REF] Michael | Depleted melt inclusions in MORB plagioclase: messages from the mantle or mirages from the magma chamber?[END_REF][START_REF] Peterson | Origin of the 'ghost plagioclase' signature in Galapagos melt inclusions: new evidence from Pb isotopes[END_REF][START_REF] Saal | The role of lithospheric gabbros on the composition of Galapagos lavas[END_REF][START_REF] Slater | Melt generation and movement beneath Theistareykir, NE Iceland[END_REF][START_REF] Sobolev | Recycled oceanic crust observed in 'ghost plagioclase' within the source of Mauna Loa lavas[END_REF].

Melt inclusions with high (Sr/Ce)N have been described from samples taken from midocean ridges (MORs; e.g., [START_REF] Danyushevsky | Crustal origin for coupled 'ultra-depleted' and 'plagioclase' signatures in MORB olivine-hosted melt inclusions: evidence from the Siqueiros Transform Fault, East Pacific Rise[END_REF][START_REF] Danyushevsky | Melt inclusions in primitive olivine phenocrysts: the role of localized reaction processes in the origin of anomalous compositions[END_REF][START_REF] Michael | Depleted melt inclusions in MORB plagioclase: messages from the mantle or mirages from the magma chamber?[END_REF] and hotspot lavas erupted at ocean islands such as Galapagos [START_REF] Peterson | Origin of the 'ghost plagioclase' signature in Galapagos melt inclusions: new evidence from Pb isotopes[END_REF], Hawai'i [START_REF] Sobolev | Recycled oceanic crust observed in 'ghost plagioclase' within the source of Mauna Loa lavas[END_REF][START_REF] Sobolev | A young source for the Hawaiian plume[END_REF], and Iceland (e.g., [START_REF] Gurenko | Enriched and depleted primitive melts included in olivine from Icelandic tholeiites: origin by continuous melting of a single mantle column[END_REF][START_REF] Maclennan | Lead isotope variability in olivine-hosted melt inclusions from Iceland[END_REF][START_REF] Slater | Melt generation and movement beneath Theistareykir, NE Iceland[END_REF]. A common geologic material with high (Sr/Ce)N ratios is cumulate gabbro, which can be a plagioclase-rich lithology. Its abundance in the deep oceanic crust represents the intrusive part of the MOR sequence, and makes gabbro an obvious candidate for imparting large positive Sr anomalies on percolating melts at MOR and ocean island settings [START_REF] Peterson | Origin of the 'ghost plagioclase' signature in Galapagos melt inclusions: new evidence from Pb isotopes[END_REF][START_REF] Saal | The role of lithospheric gabbros on the composition of Galapagos lavas[END_REF][START_REF] Sobolev | Recycled oceanic crust observed in 'ghost plagioclase' within the source of Mauna Loa lavas[END_REF][START_REF] Yaxley | High-pressure partial melting of gabbro and its role in the Hawaiian magma source[END_REF]. Plagioclase likely plays a central role in generating large positive Sr anomalies because Sr is compatible in plagioclase compared to elements of similar behavior (Sm, Nd) during peridotite melting and subsequent differentiation in mafic magmatic systems.

Melts with large, positive Sr anomalies signal interaction with plagioclase-rich lithologies like gabbro. Paradoxically, a subset of these high (Sr/Ce)N melt inclusions lack coexisting enrichments in major elements associated with plagioclase (e.g., Al), giving rise to the concept of "ghost plagioclase" signatures in rare melt inclusions trapped in magmatic phenocrysts [START_REF] Sobolev | Recycled oceanic crust observed in 'ghost plagioclase' within the source of Mauna Loa lavas[END_REF]. Three hypotheses invoked to explain the rare occurrences of large, positive Sr anomalies in melt inclusions include: (i) direct assimilation of gabbro by upwelling melts [START_REF] Danyushevsky | Crustal origin for coupled 'ultra-depleted' and 'plagioclase' signatures in MORB olivine-hosted melt inclusions: evidence from the Siqueiros Transform Fault, East Pacific Rise[END_REF], (ii) melts of recycled lower oceanic (gabbroic) crust in the mantle source that are hybridized with peridotite and trapped as melt inclusions in growing magmatic phenocrysts [START_REF] Chauvel | Melting of a complete section of recycled oceanic crust: trace element and Pb isotopic evidence from Iceland[END_REF][START_REF] Hofmann | Source characteristics derived from very incompatible trace elements in Mauna Loa and Mauna Kea basalts, Hawaii Scientific Drilling Project[END_REF][START_REF] Sobolev | Recycled oceanic crust observed in 'ghost plagioclase' within the source of Mauna Loa lavas[END_REF]Yaxley & Sobolev, 2007), and (iii) diffusive interaction between percolating melt and a plagioclase-rich crystal mush [START_REF] Peterson | Origin of the 'ghost plagioclase' signature in Galapagos melt inclusions: new evidence from Pb isotopes[END_REF][START_REF] Saal | The role of lithospheric gabbros on the composition of Galapagos lavas[END_REF].

Direct assimilation has been ruled out to explain Sr anomalies in many oceanic hotspot melt inclusions from Hawai'i [START_REF] Sobolev | Recycled oceanic crust observed in 'ghost plagioclase' within the source of Mauna Loa lavas[END_REF] and Galapagos [START_REF] Peterson | Origin of the 'ghost plagioclase' signature in Galapagos melt inclusions: new evidence from Pb isotopes[END_REF] because the ghost plagioclase melt inclusions have large, positive Sr anomalies that do not have corresponding elevated Al2O3, as would be expected for direct assimilation of Al-rich plagioclase (e.g., [START_REF] Peterson | Origin of the 'ghost plagioclase' signature in Galapagos melt inclusions: new evidence from Pb isotopes[END_REF][START_REF] Sobolev | Recycled oceanic crust observed in 'ghost plagioclase' within the source of Mauna Loa lavas[END_REF].

Regarding the second hypothesis, melts of recycled gabbroic lower oceanic crust may generate trace element chemistry similar to many high (Sr/Ce)N inclusions from ocean islands. The recycled gabbro model suggests eclogite, metamorphosed gabbroic material, would partially melt earlier (deeper) than surrounding peridotite in an upwelling mantle plume [START_REF] Sobolev | Recycled oceanic crust observed in 'ghost plagioclase' within the source of Mauna Loa lavas[END_REF][START_REF] Yaxley | High-pressure partial melting of gabbro and its role in the Hawaiian magma source[END_REF]. The melt of the eclogite is silicic (e.g., dacitic) and thus would react with surrounding peridotite, producing garnet-bearing pyroxenites [START_REF] Yaxley | Reactions between eclogite and peridotite: mantle refertilisation by subduction of oceanic crust[END_REF]. The large, positive Sr anomaly is transferred from the silicic melt to the reacted pyroxenite and resides mainly within clinopyroxene. When the reacted pyroxenite partially melts during continued plume upwelling, high-MgO liquids with elevated Sr are generated and mix with normal melts formed by partial melting of peridotite. In the recycled gabbro melting model, the Sr budget in a high (Sr/Ce)N melt will be dominated by Sr from the gabbro, because the peridotite in the melt source of this model is not assumed to have a large, positive Sr anomaly. As a result, this model predicts that Mauna Loa melt inclusions with large, positive Sr anomalies will have essentially the same 87 Sr/ 86 Sr as the recycled gabbro.

The third hypothesis predicts that diffusive interaction between percolating melt and plagioclase-rich mush will produce trace element patterns reflecting a gabbro contribution. Due to the slow diffusive nature of major elements (e.g., Al2O3), the diffusion model will not generate significant changes in the major element concentration of a melt. In addition, diffusive interaction will cause the high (Sr/Ce)N melt inclusions to have the same Pb [START_REF] Peterson | Origin of the 'ghost plagioclase' signature in Galapagos melt inclusions: new evidence from Pb isotopes[END_REF] and Sr (this study) isotopic composition as the gabbro through which they percolated (because Sr and Pb have high diffusivities in plagioclase). If the melt percolated through and interacted with the gabbro of the ~100 Ma [START_REF] Müller | Age, spreading rates, and spreading asymmetry of the world's ocean crust[END_REF]) MOR crust beneath Hawai'i, melt inclusions will adopt 87 Sr/ 86 Sr of the relatively modern MOR crust. Conversely, if the melt inclusions with high (Sr/Ce)N result from interaction with gabbroic mush in a Mauna Loa magma chamber, these inclusions will have 87 Sr/ 86 Sr that is indistinguishable from lavas erupted at Mauna Loa. In both cases (i.e., MOR gabbro or Mauna Loa gabbro), the resulting 87 Sr/ 86 Sr ratio of high (Sr/Ce)N melt inclusions is predicted to be indistinguishable from the 87 Sr/ 86 Sr of the gabbro with which the percolating melt interacted. This study presents strontium isotopes measured on melt inclusions with high (Sr/Ce)N to distinguish between the two hypotheses-diffusive interaction between percolating melt and modern plagioclase-rich mush versus melts of ancient recycled gabbro-for generating "ghost plagioclase" signatures in melt inclusions. In addition, major, volatile (Cl and S), and trace element concentrations are included for individual melt inclusions isolated from six different lavas from three Hawaiian volcanoes: Mauna Loa, Loihi, and Koolau. One of the melt inclusions from Mauna Loa reported here has the highest (Sr/Ce)N (7.2) ratio ever reported in a Hawaiian lava or melt inclusion.

Methods

Olivine-hosted melt inclusions and glasses from six Hawaiian picrites from Mauna Loa (samples Puu2, Puu7, and ML-2012-27), Loihi (samples 6K490-1 and 6K490-2), and Koolau (sample K89-6; Figure 1) were analyzed. Melt inclusions in this study were not homogenized, as most melt inclusions analyzed were naturally glassy, and characterized for 87 Sr/ 86 Sr and elemental concentrations. However, five inclusions (Puu2-1-2, Puu7-2-15, Puu7-2-92b, K89-6_52, 6K490-1_51) were partially crystalline and were characterized only for 87 Sr/ 86 Sr, and not for elemental concentrations.

The Supplement describes the samples selected, melt inclusion preparation methods, including grinding the olivines into tiny (several hundred microns on a side) cubes to remove all

Results 135

The melt inclusions are hosted in olivine crystals ranging from Fo80.4 to Fo90.1 (Table S1). 136

Melt inclusions span a wide range of sizes, most having maximum major axis lengths between 137 120 and 630 µm (Figure S3). A high, positive Sr anomaly can be quantified using (Sr/Ce)N. In a plot of Al2O3 versus MgO (Figure 3), the highest (Sr/Ce)N melt inclusion from 146

Mauna Loa is shown with new data on normal-type melt inclusions and previously published 147

Mauna Loa melt inclusions [START_REF] Reinhard | Sr and Nd isotopic compositions of individual olivine-hosted melt inclusions from Hawai'i and Samoa: Implications for the origin of isotopic heterogeneity in melt inclusions from OIB lavas[END_REF][START_REF] Sobolev | Recycled oceanic crust observed in 'ghost plagioclase' within the source of Mauna Loa lavas[END_REF][START_REF] Sobolev | A young source for the Hawaiian plume[END_REF] and Hawaiian 148 whole rock and glass data [START_REF] Frey | The geochemical components that distinguish Loa-and Kea-trend Hawaiian shield lavas[END_REF][START_REF] Garcia | An evaluation of temporal geochemical evolution of Loihi summit lavas: results from Alvin submersible dives[END_REF][START_REF] Garcia | Geochemical and isotopic evolution of Loihi Volcano, Hawaii[END_REF][START_REF] Garcia | Petrology and geochronology of basalt breccia from the 1996 earthquake swarm of Loihi seamount, Hawaii: magmatic history of its 1996 eruption[END_REF]. inclusions and all except for the target melt inclusion must be removed prior to sample leaching and dissolution. First, the target inclusion is exposed, the host olivine is mounted in epoxy, and the melt inclusion is analyzed for major, trace, and volatile elements using in situ techniques. (b) After in situ analysis, accessory melt inclusions are removed by mounting the olivine grain onto a glass slide using Crystalbond™. (c) The olivine is then ground on silicon carbide grinding mats until the accessory melt inclusions on one side of the olivine grain are removed. (d) The olivine grain is reoriented to optimally remove remaining accessory melt inclusions, and this process is repeated until only the target melt inclusion is left within a case of its olivine host (e). The "cubed" melt inclusion is then leached and cleaned in ultra-pure acid before dissolution and column chemistry.

from Mauna Loa (sampling the deep recesses of Mauna Loa volcano; [START_REF] Gaffney | Environments of crystallization and compositional diversity of Mauna Loa xenoliths[END_REF], and gabbros from the Gabal Gerf ophiolite [START_REF] Zimmer | The Gabal Gerf complex: a Precambrian N-MORB ophiolite in the Nubian shield, NE Africa[END_REF], plot above the array formed by Hawaiian melt inclusions and whole rocks. Critically, the highest (Sr/Ce)N melt inclusion (ML-2012-27_19b) is not shifted off of the Hawaiian array toward the gabbroic compositions.

Melt inclusions have major element characteristics consistent with Hawaiian whole rock and glass data reported in the literature (Figure S4). In general, melt inclusions have lower FeOt (total iron as FeO) compared to their host glass, which is similar to olivine-hosted melt inclusions from other localities that have experienced post-entrapment Fe-Mg diffusive exchange [START_REF] Danyushevsky | Re-equilibration of melt inclusions trapped by magnesian olivine phenocrysts from subduction-related magmas: petrological implications[END_REF][START_REF] Gaetani | Open system behavior of olivine-hosted melt inclusions[END_REF][START_REF] Kent | Melt inclusions in basaltic and related volcanic rocks[END_REF][START_REF] Sobolev | Petrology and geochemistry of boninites from the north termination of the Tonga Trench: constraints on the generation conditions of primary high-Ca boninite magmas[END_REF]. Some of the Mauna Loa inclusions have high CaO relative to the Hawaiian lava array, including a single ultra-calcic melt inclusion reported here (sample Puu2-1-39, seen most clearly in the panel showing CaO/Al2O3 versus MgO in Figure S4f), consistent with previous findings of high CaO melts at Hawai'i [START_REF] Huang | Petrogenesis of high-CaO lavas from Mauna Kea, Hawaii: Constraints from trace element abundances[END_REF][START_REF] Kogiso | Experimental study of clinopyroxenite partial melting and the origin of ultra-calcic melt inclusions[END_REF]. While some melt inclusions in this study have slightly different major element compositions that trend outside of the field defined by Hawaiian lavas (Figure S4), below we show that none of the melt inclusions have unusual 87 Sr/ 86 Sr that varies outside of the range found in whole rocks and glasses at each respective volcano.

The Mauna Loa melt inclusions from Pu'u Wahi reported here have a range of (Sr/Ce)N of 0.8-1.5, and the ML-2012-27 Mauna Loa melt inclusions reported here have a (Sr/Ce)N range of 1.0-7.2 (Figures 3 and4), where (Sr/Ce)N of 7.2 is the highest value reported for any Mauna Loa melt inclusion. [START_REF] Sobolev | Recycled oceanic crust observed in 'ghost plagioclase' within the source of Mauna Loa lavas[END_REF][START_REF] Sobolev | A young source for the Hawaiian plume[END_REF] reported (Sr/Ce)N values up to 5.4, with 11 inclusions that have (Sr/Ce)N>2. In a plot of (Sr/Ce)N versus Al2O3 (Figure 3), the highest (Sr/Ce)N inclusion in this study does not show an anomalous Al2O3 concentration relative to the 178 S10) and the Mauna Loa gabbro with the highest (Sr/Ce)N (sample 98-65, with (Sr/Ce)N = 13.5) from [START_REF] Gaffney | Environments of crystallization and compositional diversity of Mauna Loa xenoliths[END_REF], with 10% increments marked; a second mixing model (line with filled triangles) is shown between the average Pu'u Wahi melt inclusion composition (Table S10) and the Gabal Gerf gabbro with the highest (Sr/Ce)N (sample GG36, with (Sr/Ce)N = 148) from [START_REF] Zimmer | The Gabal Gerf complex: a Precambrian N-MORB ophiolite in the Nubian shield, NE Africa[END_REF]. (b) The same plot as in (a) except expanded to highlight melt inclusions with (Sr/Ce)N < 2. (c) In Al2O3 (wt.%) versus MgO (wt.%) space; the mixing model uses the same mixing endmembers as panels (a) and (b). We use the comprehensive Hawaiian dataset (which includes both whole rock and glass analyses) from [START_REF] Frey | The geochemical components that distinguish Loa-and Kea-trend Hawaiian shield lavas[END_REF] for comparison because it provides a compilation of the highest-quality major and trace element data from Hawai'i. The [START_REF] Frey | The geochemical components that distinguish Loa-and Kea-trend Hawaiian shield lavas[END_REF] dataset has been filtered as described in Section S1.5 of the Supplementary Methods. Loa-trend volcanoes (Loihi, Mauna Loa, Koolau, Lanai, and Kahoolawe) and Keatrend volcanoes (Mauna Kea and Kilauea) from the Frey et al. dataset are shown here. The tephra/pillow glass for each sample hosting melt inclusions is also shown for reference. The Pu'u Wahi tephra glass major and trace element concentrations are from [START_REF] Sobolev | A young source for the Hawaiian plume[END_REF]. Low (Sr/Ce)N Mauna Loa melt inclusions from [START_REF] Sobolev | Recycled oceanic crust observed in 'ghost plagioclase' within the source of Mauna Loa lavas[END_REF][START_REF] Sobolev | A young source for the Hawaiian plume[END_REF] include inclusions with (Sr/Ce)N < 2. Concentrations shown in the figure have been corrected for addition or subtraction of equilibrium olivine so that the melt inclusions are in equilibrium with the host olivine. Only data for glassy melt inclusions are shown. The two ultra-depleted melt (UDM) inclusions from [START_REF] Sobolev | A young source for the Hawaiian plume[END_REF] are identified. An outlier with low Al2O3 content, which is an ultra-calcic melt inclusion (UCMI) from Pu'u Wahi, is noticeable in all three panels. melt inclusions with lower (Sr/Ce)N.

In a plot of (Sr/Ce)N versus (La/Sm)N (Figure 4), the high (Sr/Ce)N inclusions, all of which are from Mauna Loa, tend to have lower (La/Sm)N ratios than normal-type melt inclusions and Hawaiian lavas, which is consistent with prior observations at Hawai'i [START_REF] Sobolev | Recycled oceanic crust observed in 'ghost plagioclase' within the source of Mauna Loa lavas[END_REF] and Galapagos [START_REF] Peterson | Origin of the 'ghost plagioclase' signature in Galapagos melt inclusions: new evidence from Pb isotopes[END_REF]. Excluding the ultra-depleted melt (UDM) inclusions from [START_REF] Sobolev | A young source for the Hawaiian plume[END_REF], the melt inclusion with the highest (Sr/Ce)N has the lowest (La/Sm)N observed in Hawaiian melts. Like other high (Sr/Ce)N inclusions from Hawai'i, the high (Sr/Ce)N inclusion is depleted in light rare earth elements (REEs) relative to middle REEs, an observation that has been made before at Hawai'i (e.g., [START_REF] Sobolev | Recycled oceanic crust observed in 'ghost plagioclase' within the source of Mauna Loa lavas[END_REF] and Galapagos [START_REF] Peterson | Origin of the 'ghost plagioclase' signature in Galapagos melt inclusions: new evidence from Pb isotopes[END_REF]. Notably, all Hawaiian melt inclusions with high (Sr/Ce)N in this study are hosted in Mauna Loa lavas; none of the Loihi or Koolau samples have large positive (Sr/Ce)N, but we note that fewer Loihi and Koolau melt inclusions have been characterized.

Mauna Loa melt inclusions reported here have some variability in trace element ratios. Primitive mantle [START_REF] Mcdonough | The composition of the Earth[END_REF] normalized trace element patterns (spidergrams) of all glassy melt inclusions reported in this study are shown together with spidergrams of the host glass or tephra (Figure 5a-d). The highest (Sr/Ce)N inclusion exhibits the most significant deviation in pattern shape (with overall depletion in incompatible trace element abundances compared to the other Mauna Loa inclusions). For comparison, the Mauna Loa gabbro with the highest (Sr/Ce)N (sample 98-65; [START_REF] Gaffney | Environments of crystallization and compositional diversity of Mauna Loa xenoliths[END_REF] is plotted against Mauna Loa sample ML-2012-27 (Figure 5). The highest (Sr/Ce)N inclusion has a similar spidergram to high (Sr/Ce)N inclusions from [START_REF] Sobolev | Recycled oceanic crust observed in 'ghost plagioclase' within the source of Mauna Loa lavas[END_REF][START_REF] Sobolev | A young source for the Hawaiian plume[END_REF], but different compared to the average normal Pu'u Wahi melt inclusion (Figure S5). Pu'u Wahi melt inclusions from Mauna Loa reported in [START_REF] Reinhard | Sr and Nd isotopic compositions of individual olivine-hosted melt inclusions from Hawai'i and Samoa: Implications for the origin of isotopic heterogeneity in melt inclusions from OIB lavas[END_REF] are plotted alongside this study's Pu'u Wahi inclusions, and they exhibit less variability in spidergram patterns than the Mauna Loa ML-2012-27 inclusions. Similarly, the spidergrams for the Loihi and Koolau inclusions show relatively little variability and are similar to the host glass.

Figure 5 also shows that the Mauna Loa gabbros from [START_REF] Gaffney | Environments of crystallization and compositional diversity of Mauna Loa xenoliths[END_REF] contain positive Pb anomalies whereas the Mauna Loa melt inclusions have negative Pb anomalies. Sulfides are observed in Hawaiian lavas [START_REF] Stone | Nickel-copper sulfides from the 1959 eruption of Kilauea Volcano, Hawaii: Contrasting compositions and phase relations in eruption pumice and Kilauea Iki lava lake[END_REF]. If sulfides are responsible for the positive Pb anomalies in Mauna Loa gabbros (which are cumulates of Mauna Loa melts), this can be taken as evidence for sulfide fractionation from Hawaiian magmas at depth as being the mechanism generating the negative Pb anomalies in high (Sr/Ce)N inclusions.

The 87 Sr/ 86 Sr of melt inclusions from the five lavas examined here (Table 1) are similar to, or slightly larger, than the range observed for their respective host volcano. The 87 Sr/ 86 Sr range for all of the Mauna Loa inclusions reported here is relatively small, ranging from 0.703700 to 0.703986 ( 87 Sr/ 86 Sr range of 406 ppm, Figure 5). The inclusions fall within the range reported for Mauna Loa lavas (0.703599-0.703967; [START_REF] Hauri | Osmium isotope systematics of drilled lavas from Mauna Loa, Hawaii[END_REF][START_REF] Kurz | Isotopic evolution of Mauna Loa Volcano: A view from the submarine southwest rift zone[END_REF]. The highest (Sr/Ce)N melt inclusion (ML-2012-27_19b) has an 87 Sr/ 86 Sr of 0.703828 ± 0.000045, and this inclusion, which also has the lowest (La/Sm)N in this study, has indistinguishable 87 Sr/ 86 Sr from the other Mauna Loa melt inclusions from the same lava (including Mauna Loa melt inclusions with low (Sr/Ce)N (Figure 6)). The Loihi melt inclusions (from two different lavas) have 87 Sr/ 86 Sr ratios ranging from 0.70328 to 0.70367 ( 87 Sr/ 86 Sr range of 555 ppm), which extends the range of 87 Sr/ 86 Sr identified for Loihi lavas (0.70344 to 0.70378; [START_REF] Bennett | Two mantle-plume components in Hawaiian picrites inferred from correlated Os-Pb isotopes[END_REF][START_REF] Garcia | Geochemical and isotopic evolution of Loihi Volcano, Hawaii[END_REF] to slightly lower 87 Sr/ 86 Sr. The Koolau melt inclusions (all from a single lava sample) exhibit the largest range of 87 Sr/ 86 Sr among melt inclusions in this study (0.703654 ± 0.000079 to 0.704401 ± 0.000031, 1062 ppm total variability), which is encompassed by the range of 87 Sr/ 86 Sr in Koolau lavas (0.703487 to 0.70451; [START_REF] Roden | New He, Nd, Pb, and Sr isotopic constraints on the constitution of the Hawaiian plume: Results from Koolau Volcano, Oahu, Hawaii, USA[END_REF][START_REF] Tanaka | Geochemical evolution of Koolau volcano, Hawaii[END_REF]. While there is 87 Sr/ 86 Sr heterogeneity in the Loihi and Koolau inclusions examined here, the heterogeneity is not surprising given heterogeneity observed in olivine-hosted melt inclusions at other OIB localities [START_REF] Jackson | Strontium isotopes in melt inclusions from Samoan basalts: Implications for heterogeneity in the Samoan plume[END_REF][START_REF] Harlou | Combined Sr isotope and trace element analysis of melt inclusions at sub-ng levels using micro-milling, TIMS and ICPMS[END_REF][START_REF] Reinhard | Extreme differences in 87 Sr/ 86 Sr between magmatic olivines and Samoan host lavas: Evidence for highly heterogeneous 87 Sr/ 86 Sr in the magmatic plumbing system sourcing a single lava[END_REF][START_REF] Reinhard | Sr and Nd isotopic compositions of individual olivine-hosted melt inclusions from Hawai'i and Samoa: Implications for the origin of isotopic heterogeneity in melt inclusions from OIB lavas[END_REF]. What is surprising is the remarkable 87 Sr/ 86 Sr homogeneity across the different Mauna Loa melt inclusions examined here, in spite of extreme trace element variability (e.g., (Sr/Ce)N). Below we focus the discussion on this unusual 87 Sr/ 86 Sr homogeneity.

Loihi melt inclusions have higher Cl contents (319 to 606 ppm) than the melt inclusions from Mauna Loa (measured concentration of 10 to 183 ppm; see Table S1) or Koolau (20 to 45 ppm) (Figure 6e). Elevated Cl in Loihi melts was observed previously (Kent et al., 1999a(Kent et al., , 1999b[START_REF] Kent | Chlorine in submarine glasses from the Lau Basin: seawater contamination and constraints on the composition of slab-derived fluids[END_REF]. Similarly, the three Loihi inclusions have the largest range in Cl/Nb (14 to 30), consistent with the high Cl concentrations observed in Loihi glasses (Kent et al., 1999a(Kent et al., , 1999b[START_REF] Kent | Chlorine in submarine glasses from the Lau Basin: seawater contamination and constraints on the composition of slab-derived fluids[END_REF]. In comparison, Cl/Nb ratios tend to lower values in Koolau melt inclusions (5 to 7) and Mauna Loa inclusions (4 to 14, excluding a single melt inclusion, sample Puu7-2-7a, with Cl/Nb = 21). Critically, 87 Sr/ 86 Sr does not covary with Cl/Nb in the melt inclusion suite examined here, suggesting seawater-derived materials are not responsible for generating the 87 Sr/ 86 Sr heterogeneity (see Sections 4.1 and 4.3 for discussion on the interpretation).

Melt inclusions from Pu'u Wahi were previously analyzed for 87 Sr/ 86 Sr by [START_REF] Sobolev | A young source for the Hawaiian plume[END_REF] and [START_REF] Reinhard | Sr and Nd isotopic compositions of individual olivine-hosted melt inclusions from Hawai'i and Samoa: Implications for the origin of isotopic heterogeneity in melt inclusions from OIB lavas[END_REF]. [START_REF] Sobolev | A young source for the Hawaiian plume[END_REF] analyzed a suite of 137 inclusions from Pu'u Wahi using a laser ablation (LA) single-collector ICP-MS technique and reported an extraordinary range in 87 Sr/ 86 Sr, from 0.7021 to 0.7081 (which is a range of ~8500 ppm, or approximately ±3000 ppm 2σ relative standard deviation, or 2RSD; Figure 7). They showed that the two UDMs identified in Pu'u Wahi inclusions yield the most extreme high 87 Sr/ 86 Sr values (0.7081 ± 0.0004; two melt inclusions analyzed at least ten times each), and if these UDM inclusions are excluded, the 87 Sr/ 86 Sr in their dataset has an average of 0.7039 ± 0.0019 (2SD) (approximately ±2700 ppm 2RSD). In contrast, the 33 Pu'u Wahi melt inclusions analyzed for 87 Sr/ 86 Sr by TIMS in this study and the study of [START_REF] Reinhard | Sr and Nd isotopic compositions of individual olivine-hosted melt inclusions from Hawai'i and Samoa: Implications for the origin of isotopic heterogeneity in melt inclusions from OIB lavas[END_REF] show very little variability (i.e., 0.703700 to 0.703986, or approximately ±200 ppm 2RSD across both TIMS studies). Like [START_REF] Reinhard | Sr and Nd isotopic compositions of individual olivine-hosted melt inclusions from Hawai'i and Samoa: Implications for the origin of isotopic heterogeneity in melt inclusions from OIB lavas[END_REF], we did not identify UDM inclusions, which may partially explain the lack of extreme 87 Sr/ 86 Sr in our study (but see below). However, even if the two UDM inclusions are excluded from the [START_REF] Sobolev | A young source for the Hawaiian plume[END_REF] dataset, the 2RSD in 87 Sr/ 86 Sr of the remaining 135 inclusions (i.e., approximately ±2700 ppm) is still ~13 times greater than the combined 2RSD in 87 Sr/ 86 Sr identified in this study and the study of Reinhard et al. (2018) (i.e., approximately ±200 ppm).

In summary, the TIMS 87 Sr/ 86 Sr results for Pu'u Wahi inclusions from two different labs-Vrije University (N = 9 inclusions; [START_REF] Reinhard | Sr and Nd isotopic compositions of individual olivine-hosted melt inclusions from Hawai'i and Samoa: Implications for the origin of isotopic heterogeneity in melt inclusions from OIB lavas[END_REF] and UCSB (N = 24 inclusions; this study)-are in close agreement, but disagree substantially with the reported 87 Sr/ 86 Sr variability in Pu'u Wahi inclusions from [START_REF] Sobolev | A young source for the Hawaiian plume[END_REF] (Figure 7). One explanation is that there is an inherent difference in precision between the two techniques. Rubidium (as well as other isobaric interferences, e.g., 84 Kr, 86 Kr) limits the precision of 87 Sr/ 86 Sr analyses performed by LA-ICP-MS, whereas chemical separation of Sr provides a means to minimize Rb prior to analysis by TIMS, and TIMS does not suffer from the other isobaric interferences from the carrier gas. We suggest that the difference in Pu'u Wahi melt inclusion 87 Sr/ 86 Sr variability determined by LA single-collector ICP-MS [START_REF] Sobolev | A young source for the Hawaiian plume[END_REF] and TIMS (this study; [START_REF] Reinhard | Sr and Nd isotopic compositions of individual olivine-hosted melt inclusions from Hawai'i and Samoa: Implications for the origin of isotopic heterogeneity in melt inclusions from OIB lavas[END_REF] is the result of the former technique generating lower-precision analyses of a relatively-homogeneous melt inclusion population (i.e., a population with 87 Sr/ 86 Sr variability similar to that identified by TIMS). To test this hypothesis, we calculate the average 87 Sr/ 86 Sr and 2SD of the Pu'u Wahi melt inclusions analyzed by the LA-ICP-MS technique, and compare this [START_REF] Sobolev | A young source for the Hawaiian plume[END_REF] and TIMS [START_REF] Reinhard | Sr and Nd isotopic compositions of individual olivine-hosted melt inclusions from Hawai'i and Samoa: Implications for the origin of isotopic heterogeneity in melt inclusions from OIB lavas[END_REF] this study) are compared to the 87 Sr/ 86 Sr range of Mauna Loa lavas (orange bar = 0.703599-0.703967; [START_REF] Hauri | Osmium isotope systematics of drilled lavas from Mauna Loa, Hawaii[END_REF][START_REF] Kurz | Isotopic evolution of Mauna Loa Volcano: A view from the submarine southwest rift zone[END_REF] to the average 87 Sr/ 86 Sr and 2SD of the Pu'u Wahi melt inclusions analyzed by TIMS. The average of Sobolev et al.'s (2011) 87 Sr/ 86 Sr measurements is 0.7040 ±0.0021 (2SD, N = 137) (with the two UDM inclusions), or 0.7039 ±0.0019 (2SD, N = 135) (without the two UDM inclusions). These average 87 Sr/ 86 Sr values are indistinguishable from the average 87 Sr/ 86 Sr obtained on Pu'u Wahi melt inclusions at the Vrije University TIMS lab (0.703867 ±0.00013, 2SD, N = 9) and the average 87 Sr/ 86 Sr of melt inclusions from the UCSB TIMS lab reported here (0.703873 ±0.000152, 2SD, N = 24), which are also indistinguishable from the Pu'u Wahi tephra glass 87 Sr/ 86 Sr (0.703912±0.000008, 2SE) and the range in 87 Sr/ 86 Sr reported in Mauna Loa whole rocks (0.70360 to 0.703967; [START_REF] Hauri | Osmium isotope systematics of drilled lavas from Mauna Loa, Hawaii[END_REF][START_REF] Kurz | Isotopic evolution of Mauna Loa Volcano: A view from the submarine southwest rift zone[END_REF]. This result is consistent with the hypothesis that the disagreement between the TIMS 87 Sr/ 86 Sr analyses and the LA-ICP-MS 87 Sr/ 86 Sr analyses are a result of the significantly larger errors associated with the [START_REF] Sobolev | A young source for the Hawaiian plume[END_REF] 87 Sr/ 86 Sr measurements.

In order to further test the influence of measurement reproducibility on the total observed 87 Sr/ 86 Sr variability in the Pu'u Wahi melt inclusion suite, we performed a Monte Carlo simulation. This Monte Carlo simulation (Figure 8) evaluates the 87 Sr/ 86 Sr variability in Pu'u Wahi melt inclusions that would result if a relatively homogeneous population of Pu'u Wahi melt inclusions (like that found by the TIMS studies) is assigned the larger measurement uncertainties associated with the [START_REF] Sobolev | A young source for the Hawaiian plume[END_REF] single-collector ICP-MS method. In the simulation, we first calculate an uncertainty equal to the average 2SD of the 135 Pu'u Wahi melt inclusion measurements (i.e., including only the melt inclusions with at least one replicate analysis) reported by [START_REF] Sobolev | A young source for the Hawaiian plume[END_REF], which is ±2919 ppm. This is used to generate a Gaussian distribution, which has a 2RSD of ±2919 ppm, and from this distribution values are drawn randomly in each iteration of the model and then assigned as errors to each of the 33 Pu'u Wahi melt inclusions analyzed by TIMS in this study and [START_REF] Reinhard | Sr and Nd isotopic compositions of individual olivine-hosted melt inclusions from Hawai'i and Samoa: Implications for the origin of isotopic heterogeneity in melt inclusions from OIB lavas[END_REF]. The range of 87 Sr/ 86 Sr in the 33 melt inclusions in the model is then calculated, and this process was then repeated 10 6 times. This simulation yields a range in 87 Sr/ 86 Sr for each of a million different model melt inclusion populations, giving a 95% confidence interval of ~8200 ppm for the ranges in 87 Sr/ 86 Sr across all simulations. The 95% confidence interval in the range in 87 Sr/ 86 Sr for the simulation approaches the ~8500 ppm range in 87 Sr/ 86 Sr reported in the suite of 135 melt inclusions analyzed by [START_REF] Sobolev | A young source for the Hawaiian plume[END_REF], and the comparison is shown in Figure 8. In summary, if the larger measurement errors of [START_REF] Sobolev | A young source for the Hawaiian plume[END_REF] data are applied to a relatively homogeneous population of melt inclusions analyzed by TIMS, it is possible to generate apparent 87 Sr/ 86 Sr variability that is comparable to the reported 87 Sr/ 86 Sr variability in [START_REF] Sobolev | A young source for the Hawaiian plume[END_REF]. Thus, the large reported 87 Sr/ 86 Sr variability previously found in Pu'u Wahi melt inclusions appears to be the result of larger uncertainties associated with the 87 Sr/ 86 Sr analyses by ICP-MS.

We did not encounter any melt inclusions with the UDM trace element patterns identified by [START_REF] Sobolev | A young source for the Hawaiian plume[END_REF]. Therefore, we acknowledge that these UDM melt inclusions could have different 87 Sr/ 86 Sr compositions than the Pu'u Wahi inclusions that we examine here. However, we note that the high 87 Sr/ 86 Sr values (~0.708) reported in the UDM inclusions are generated in our Monte Carlo simulation, which can be seen in Figure 8 by the overlap of the model melt inclusions in red with the [START_REF] Sobolev | A young source for the Hawaiian plume[END_REF] melt inclusions in blue at ~0.708. Therefore, the 87 Sr/ 86 Sr data for Pu'u Wahi melt inclusions from [START_REF] Sobolev | A young source for the Hawaiian plume[END_REF] are not included in Figure 6 or in the interpretation of Mauna Loa 87 Sr/ 86 Sr data, but we do show the [START_REF] Sobolev | A young source for the Hawaiian plume[END_REF] melt inclusions 87 Sr/ 86 Sr data in comparison to the TIMS data in Figure 7. Below we address only the origin of the non-UDM inclusions with high (Sr/Ce)N identified by [START_REF] Sobolev | Recycled oceanic crust observed in 'ghost plagioclase' within the source of Mauna Loa lavas[END_REF][START_REF] Sobolev | A young source for the Hawaiian plume[END_REF], which were argued by [START_REF] Sobolev | Recycled oceanic crust observed in 'ghost plagioclase' within the source of Mauna Loa lavas[END_REF] to be sourced by ancient recycled gabbro.

Discussion

Processes that can influence melt inclusion compositions prior to, and following, entrapment.

When working with melt inclusions, it is necessary to consider how the melts may have been modified before and after entrapment. For example, following entrapment, melt inclusion compositions can be affected by diffusive exchange, through the host crystal, with the surrounding melt. Relative to Hawaiian lavas, and host glasses, the melt inclusions in this study tend to have lower FeOt (Figure S4), which is indicative of diffusive Fe-Mg exchange between the melt inclusion and the host melt. Fe-Mg diffusive exchange in melt inclusions is relatively common, and has been attributed to slower cooling, as a longer residence time is required for Fe to diffuse out of the host mineral (e.g., [START_REF] Danyushevsky | Re-equilibration of melt inclusions trapped by magnesian olivine phenocrysts from subduction-related magmas: petrological implications[END_REF][START_REF] Gaetani | Open system behavior of olivine-hosted melt inclusions[END_REF][START_REF] Sobolev | Petrology and geochemistry of boninites from the north termination of the Tonga Trench: constraints on the generation conditions of primary high-Ca boninite magmas[END_REF]. However, Fe-Mg exchange does not influence trace element ratios or the 87 Sr/ 86 Sr of the melt inclusion, therefore "Fe loss" does not affect the conclusions of this study and we do not attempt to correct for it.

Additionally, melt inclusions experience post-entrapment crystallization during cooling, and we correct for post-entrapment loss of olivine to the melt inclusion wall. All Hawaiian melt inclusion major and trace element data shown in the figures have been fractionation corrected to be in equilibrium with the forsterite (Fo) content of the host olivine by adding or subtracting equilibrium olivine at 0.1% increments. For the calculation, we assume (i) an olivine-melt Fe-Mg Kd of 0.30 [START_REF] Ford | Olivine-liquid equilibria: temperature, pressure and composition dependence of the crystal/liquid cation partition coefficients for Mg, Fe 2+ , Ca and Mn[END_REF]; Kd = (Fe 2+ /Mg)olivine / (Fe 2+ /Mg)melt) and (ii) 10% of the total iron in the melt is Fe 3+ (following [START_REF] Hauri | Major-element variability in the Hawaiian mantle plume[END_REF]. Major, volatile, and trace element concentrations corrected for olivine addition or subtraction are shown in Table S1, together with measured concentrations.

Prior to entrapment, melts can assimilate altered oceanic crust. Chlorine is an indicator for assimilation of seawater-derived materials, including altered oceanic crust. Thus, melts that have assimilated seawater-derived materials can have elevated Cl, Cl/K2O, and Cl/Nb ratios [START_REF] Jambon | Chlorine and bromine abundance in MORB: the contrasting behaviour of the Mid-Atlantic Ridge and East Pacific Rise and implications for chlorine geodynamic cycle[END_REF]Kendrick et al., 2013a[START_REF] Kendrick | The halogen (F, Cl, Br, I) and H2O systematics of Samoan lavas: Assimilated-seawater, EM2 and high-3 He/ 4 He components[END_REF]Kent et al., 1999aKent et al., , 1999b[START_REF] Kent | Chlorine in submarine glasses from the Lau Basin: seawater contamination and constraints on the composition of slab-derived fluids[END_REF][START_REF] Koleszar | The volatile contents of the Galapagos plume; evidence for H2O and F open system behavior in melt inclusions[END_REF][START_REF] Lassiter | Chlorine-potassium variations in melt inclusions from Raivavae and Rapa, Austral Islands: constraints on chlorine recycling in the mantle and evidence for brine-induced melting of oceanic crust[END_REF][START_REF] Michael | Influence of spreading rate and magma supply on crystallization and assimilation beneath mid-ocean ridges: Evidence from chlorine and major element chemistry of mid-ocean ridge basalts[END_REF]. Chlorine is fluid mobile (e.g., [START_REF] Debret | F, Cl and S input via serpentinite in subduction zones: Implications for the nature of the fluid released at depth[END_REF][START_REF] John | Dehydration of subducting serpentinite: Implications for halogen mobility in subduction zones and the deep halogen cycle[END_REF][START_REF] Kendrick | Subduction zone fluxes of halogens and noble gases in seafloor and forearc serpentinites[END_REF][START_REF] Rose-Koga | Mantle source heterogeneity for South Tyrrhenian magmas revealed by Pb isotopes and halogen contents of olivine-hosted melt inclusions[END_REF][START_REF] Straub | The systematics of chlorine, fluorine, and water in Izu arc front volcanic rocks: Implications for volatile recycling in subduction zones[END_REF], therefore recycled oceanic crust that has gone through a subduction filter is not predicted to retain high Cl/K2O and Cl/Nb ratios (e.g., Kendrick et al., 2013a[START_REF] Kendrick | The halogen (F, Cl, Br, I) and H2O systematics of Samoan lavas: Assimilated-seawater, EM2 and high-3 He/ 4 He components[END_REF][START_REF] Kendrick | Seawater cycled throughout Earth's mantle in partially serpentinized lithosphere[END_REF][START_REF] Rowe | Chlorine enrichment in central Rio Grande Rift basaltic melt inclusions: Evidence for subduction modification of the lithospheric mantle[END_REF]. Mantle-derived lavas have low Cl/Nb ratios relative to lavas influenced by assimilation of altered oceanic crust (e.g., 5-17; [START_REF] Michael | Influence of spreading rate and magma supply on crystallization and assimilation beneath mid-ocean ridges: Evidence from chlorine and major element chemistry of mid-ocean ridge basalts[END_REF][START_REF] Rowe | Chlorine enrichment in central Rio Grande Rift basaltic melt inclusions: Evidence for subduction modification of the lithospheric mantle[END_REF][START_REF] Rowe | Basalt volatile fluctuations during continental rifting: An example from the Rio Grande Rift, USA[END_REF][START_REF] Saal | Vapour undersaturation in primitive mid-ocean-ridge basalt and the volatile content of Earth's upper mantle[END_REF][START_REF] Stroncik | Chlorine in oceanic intraplate basalts: Constraints on mantle sources and recycling processes[END_REF]. The Hawaiian melt inclusions considered here generally have mantle-like Cl/Nb (ratios of 4 to 14, but inclusion Puu7-2-7a has a higher ratio, 21), except for Loihi glasses (ratios of 34 to 65) and their melt inclusions (ratios of 14 to 30), which confirms observations of elevated Cl and Cl/Nb in Loihi glasses and melt inclusions (Kent et al., 1999a(Kent et al., , 1999b)). Critically for this study, the highest (Sr/Ce)N melt inclusion has mantle-like Cl/Nb, so assimilation of shallow-level altered oceanic crust is unlikely to be involved in its origin. However, the low Cl/Nb ratio of the high (Sr/Ce)N inclusion does not exclude a contribution from the Cretaceous lower (gabbroic) oceanic crust beneath Hawai'i (which may have mantle-like Cl/Nb, see Section 4.2), which is discussed below. None of the high Cl/Nb inclusions (i.e., Loihi) have elevated (Sr/Ce)N.

Source of high (Sr/Ce)N "ghost plagioclase" in Mauna Loa melt inclusions: bulk assimilation of gabbro?

This study presents the highest magmatic (Sr/Ce)N ratio in Hawaiian melts measured to date, suggesting a role for a plagioclase-bearing lithology, such as cumulate gabbro, in the petrogenesis of this, and similar, high (Sr/Ce)N inclusions from Hawai'i. However, the mechanism for the incorporation of the high (Sr/Ce)N "ghost plagioclase" signature (i.e., elevated (Sr/Ce)N without concomitant enrichment in Al2O3) remains controversial [START_REF] Peterson | Origin of the 'ghost plagioclase' signature in Galapagos melt inclusions: new evidence from Pb isotopes[END_REF][START_REF] Saal | The role of lithospheric gabbros on the composition of Galapagos lavas[END_REF][START_REF] Sobolev | Recycled oceanic crust observed in 'ghost plagioclase' within the source of Mauna Loa lavas[END_REF][START_REF] Yaxley | High-pressure partial melting of gabbro and its role in the Hawaiian magma source[END_REF].

Gabbros from the deeper regions of Mauna Loa volcano may have mantle-like Cl/Nb, so assimilation of such gabbros may not be detected with Cl/Nb. In order to test for direct gabbro assimilation, we present a mixing model between the average "normal" Pu'u Wahi melt inclusion composition (an average composition of Pu'u Wahi melt inclusions lacking anomalous major and trace elements signatures, defined in Table S10) and the Mauna Loa gabbroic xenolith with the highest (Sr/Ce)N-to minimize the quantity of gabbro needed to generate the elevated (Sr/Ce)N in the melt inclusion-from Gaffney (2002; Figure 3). The highest (Sr/Ce)N melt inclusion (sample ML-2012-27_19b) is offset from the normal melt inclusion-Mauna Loa gabbro mixing line to lower Al2O3 at a given (Sr/Ce)N, and is therefore not well described by assimilation of this or any other available Mauna Loa gabbro composition. Additionally, the mixing line in Figure 3a informs the minimum amount of Mauna Loa gabbro assimilation (90%) required to generate the high (Sr/Ce)N in this melt inclusion, given available gabbro compositions at Mauna Loa. This high proportion of Mauna Loa gabbro is also inconsistent with the same mixing model in Al2O3 versus MgO space (Figure 3c): This is because 90% Mauna Loa gabbro assimilation by the inclusion would cause it to plot off (toward higher Al2O3) of the array formed by Hawaiian lavas in Al2O3 versus MgO space, but the high (Sr/Ce)N inclusion is not displaced from this array (Figure 3c).

Assimilation of gabbro from the Cretaceous oceanic crust that underlies Hawai'i was also tested using Gabal Gerf ophiolite gabbros [START_REF] Zimmer | The Gabal Gerf complex: a Precambrian N-MORB ophiolite in the Nubian shield, NE Africa[END_REF], which serve as a proxy for Cretaceous oceanic crust gabbro. However, there is no mixing model between normal-type Pu'u Wahi melts and Gabal Gerf gabbros that can account for the ghost plagioclase inclusion (one mixing line is shown, which trends to the highest (Sr/Ce)N Gabal Gerf composition, in Figure 3). The mixing lines generate Al2O3 that is too high for the high (Sr/Ce)N inclusion in (Sr/Ce)N versus Al2O3 and Al2O3 versus MgO space. Thus, we can exclude bulk assimilation of gabbro in the genesis of the high (Sr/Ce)N melt inclusion. This observation is central to the paradox of the "ghost plagioclase" signature, where trace element signatures (i.e, high (Sr/Ce)N) indicate gabbroic influence, whereas major elements (i.e., Al2O3) are inconsistent with direct assimilation of gabbro. While we can exclude direct assimilation of gabbro, these mixing models do not address the two remaining hypotheses for the origin of high (Sr/Ce)N signatures at hotspotsancient recycled gabbro or diffusive interaction between Hawaiian melts and Mauna Loa gabbros-which we test with Sr isotopes below.

Source of high (Sr/Ce)N "ghost plagioclase" in Mauna Loa melt inclusions: diffusive exchange between upwelling melts and shallow gabbro?

Examining lavas and melt inclusions from the Galapagos that exhibit the trace element signature commonly associated with plagioclase, [START_REF] Saal | The role of lithospheric gabbros on the composition of Galapagos lavas[END_REF] and [START_REF] Peterson | Origin of the 'ghost plagioclase' signature in Galapagos melt inclusions: new evidence from Pb isotopes[END_REF] argue against the presence of ancient recycled oceanic gabbro in the mantle source. Instead, they proposed that diffusive exchange between mantle-derived melts and gabbros in the deep volcanic sections of Galapagos volcanoes generate the measured, plagioclase-related (i.e., high (Sr/Ce)N) trace element signatures. In addition to melts with plagioclase-influenced compositions, Galapagos olivine-hosted melt inclusions from Fernandina exhibit the ghost plagioclase signature. [START_REF] Peterson | Origin of the 'ghost plagioclase' signature in Galapagos melt inclusions: new evidence from Pb isotopes[END_REF] examined the range of trace element and Pb isotopic compositions that could be generated from both melting an ancient recycled oceanic gabbro in the deep mantle and from diffusive interaction in the shallow crust. [START_REF] Peterson | Origin of the 'ghost plagioclase' signature in Galapagos melt inclusions: new evidence from Pb isotopes[END_REF] demonstrated that the recycled oceanic gabbro model cannot reproduce the trace element signature and the Pb isotope compositions of the ghost plagioclase inclusions simultaneously. However, the diffusive exchange model generates both the trace element and Pb isotope compositions of the high (Sr/Ce)N inclusions with the ghost plagioclase signature.

Therefore, instead of reflecting a source signature related to recycled gabbro heterogeneities embedded in the plume, as advocated by [START_REF] Sobolev | Recycled oceanic crust observed in 'ghost plagioclase' within the source of Mauna Loa lavas[END_REF] for Hawai'i, the model for the generation of ghost plagioclase signatures proposed by [START_REF] Saal | The role of lithospheric gabbros on the composition of Galapagos lavas[END_REF] and [START_REF] Peterson | Origin of the 'ghost plagioclase' signature in Galapagos melt inclusions: new evidence from Pb isotopes[END_REF] suggests that it is a shallow process, where diffusive interaction between plagioclase in lithospheric gabbros and upwelling hotspot melts results in the hotspot melts inheriting high (Sr/Ce)N signatures. In this diffusive exchange model, Sr diffuses through the crustal plagioclase toward the upwelling plume melt because it has a higher diffusivity in plagioclase relative to other trace elements, such as La and Nd. In this way, a large positive Sr anomaly can be inherited by the upwelling plume melt due to diffusive interaction with the plagioclase, thereby generating the ghost plagioclase composition.

We apply the Peterson et al. ( 2014) "diffusive exchange" approach used in the Galapagos to evaluate whether melt-gabbro diffusive interaction can generate the elevated (Sr/Ce)N signatures in Mauna Loa inclusions. The model parameters follow [START_REF] Peterson | Origin of the 'ghost plagioclase' signature in Galapagos melt inclusions: new evidence from Pb isotopes[END_REF], except that a Mauna Loa lava (sample J2-15-13, with a relatively high Sr content of 689 ppm; [START_REF] Wanless | Shield-stage alkalic volcanism on Mauna Loa volcano, Hawaii[END_REF] is used instead of the high-Sr concentration Galapagos melt used in [START_REF] Peterson | Origin of the 'ghost plagioclase' signature in Galapagos melt inclusions: new evidence from Pb isotopes[END_REF], and we track the influence of the diffusive exchange model on 87 Sr/ 86 Sr instead of Pb isotopes. (An incompatible element rich melt, like J2-15-13 used here, may have been more common during the pre-shield alkali volcanism at Mauna Loa.) A plagioclase trace element composition is calculated that is in equilibrium with Mauna Loa lava J2-15-13 using a plagioclase An80 composition at 1200 °C and plagioclase-melt partition coefficients from [START_REF] Bédard | Trace element partitioning in plagioclase feldspar[END_REF]. Hawaiian melt inclusions with ghost plagioclase signatures (similar to Galapagos melt inclusions with ghost plagioclase signatures) are depleted in incompatible trace elements, except those associated with plagioclase, which is reflected in the low (La/Sm)N of the ghost plagioclase inclusions. Because of this depleted nature, we use a 12% aggregated fractional melt of [START_REF] Workman | Major and trace element composition of the depleted MORB mantle (DMM)[END_REF] depleted MORB mantle (DMM) as the percolating melt that diffusively exchanges with the plagioclase-rich lithology. The average of East Pacific Rise ridge segments from [START_REF] Gale | The mean composition of ocean ridge basalts[END_REF] is used for the initial 87 Sr/ 86 Sr composition of the percolating melt. This percolating melt undergoes diffusive exchange with a troctolite (for simplicity) hosting 50% modal plagioclase with the modeled trace element composition, where diffusive exchange uses published trace element diffusivities [START_REF] Cherniak | Diffusion of lead in plagioclase and K-feldspar: an investigation using Rutherford backscattering and resonant nuclear reaction analysis[END_REF][START_REF] Cherniak | Ba diffusion in feldspar[END_REF][START_REF] Cherniak | REE diffusion in feldspar[END_REF][START_REF] Cherniak | A study of strontium diffusion in plagioclase using Rutherford backscattering spectroscopy[END_REF][START_REF] Giletti | Strontium diffusion kinetics in plagioclase feldspars[END_REF][START_REF] Giletti | Alkali diffusion in plagioclase feldspar[END_REF] at 1200°C (see Table 2 for diffusivities used). Hawaiian lava temperatures approach 1200°C [START_REF] Gansecki | The tangled tale of Kīlauea's 2018 eruption as told by geochemical monitoring[END_REF], making this an appropriate temperature for model calculation. The duration of diffusive interaction varies from 1 year to 400 years in our model, as plagioclase trace element signatures are inherited by the percolating melt as a function of time (Table 2). Because Sr has a higher diffusivity than Ce and Al in plagioclase, the percolating DMM melt can inherit high (Sr/Ce)N, but not elevated Al2O3, thereby providing an explanation for the ghost plagioclase signature without invoking direct gabbro assimilation [START_REF] Danyushevsky | Crustal origin for coupled 'ultra-depleted' and 'plagioclase' signatures in MORB olivine-hosted melt inclusions: evidence from the Siqueiros Transform Fault, East Pacific Rise[END_REF] or ancient recycled gabbro [START_REF] Sobolev | Recycled oceanic crust observed in 'ghost plagioclase' within the source of Mauna Loa lavas[END_REF]. Depletion in light REEs relative to middle REEs is an outcome of the diffusive exchange model, where lower (La/Sm)N are generated as higher (Sr/Ce)N are produced (Figure 4). Finally, we mix the diffusively modified melts with the host glass associated with the highest (Sr/Ce)N inclusion, sample ML-2012-27 (though mixing with average Pu'u Wahi normal-type melt inclusions would not change the result), and then compare the mixtures to measured Hawaiian manuscript submitted to Geochemistry, Geophysics, Geosystems 20 melt inclusion compositions. Following 1 to 5 years of diffusive exchange (i.e., timescales that are well within crystal residence times in Hawaiian magmas; e.g., [START_REF] Cooper | Crystal and magma residence at Kilauea Volcano, Hawaii: 230Th-226Ra dating of the 1955 east rift eruption[END_REF][START_REF] Vinet | Magma solidification processes beneath Kilauea volcano, Hawaii: A quantitative textural and geochemical study of the 1969-1974 Mauna Ulu Lavas[END_REF][START_REF] Wieser | Crystal scavenging from mush piles recorded by melt inclusions[END_REF], the (La/Sm)N, (Sr/Ce)N, and 87 Sr/ 86 Sr composition of the highest Mauna Loa (Sr/Ce)N inclusion is matched in the diffusive exchange model.

This model requires the presence of Mauna Loa gabbros deep in the volcanic pile of the volcano. [START_REF] Gaffney | Environments of crystallization and compositional diversity of Mauna Loa xenoliths[END_REF] examined a suite of Mauna Loa gabbros (crystallized from Mauna Loa magmas), which provide evidence of cumulus plagioclase in the deep stratigraphy of the volcano. Although gabbroic xenoliths from Mauna Loa are uncommon, the lava pile is many kilometers thick, and only a fraction of the lava pile has been sampled directly. Therefore, gabbro could be more abundant in the deep shield than is suggested by the low abundance of gabbroic xenoliths that have been transported to the surface.

The diffusive exchange model for the high (Sr/Ce)N melt inclusions relies on the fact that the percolating melt is depleted, and this may seem unexpected for a hotspot volcano far from a MOR. Nonetheless, depleted components have been suggested to exist in the Hawaiian plume (e.g., [START_REF] Garcia | Petrology, geochemistry and geochronology of Kaua'i lavas over 4.5 Myr: Implications for the origin of rejuvenated volcanism and the evolution of the Hawaiian plume[END_REF][START_REF] Harrison | The multiple depleted mantle components in the Hawaiian-Emperor chain[END_REF]. [START_REF] Garcia | Petrology, geochemistry and geochronology of Kaua'i lavas over 4.5 Myr: Implications for the origin of rejuvenated volcanism and the evolution of the Hawaiian plume[END_REF] hypothesize that an ancient depleted upper mantle component exists in the Hawaiian plume, that could potentially supply the depleted percolating melt that interacts with the Mauna Loa gabbro in our model. Additionally, [START_REF] Mukhopadhyay | Geochemistry of Kauai shield-stage lavas: Implications for the chemical evolution of the Hawaiian plume[END_REF] state that they "favor an asthenospheric origin for the DM component" in Hawai'i, and that "the DM component is most apparent in lavas from the Kauai shield and is present in varying proportion in other Hawaiian shield volcanoes," including Mauna Loa (which has ~20% of the DM component in Figure 14 of [START_REF] Mukhopadhyay | Geochemistry of Kauai shield-stage lavas: Implications for the chemical evolution of the Hawaiian plume[END_REF]. As such, evidence exists that supports the existence of a depleted component in the Hawaiian plume that sources shield stage lavas, consistent with our model. While the precise origin of the depleted component is unknown, we use the composition of the [START_REF] Workman | Major and trace element composition of the depleted MORB mantle (DMM)[END_REF] depleted mantle component to approximate its trace element composition.

The results of the melt-plagioclase diffusive exchange model are compared with the Hawaiian melt inclusion data in Figures 4 and6, and the model encompasses both the 87 Sr/ 86 Sr composition and the unusual trace element composition-high (Sr/Ce)N and low (La/Sm)N-of the Mauna Loa ghost plagioclase inclusion examined here. While diffusive exchange with a Mauna Loa cumulate gabbro is consistent with the high (Sr/Ce)N inclusion data presented here, the Mauna Loa-like 87 Sr/ 86 Sr in the high (Sr/Ce)N inclusion is inconsistent with diffusive exchange between upwelling melts and MOR-basement gabbro. Diffusive exchange between melts and MOR-basement gabbro in the Pacific lithosphere would predict low, MORB-like 87 Sr/ 86 Sr in the melt inclusion. This is because the model predicts that the percolating melt will rapidly (>5 years; Figure 6) become dominated by the 87 Sr/ 86 Sr of the gabbro, and the average xenoliths from Hualalai sampling MOR-basement gabbros indicate that the Cretaceous oceanic crustal gabbros beneath Hawai'i have 87 Sr/ 86 Sr (0.702733 ± 0.000392 (2SD); [START_REF] Gao | Geochemical investigation of Gabbroic Xenoliths from Hualalai Volcano: Implications for lower oceanic crust accretion and Hualalai Volcano magma storage system[END_REF] that is indistinguishable from East Pacific Rise MORB (0.70257 ± 0.00024; [START_REF] Gale | The mean composition of ocean ridge basalts[END_REF] due to relatively little modification by seawater. Furthermore, the low Cl/K (<0.01) in the highest (Sr/Ce)N inclusion rules out interaction with seawater-altered MOR gabbro with higher (secondary) 87 Sr/ 86 Sr, because such a model would predict a high Cl/K ratio in the melt inclusion. Incidentally, [START_REF] Peterson | Origin of the 'ghost plagioclase' signature in Galapagos melt inclusions: new evidence from Pb isotopes[END_REF] exclude diffusive melt exchange with MORBrelated gabbros in the Galapagos because this would generate a negative Sr anomaly, due to lower Sr concentrations in oceanic gabbros than melts from oceanic hotspot volcanoes, a result that is directly applicable to the Hawaiian case examined here. Thus, we can rule out Cretaceous oceanic crustal gabbro as the origin of the ghost plagioclase signature.

An important remaining question is to explore whether the 87 Sr/ 86 Sr we measured in the Mauna Loa inclusion with the ghost plagioclase signature is consistent with the recycled gabbro model proposed by [START_REF] Sobolev | Recycled oceanic crust observed in 'ghost plagioclase' within the source of Mauna Loa lavas[END_REF]. We explore this question below.

Using Sr isotopes to test models for the origin of the ghost plagioclase signature in Mauna Loa inclusions.

The primary result of this study is that the Mauna Loa melt inclusion with high (Sr/Ce)N is indistinguishable in 87 Sr/ 86 Sr from other melt inclusions from the same lava (sample ML-2012-27; Figure 6). This melt inclusion also has 87 Sr/ 86 Sr that falls within the range of 87 Sr/ 86 Sr identified in Mauna Loa lavas. We explore the implications of this observation below.

While a recycled gabbro signature may be present in the mantle for most Loa-trend volcanoes, including Mauna Loa [START_REF] Frey | The geochemical components that distinguish Loa-and Kea-trend Hawaiian shield lavas[END_REF], recycled gabbro is unlikely to have contributed the high (Sr/Ce)N signature to the high (Sr/Ce)N Mauna Loa inclusion examined here. If high (Sr/Ce)N is a measure of magnitude of the contribution of the recycled gabbro component, as proposed by [START_REF] Sobolev | Recycled oceanic crust observed in 'ghost plagioclase' within the source of Mauna Loa lavas[END_REF], this raises the question as to why the highest (Sr/Ce)N melt inclusion has the same 87 Sr/ 86 Sr as the Mauna Loa melt inclusions and lavas with normal (Sr/Ce)N. In their model, the recycled gabbro contributes approximately 73 to 79% of the total Sr budget in ghost plagioclase melts, which is much larger than gabbro contributions suggested for Hawaiian lavas. Therefore, if an excess contribution from recycled gabbro were responsible for the high (Sr/Ce)N signature in the unusual, high (Sr/Ce)N Mauna Loa melt inclusion examined here, then the high (Sr/Ce)N melt inclusions should have 87 Sr/ 86 Sr that is shifted closer to the manuscript submitted to Geochemistry, Geophysics, Geosystems 22 87 Sr/ 86 Sr of the recycled gabbro compositions than the Mauna Loa melt inclusions with normal (Sr/Ce)N. This is not observed: The high (Sr/Ce)N melt inclusion and inclusions with normal (Sr/Ce)N have indistinguishable 87 Sr/ 86 Sr. If one appeals to coincidence, and assumes that the recycled gabbro has evolved to have exactly the same 87 Sr/ 86 Sr composition as the other component(s) sampled by the Mauna Loa inclusions with normal (Sr/Ce)N, then one can explain why high (Sr/Ce)N and normal (Sr/Ce)N inclusions from Mauna Loa have the same 87 Sr/ 86 Sr. However, we do not accept such a coincidence as plausible, for two reasons. First, possible compositions of the ancient recycled gabbro protolith are highly variable-including, but not limited to, gabbro from recycled seamounts, large igneous provinces, or oceanic lithosphere (depleted-MORB, normal-MORB, or enriched-MORB)-and thus will run the gamut of Srisotopic compositions, making it unlikely that ancient recycled gabbro would coincidently evolve to have 87 Sr/ 86 Sr like Mauna Loa lavas that lack the ghost plagioclase inclusions. Second, variable dehydration and melting processes operating on heterogeneous protoliths at different times in distinct subduction zones, followed by varying periods of storage in the mantle and admixture with diverse reservoirs, are unlikely to generate different components-a high (Sr/Ce)N recycled gabbro component and low (Sr/Ce)N components-in the plume with indistinguishable 87 Sr/ 86 Sr. In short, an ancient recycled gabbro component is unlikely to be responsible for the high (Sr/Ce)N "ghost plagioclase" melt inclusions.

A more straightforward explanation for the identical 87 Sr/ 86 Sr in the high (Sr/Ce)N melt inclusions and "normal" (Sr/Ce)N inclusions in Mauna Loa is that the former inherited the high (Sr/Ce)N signature by interacting with Mauna Loa gabbros. Gabbros related to construction of the hotspot volcano will have 87 Sr/ 86 Sr ratios that are similar to Mauna Loa lavas, normal-type inclusions, and the ghost plagioclase inclusion in this study. The diffusive exchange model generates the high (Sr/Ce)N in ghost plagioclase melt inclusions-indicative of plagioclase-melt interaction-and is also consistent with the relationships between (Sr/Ce)N and 87 Sr/ 86 Sr (Figures 4 and6). This result, which employs Sr isotopic constraints on the origin of ghost plagioclase melt inclusions, mirrors the findings of [START_REF] Peterson | Origin of the 'ghost plagioclase' signature in Galapagos melt inclusions: new evidence from Pb isotopes[END_REF], who also showed that the Pb isotopic compositions in Galapagos ghost plagioclase melt inclusions are inconsistent with an ancient recycled oceanic gabbro origin.

Conclusion

This study uses Sr isotopic measurements in individual melt inclusions to evaluate the origin of the ghost plagioclase signature-elevated (Sr/Ce)N, but similar Al2O3, as melt inclusions with (Sr/Ce)N<2-in Mauna Loa melt inclusions. The 87 Sr/ 86 Sr of the highest (Sr/Ce)N melt inclusion ((Sr/Ce)N =7.2) matches the 87 Sr/ 86 Sr in lower (Sr/Ce)N melt inclusions ((Sr/Ce)N < 2) from the same lava, and is also indistinguishable from 87 Sr/ 86 Sr in Mauna Loa lavas. Because the highest (Sr/Ce)N melt inclusion is isotopically indistinguishable from Mauna Loa melts with small Sr anomalies, the source of the high (Sr/Ce)N melt inclusions should have the same 87 Sr/ 86 Sr as the component that generates other Mauna Loa lavas with smaller (Sr/Ce)N ratios. According to [START_REF] Sobolev | Recycled oceanic crust observed in 'ghost plagioclase' within the source of Mauna Loa lavas[END_REF], the 87 Sr/ 86 Sr of the recycled gabbro will dominate the 87 Sr/ 86 Sr signature in ghost plagioclase melt inclusions because the recycled gabbro contributes to the majority of the total Sr budget in ghost plagioclase melts. While we cannot rule out recycled gabbro as the source of the ghost plagioclase signature, it would be a great coincidence that any recycled gabbro component in the Hawaiian mantle plume melting beneath Mauna Loa would have the same 87 Sr/ 86 Sr as the source of other Mauna Loa lavas that lack a recycled gabbro signature. Therefore, the observation that the 87 Sr/ 86 Sr of the highest (Sr/Ce)N inclusion matches Mauna Loa lavas supports a petrogenetic origin for the ghost plagioclase melt inclusions that relates to the Mauna Loa magma plumbing system. We find that the origin of the ghost plagioclase signature within melt inclusions can be explained by diffusive interaction between rising melt and plagioclase-rich lithologies in the deep magma cumulates of Hawaiian volcanoes. Thus, the ghost plagioclase signature may not be a signature directly derived from the mantle source, but instead is likely a result of recent crustal processes operating in the deep regions of Hawaiian volcanoes.

158° W 157° W 156° W 155° W 154° W 19° N 20° N 21° N 22° N Loihi 6K490-1 & 6K490-2
Hawaiian Islands [START_REF] Sobolev | Recycled oceanic crust observed in 'ghost plagioclase' within the source of Mauna Loa lavas[END_REF][START_REF] Sobolev | A young source for the Hawaiian plume[END_REF] Low (Sr/Ce) N Mauna Loa melt inclusions [START_REF] Sobolev | Recycled oceanic crust observed in 'ghost plagioclase' within the source of Mauna Loa lavas[END_REF][START_REF] Sobolev | A young source for the Hawaiian plume[END_REF] Mauna Loa gabbros [START_REF] Gaffney | Environments of crystallization and compositional diversity of Mauna Loa xenoliths[END_REF] Gabal Gerf gabbros [START_REF] Zimmer | The Gabal Gerf complex: a Precambrian N-MORB ophiolite in the Nubian shield, NE Africa[END_REF] Previously published data Ultra-depleted melt (UDM) inclusions [START_REF] Sobolev | A young source for the Hawaiian plume[END_REF] Pu'u Wahi melt inclusions [START_REF] Reinhard | Sr and Nd isotopic compositions of individual olivine-hosted melt inclusions from Hawai'i and Samoa: Implications for the origin of isotopic heterogeneity in melt inclusions from OIB lavas[END_REF] High (Sr/Ce) N melt inclusions [START_REF] Sobolev | Recycled oceanic crust observed in 'ghost plagioclase' within the source of Mauna Loa lavas[END_REF][START_REF] Sobolev | A young source for the Hawaiian plume[END_REF] Low (Sr/Ce) N Mauna Loa melt inclusions [START_REF] Sobolev | Recycled oceanic crust observed in 'ghost plagioclase' within the source of Mauna Loa lavas[END_REF][START_REF] Sobolev | A young source for the Hawaiian plume[END_REF] Mauna Loa gabbros [START_REF] Gaffney | Environments of crystallization and compositional diversity of Mauna Loa xenoliths[END_REF] Gabal Gerf gabbros [START_REF] Zimmer | The Gabal Gerf complex: a Precambrian N-MORB ophiolite in the Nubian shield, NE Africa[END_REF] Previously published data Ultra-depleted melt (UDM) inclusions [START_REF] Sobolev | A young source for the Hawaiian plume[END_REF] Pu'u Wahi melt inclusions [START_REF] Reinhard | Sr and Nd isotopic compositions of individual olivine-hosted melt inclusions from Hawai'i and Samoa: Implications for the origin of isotopic heterogeneity in melt inclusions from OIB lavas[END_REF] For the diffusion model we assume that the plagioclase grain size is 0.001 m, there is 1% melt, and 50% of the solid is plagioclase.

a [START_REF] Bédard | Trace element partitioning in plagioclase feldspar[END_REF] for plagioclase of An 80 at 1200°C b Diffusion coefficients for plagioclase at 1200°C from [START_REF] Cherniak | A study of strontium diffusion in plagioclase using Rutherford backscattering spectroscopy[END_REF], [START_REF] Giletti | Strontium diffusion kinetics in plagioclase feldspars[END_REF], [START_REF] Cherniak | Diffusion of lead in plagioclase and K-feldspar: an investigation using Rutherford backscattering and resonant nuclear reaction analysis[END_REF][START_REF] Cherniak | Ba diffusion in feldspar[END_REF][START_REF] Cherniak | REE diffusion in feldspar[END_REF] and [START_REF] Giletti | Alkali diffusion in plagioclase feldspar[END_REF]. However, some trace elements do not have experimentally determined diffusion coefficients. For trace elements without this data, [START_REF] Peterson | Origin of the 'ghost plagioclase' signature in Galapagos melt inclusions: new evidence from Pb isotopes[END_REF] estimated based on cation size and charge [START_REF] Behrens | On the mechanisms of cation diffusion processes in ternary feldspars[END_REF][START_REF] Saal | The 226 Ra enrichment in oceanic basalts: Evidence for melt-cumulate diffusive interaction processes within the oceanic lithosphere[END_REF]. [START_REF] Peterson | Origin of the 'ghost plagioclase' signature in Galapagos melt inclusions: new evidence from Pb isotopes[END_REF] assumed that the diffusion coefficients for Nb, Zr, and Ti are similar to those of Th and U. Like [START_REF] Peterson | Origin of the 'ghost plagioclase' signature in Galapagos melt inclusions: new evidence from Pb isotopes[END_REF], we assumed that Eu is 50% Eu 2+ , and that the diffusion coefficient for Eu 2+ is similar to that of Sr. c While [START_REF] Peterson | Origin of the 'ghost plagioclase' signature in Galapagos melt inclusions: new evidence from Pb isotopes[END_REF] used a Galapagos lava to calculate an equilibrium plagioclase composition, we use a Mauna Loa lava (Mauna Loa sample J2-15-13; [START_REF] Wanless | Shield-stage alkalic volcanism on Mauna Loa volcano, Hawaii[END_REF]. The plagioclase composition in equilibrium with this melt is calculated using the partition coefficients in the table. d Like [START_REF] Peterson | Origin of the 'ghost plagioclase' signature in Galapagos melt inclusions: new evidence from Pb isotopes[END_REF], the initial melt is a 12% aggregated fractional melt of DMM composition from [START_REF] Workman | Major and trace element composition of the depleted MORB mantle (DMM)[END_REF], and the isotopic value is the average of the East Pacific Rise Ridge segment averages from [START_REF] Gale | The mean composition of ocean ridge basalts[END_REF].

Figure 2 .

 2 Figure 2. Method for isolating individual olivine-hosted melt inclusions. (a) Olivines often have multiple meltinclusions and all except for the target melt inclusion must be removed prior to sample leaching and dissolution. First, the target inclusion is exposed, the host olivine is mounted in epoxy, and the melt inclusion is analyzed for major, trace, and volatile elements using in situ techniques. (b) After in situ analysis, accessory melt inclusions are removed by mounting the olivine grain onto a glass slide using Crystalbond™. (c) The olivine is then ground on silicon carbide grinding mats until the accessory melt inclusions on one side of the olivine grain are removed. (d) The olivine grain is reoriented to optimally remove remaining accessory melt inclusions, and this process is repeated until only the target melt inclusion is left within a case of its olivine host (e). The "cubed" melt inclusion is then leached and cleaned in ultra-pure acid before dissolution and column chemistry.

Figure 3 .

 3 Figure 3. High (Sr/Ce)N Hawaiian melt inclusions and host pillow/tephra glasses compared to Hawaiian lavas, and to Mauna Loa and Gabal Gerf gabbros. (a) In (Sr/Ce)N versus Al2O3 (wt.%) space, the melt inclusion data do not show a positive correlation. A mixing model (line with filled diamonds) is shown between the average Pu'u Wahi melt inclusion composition from this study (TableS10) and the Mauna Loa gabbro with the highest (Sr/Ce)N (sample 98-65, with (Sr/Ce)N = 13.5) from[START_REF] Gaffney | Environments of crystallization and compositional diversity of Mauna Loa xenoliths[END_REF], with 10% increments marked; a second mixing model (line with filled triangles) is shown between the average Pu'u Wahi melt inclusion composition (TableS10) and the Gabal Gerf gabbro with the highest (Sr/Ce)N (sample GG36, with (Sr/Ce)N = 148) from[START_REF] Zimmer | The Gabal Gerf complex: a Precambrian N-MORB ophiolite in the Nubian shield, NE Africa[END_REF]. (b) The same plot as in (a) except expanded to highlight melt inclusions with (Sr/Ce)N < 2. (c) In Al2O3 (wt.%) versus MgO (wt.%) space; the mixing model uses the same mixing endmembers as panels (a) and (b). We use the comprehensive Hawaiian dataset (which includes both whole rock and glass analyses) from Frey et al. (2016) for comparison because it provides a compilation of the highest-quality major and trace element data from Hawai'i. The Frey et al. (2016) dataset has been filtered as described in Section S1.5 of the Supplementary Methods. Loa-trend volcanoes (Loihi, Mauna Loa, Koolau, Lanai, and Kahoolawe) and Keatrend volcanoes (Mauna Kea and Kilauea) from the Frey et al. dataset are shown here. The tephra/pillow glass for each sample hosting melt inclusions is also shown for reference. The Pu'u Wahi tephra glass major and trace element concentrations are from[START_REF] Sobolev | A young source for the Hawaiian plume[END_REF]. Low (Sr/Ce)N Mauna Loa melt inclusions from[START_REF] Sobolev | Recycled oceanic crust observed in 'ghost plagioclase' within the source of Mauna Loa lavas[END_REF][START_REF] Sobolev | A young source for the Hawaiian plume[END_REF] include inclusions with (Sr/Ce)N < 2. Concentrations shown in the figure have been corrected for addition or subtraction of equilibrium olivine so that the melt inclusions are in equilibrium with the host olivine. Only data for glassy melt inclusions are shown. The two ultra-depleted melt (UDM) inclusions from[START_REF] Sobolev | A young source for the Hawaiian plume[END_REF] are identified. An outlier with low Al2O3 content, which is an ultra-calcic melt inclusion (UCMI) from Pu'u Wahi, is noticeable in all three panels.

Figure 4 .

 4 Figure 4. (Sr/Ce)N versus (La/Sm)N plot shows the diffusive interaction model results (black crosses) for Mauna Loa based on the Peterson et al. (2014) model, and the numbers next to the data points represent the number of years of diffusion. Mixing lines are shown between the ML-2012-27 host tephra composition (TableS8) and compositions generated at 1, 20, and 400 years of diffusive interaction. Average 2σ error bars are shown in the top right corner of plot.

225Figure 5 .Figure 6 .

 56 Figure 5. Primitive mantle normalized trace element patterns, or spidergrams, (left panels) and corresponding 87 Sr/ 86 Sr values (right panels) of all Hawaiian melt inclusions and host pillow/tephra glass in this study (note that 5 melt inclusions-Puu2-1-2, Puu7-2-15, Puu7-2-92b, K89-6_52, 6K490-1_51-are crystalline, so their spidergrams are not shown, but 87 Sr/ 86 Sr are). Concentrations shown in the figure have been corrected for addition or subtraction of equilibrium olivine so that the melt inclusions are in equilibrium with the host olivine. (a-b) Spidergrams for melt inclusions and host tephra from the three Mauna Loa samples-ML-2012-27 and the Pu'u Wahi samples (Puu2 and Puu7)-are shown together with a spidergram from a Mauna Loa gabbro with the highest (Sr/Ce)N (sample 98-65 from Gaffney (2002)); spidergrams for melt inclusions from Pu'u Wahi from Reinhard et al. (2018) are also shown. The Pu'u Wahi tephra trace element concentrations are from Sobolev et al. (2011). (c) Spidergrams of Koolau melt inclusions from sample K89-6 with the host glass. (d) Spidergrams of Loihi melt inclusions from samples 6K490-1 and 6K490-2 are shown with the two respective host glasses. (e-f) The 87 Sr/ 86 Sr of the host pillow/tephra glass is shown as a straight line and dashed lines represent the 2σ (2SE) error bars. Panel (f) compares the 87 Sr/ 86 Sr of melt inclusions from Mauna Loa samples "Puu2" and "Puu7" analyzed here (orange symbols) and by Reinhard et al. (2018) (grey symbols). The 87 Sr/ 86 Sr results (generated in two different labs, UCSB and Vrije University, respectively) are remarkably consistent (the 87 Sr/ 86 Sr of the host tephra glass is shown as a straight line and was analyzed by Reinhard et al. (2018)). Partially crystalline inclusions are indicated in panels (f-h), and spidergrams are not available for these inclusions. Note that the host pillow glass 87 Sr/ 86 Sr ratios for the two Loihi lavas-6K490-1 and 6K490-2-are indistinguishable in panel (h).

Figure 7 .

 7 Figure 7. 87 Sr/ 86 Sr of Mauna Loa Pu'u Wahi melt inclusions by two different methods. (a) The 87 Sr/ 86 Sr of Pu'u Wahi melt inclusions measured by LA-ICP-MS[START_REF] Sobolev | A young source for the Hawaiian plume[END_REF] and TIMS[START_REF] Reinhard | Sr and Nd isotopic compositions of individual olivine-hosted melt inclusions from Hawai'i and Samoa: Implications for the origin of isotopic heterogeneity in melt inclusions from OIB lavas[END_REF] this study) are compared to the 87 Sr/ 86 Sr range of Mauna Loa lavas (orange bar = 0.703599-0.703967;[START_REF] Hauri | Osmium isotope systematics of drilled lavas from Mauna Loa, Hawaii[END_REF][START_REF] Kurz | Isotopic evolution of Mauna Loa Volcano: A view from the submarine southwest rift zone[END_REF] and of the Pu'u Wahi glass (horizontal black line; Reinhard et al., 2018). The ultra-depleted melt (UDM) inclusions from Sobolev et al. (2011) are marked separately. Even when the UDM inclusions are excluded, the 2RSD in 87 Sr/ 86 Sr of the Pu'u Wahi melt inclusions determined by LA-ICP-MS greatly exceeds (by a factor of 13) the 2RSD determined by TIMS. Panel (b) shows only the 87 Sr/ 86 Sr of Pu'u Wahi melt inclusions analyzed by TIMS compared to the Pu'u Wahi matrix glass (horizontal black line with 2SE represented by the dashed lines) analyzed by Reinhard et al. (2018).

  Figure 7. 87 Sr/ 86 Sr of Mauna Loa Pu'u Wahi melt inclusions by two different methods. (a) The 87 Sr/ 86 Sr of Pu'u Wahi melt inclusions measured by LA-ICP-MS[START_REF] Sobolev | A young source for the Hawaiian plume[END_REF] and TIMS[START_REF] Reinhard | Sr and Nd isotopic compositions of individual olivine-hosted melt inclusions from Hawai'i and Samoa: Implications for the origin of isotopic heterogeneity in melt inclusions from OIB lavas[END_REF] this study) are compared to the 87 Sr/ 86 Sr range of Mauna Loa lavas (orange bar = 0.703599-0.703967;[START_REF] Hauri | Osmium isotope systematics of drilled lavas from Mauna Loa, Hawaii[END_REF][START_REF] Kurz | Isotopic evolution of Mauna Loa Volcano: A view from the submarine southwest rift zone[END_REF] and of the Pu'u Wahi glass (horizontal black line; Reinhard et al., 2018). The ultra-depleted melt (UDM) inclusions from Sobolev et al. (2011) are marked separately. Even when the UDM inclusions are excluded, the 2RSD in 87 Sr/ 86 Sr of the Pu'u Wahi melt inclusions determined by LA-ICP-MS greatly exceeds (by a factor of 13) the 2RSD determined by TIMS. Panel (b) shows only the 87 Sr/ 86 Sr of Pu'u Wahi melt inclusions analyzed by TIMS compared to the Pu'u Wahi matrix glass (horizontal black line with 2SE represented by the dashed lines) analyzed by Reinhard et al. (2018).

Figure 8 .

 8 Figure 8. The red histogram displays the resulting model variability in87 Sr/ 86 Sr if a relatively homogeneous population (i.e., 87 Sr/ 86 Sr variability is approximately ±200 ppm, 2RSD) of melt inclusions, like that found by the TIMS studies of Pu'u Wahi melt inclusions[START_REF] Reinhard | Sr and Nd isotopic compositions of individual olivine-hosted melt inclusions from Hawai'i and Samoa: Implications for the origin of isotopic heterogeneity in melt inclusions from OIB lavas[END_REF] this study), is modelled using a Monte Carlo method that assigns the melt inclusions larger uncertainties from the distribution of measurement uncertainties associated with the[START_REF] Sobolev | A young source for the Hawaiian plume[END_REF] ICP-MS analyses. The red histogram represents the 87 Sr/ 86 Sr of model melt inclusions resulting from 10 6 iterations of the Monte Carlo simulation. The 87 Sr/ 86 Sr values of the Pu'u Wahi melt inclusions reported by[START_REF] Sobolev | A young source for the Hawaiian plume[END_REF] are shown as a blue histogram). In summary, larger measurement uncertainties associated with a relatively homogeneous population of melt inclusions can generate apparent heterogeneity that mimics the extreme 87 Sr/ 86 Sr heterogeneity reported in the Puu Wahi inclusions by the[START_REF] Sobolev | A young source for the Hawaiian plume[END_REF].

Table 1 .

 1 Rb Ba Th U Nb K La Ce Pb Nd Sr Zr Sm Ti Gd Y Yb Lu Rb Ba Th U Nb K La Ce Pb Nd Sr Zr Sm Ti Gd Y Yb Lu 87 Sr/ 86 Sr measurements made on melt inclusions and the glass of the host lava in this study.

						0.7041
	Sample/Primi�ve mantle	a Highest (Sr/Ce) N melt inclusion Glass	Mauna Loa Sample ML-2012-27 Mauna Loa gabbro	87 Sr/ 86 Sr	0.7039 0.7040 0.7038	e	Mauna Loa Sample ML-2012-27 Highest (Sr/Ce) N melt inclusion
	0.1
		Rb Ba Th U Nb K La Ce Pb Nd Sr Zr Sm Ti Gd Y Yb Lu
	Sample/Primi�ve mantle	b	Glass (Sobolev et al., 2011) Reinhard et al. (2018) melt inclusions	Mauna Loa Samples Puu2 & Puu7	87 Sr/ 86 Sr	0.7038 0.7039 0.7040 0.7037	f	Mauna Loa Samples Puu2 & Puu7 Par�ally crystalline
							Reinhard et al. (2018)	This study
	Sample/Primi�ve mantle	c	Glass	Koolau Sample K89-6	87 Sr/ 86 Sr	0.7038 0.7040 0.7042 0.7044	g	Par�ally crystalline	Koolau Sample K89-6
						0.7036
		Rb Ba Th U Nb K La Ce Pb Nd Sr Zr Sm Ti Gd Y Yb Lu
						0.7038
	Sample/Primi�ve mantle	d	6K490-1 glass 6K490-1 inclusion	6K490-2 glass 6K490-2 inclusion Loihi Samples 6K490-1 & -2	87 Sr/ 86 Sr	0.7036 0.7034	h		Loihi Samples 6K490-1 & -2
						0.7032		Par�ally crystalline

Note: The Sr and Ce frac�ona�on-corrected concentra�ons are reported here, but not for par�ally crystalline inclusions. ᵃ ⁸⁷Sr/⁸⁶Sr values have been blank corrected and corrected for the offset between the preferred (0.710240) and the measured ⁸⁷Sr/⁸⁶Sr of NBS987. b The change in 87 Sr/ 86 Sr ra�o due to the blank correc�on (ppm) is calculated as ( 87 Sr/ 86 Sr meas-norm987 -87 Sr/ 86 Sr blank-corrected )/ 87 Sr/ 86 Sr meas-norm987 *10 6 .

Table 2 . Model parameters and output data for the diffusive interaction model based on the model of Peterson et al. (2014).

 2

		K d (plag-melt) a D plag (1200°C, Plagioclase Initial Output data (concentrations in ppm)
			m² s⁻¹) b	melt c	melt d
				(ppm)	(ppm)	1 year	5 years	10 years	20 years	50 years	100 years 200 years 400 years
	Ba	0.230	8.09E -19	198	4.69	4.86	5.52	6.35	7.99	12.82	20.57	35.03	60.18
	Th	0.050	3.10E -21	1.37	0.07	0.07	0.07	0.07	0.07	0.07	0.07	0.07	0.07
	U	0.024	3.10E -21	0.47	0.03	0.03	0.03	0.03	0.03	0.03	0.03	0.03	0.03
	Nb	0.030	3.10E -21	20.4	1.24	1.24	1.24	1.24	1.24	1.24	1.24	1.24	1.24
	K	0.171	4.38E -16	7222	408	2364	5618	6368	6491	6494	6494	6494	6494
	La	0.106	3.87E -19	21	1.60	1.60	1.62	1.64	1.67	1.78	1.96	2.32	3.01
	Ce	0.081	3.87E -19	53.5	4.57	4.58	4.61	4.64	4.71	4.92	5.28	5.97	7.32
	Pb	0.511	1.41E -17	1.69	0.15	0.23	0.52	0.80	1.17	1.55	1.63	1.63	1.63
	Nd	0.084	2.92E -19	36	4.76	4.77	4.78	4.80	4.83	4.94	5.11	5.46	6.14
	Sr	1.813	3.37E -17	689	63.5	217	534	647	680	682	682	682	682
	Zr	0.004	3.10E -21	264	41.5	41.5	41.5	41.5	41.5	41.5	41.5	41.5	41.5
	Hf	0.015	3.10E -21	6.33	1.27	1.27	1.27	1.27	1.27	1.27	1.27	1.27	1.27
	Sm	0.056	2.92E -19	9.3	1.88	1.88	1.88	1.88	1.89	1.90	1.93	1.99	2.10
	Eu	0.534	2.92E -19	3.06	0.74	0.83	1.13	1.39	1.67	1.88	1.94	2.01	2.15
	Ti	0.076	3.10E -21	21049	5310	5310	5311	5311	5311	5311	5312	5314	5317
	Dy	0.019	3.24E -19	6.77	3.37	3.58	3.58	3.58	3.58	3.58	3.58	3.58	3.58
	Yb	0.015	5.06E -19	2.09	2.04	2.04	2.04	2.04	2.04	2.04	2.04	2.04	2.04
	⁸⁷Sr/⁸⁶Sr			0.703872 0.702569 0.703585 0.703833 0.703863 0.703870 0.703871 0.703871 0.703871 0.703871

manuscript submitted to Geochemistry, Geophysics, Geosystems 10

c Sr concentra�on and ⁸⁷Sr/⁸⁶Sr of Pu'u Wahi glass is from[START_REF] Reinhard | Sr and Nd isotopic compositions of individual olivine-hosted melt inclusions from Hawai'i and Samoa: Implications for the origin of isotopic heterogeneity in melt inclusions from OIB lavas[END_REF].

Acknowledgments and Data

We thank Al Hofmann, Jonathan Snow, Peter Michael, and John Maclennan for reviews; John Maclennan requested a robust comparison of the TIMS and single-collector ICP-MS 87 Sr/ 86 Sr datasets on the Puu Wahi melt inclusions. Shichun Huang is acknowledged for providing thoughtful discussion. OEA acknowledges support from UCSB's Earth Research Institute for support through the Graduate Student Fellowship. MGJ acknowledges NSF grants OCE-1736984, EAR-1624840, and EAR-1429648. Gareth Seward's skillful assistance with UCSB's electron microprobe is gratefully acknowledged. JPM also thanks Mike Garcia and Aaron Pietruszka for supplying samples. EFR-K thanks J-L. Devidal for his time, advice and help during the LA-ICPMS analysis and acknowledges the support of the French Government Laboratory of Excellence initiative ANR-10-LABX-0006. This is Laboratory of Excellence ClerVolc contribution number xxx. This publication is LANL LA-UR-21-20540. All data published in this manuscript are available in the EarthChem data repository (https://doi.org/10.1594/IEDA/111193 and https://doi.org/10.26022/IEDA/111591).