Subduction zone magmas are characterized by high concentrations of H2O, presumably derived from the subducted plate and ultimately responsible for melting at this tectonic setting. Previous studies of the role of water during mantle melting beneath back-arc basins found positive correlations between the H2O concentration of the mantle (H2Oo) and the extent of melting (F), in contrast to the negative correlations observed at mid-ocean ridges. Here we examine data compiled from six back-arc basins and three mid-ocean ridge regions. We use TiO2 as a proxy for F, then use F to calculateH2Oo from measured H2O concentrations of submarine basalts. Back-arc basins record up to 0.5 wt % H2O or more in their mantle sources and define positive, approximately linear correlations between H2Oo and F that vary regionally in slope and intercept. Ridge-like mantle potential temperatures at back-arc basins, constrained from Na-Fe systematics (1350°–1500°C), correlate with variations in axial depth and wet melt productivity (∼30–80% F/wt % H2Oo). Water concentrations in back-arc mantle sources increase toward the trench, and back-arc spreading segments with the highest mean H2Oo are at anomalously shallow water depths, consistent with increases in crustal thickness and total melt production resulting from high H2O. These results contrast with those from ridges, which record low H2Oo (<0.05 wt %) and broadly negative correlations between H2Oo and F that result from purely passive melting and efficient melt focusing, where water and melt distribution are governed by the solid flow field. Back-arc basin spreading combines ridge-like adiabatic melting with nonadiabatic mantle melting paths that may be independent of the solid flow field and derive from the H2O supply from the subducting plate. These factors combine significant quantitative and qualitative differences in the integrated influence of water on melting phenomena in back-arc basin and mid-ocean ridge settings.
 Water has long been understood to play a major role in the generation of subduction zone magmas. In essence, water lowers the mantle solidus [e.g., Kushiro et al., 1968], which ultimately drives melting of the mantle wedge beneath arcs and back-arc basins due to a flux of water originating from the dehydrating, subducting slab. This has been the working paradigm for subduction zone magma genesis for more than 20 years, supported by the widespread observations that subduction zone lavas are vesicular and explosive, contain hydrous phenocrysts [e.g., Gill, 1981], follow hydrous liquid lines of descent [Sisson and Grove, 1993a], are enriched in fluid-mobile trace elements [e.g.,Morris et al., 1990], and carry trace element and isotopic signatures characteristic of subducting sediment and oceanic crust [e.g., Tera et al., 1986; Plank and Langmuir, 1993; Miller et al., 1994]. High H2O concentrations in arc magmas have been inferred or estimated using innovative analytical and experimental techniques, [e.g., Anderson, 1979, 1982; Sisson and Grove, 1993a, 1993b; Gaetani et al., 1994], and direct measurements of H2O in submarine glasses and melt inclusions have supported these earlier estimates of dissolved H2O in arc and back-arc lavas [e.g., Muenow et al., 1980; Aggrey et al., 1988; Muenow et al., 1991; Danyushevsky et al., 1993; Sisson and Layne, 1993; Stolper and Newman, 1994] (hereinafter referred to as S&N94). Notably, a significant increase in the number of direct measurements of volatile contents in arc and back-arc magmas in recent years [e.g., Kamenetsky et al., 1997; Roggensack et al., 1997; Sisson and Bronto, 1998; Newman et al., 2000; Fretzdorff et al., 2002; Kent et al., 2002; Cervantes and Wallace, 2003; Sinton et al., 2003; Walker et al., 2003] has set the stage for a quantitative investigation of water in natural subduction zone settings.
 Back-arc basins are natural places to begin such a study because they can be treated, in many ways, like mid-ocean ridges. The driest back-arc basin melts are compositionally equivalent to mid-ocean ridge melts and thus, like mid-ocean ridge magmas, can be interpreted as melts generated by varying extents of adiabatic decompression melting of ascending mantle. For example, the driest back-arc basin basalts overlap with MORBs on Na8.0-axial depth plots (Figure 1 [see also Klein and Langmuir, 1987]) and plots of Na2O versus FeO (Figure 2 [see also Langmuir et al., 1992; Taylor and Martinez, 2003]). Both inter- and intrabasin systematics of back arcs were recently explored by Taylor and Martinez , who compared major and trace element variations (e.g., Na8.0, Fe8.0, Ti8.0, H2O(8.0), Ba/La) of four back-arc basins to global MORB; their work emphasizes the hybrid nature of the back-arc basin melting process, identifying MORB-like geochemical systematics in relatively dry back-arc melts and showing how these systematics are perturbed in wetter samples by the addition of H2O-rich material from the subducted slab. The melting process in back arcs is also not complicated, as it may be in arcs, by the effects of overlying crust, since crustal assimilation is a small concern and crustal thickness will not impact the melting column because it is a passive consequence of melting just as at ridges. Additionally, back arcs are less subject to the thermal influence of the cold subducting slab, and may reflect ambient upper mantle temperature variations as ridges do. Back-arc basins are therefore potentially ideal sites for studying the effects of variations in mantle temperature and water contents on mantle melting with fewer complicating factors than arcs.
 The quantitative relationship between water and mantle melting over the range of tectonic settings has been investigated in only a few localities, with contrasting results. S&N94 evaluated the importance of water in the formation of magmas at the Mariana trough back-arc spreading center using concentrations of volatile, major, and trace elements from submarine glasses. This work was the first to recognize correlations between trace elements and water contents of subduction-related lavas and suggested a positive, roughly linear relationship between the extent of mantle melting (i.e., melt fraction; F) and the H2O concentration of the mantle (Figure 3a). The basis for pure “flux melting” models originates from this study. Correlations between H2O and trace elements in volcanic arc melts [e.g., Grove et al., 2002; Cervantes and Wallace, 2003; Walker et al., 2003] provide supporting evidence for the importance of the flux melting mechanism beneath arcs, although nominally dry arc melts from Japan [Tatsumi et al., 1983], the Cascades [Bartels et al., 1991], and Java [Sisson and Bronto, 1998] implicate mantle decompression as another means of melt generation beneath arcs. In contrast to the positive correlation between H2O and F described or inferred for back-arc basin and arc lavas, recent models of hot spot-influenced, “damp” mid-ocean ridges [Detrick et al., 2002; Asimow et al., 2004; Cushman et al., 2004] suggest a negative correlation between H2O and F (e.g., Figure 3b, hLKP curve). The differences in the relationships between water content and extent of melting in two such similar tectonic settings as back-arc basins and mid-ocean ridges present a dilemma that we address in this study.
 Theoretical, empirical, and experimental investigations of the role of water in mantle melting underscore the differences observed in natural settings. For example, experimental work [Gaetani and Grove, 1998] (hereinafter referred to as G&G98), thermodynamic modeling [Hirschmann et al., 1999], and empirical parameterizations of experimental and thermodynamic data [Katz et al., 2003] have shown that the positive melting trend observed in the Mariana trough is readily reproduced through isothermal, isobaric equilibration of fertile mantle with increasing H2O content (Figure 3b, MELTS, G&G98, and KSL1 curves), although such conditions do not translate easily into a physical melting process in the earth [S&N94; Hirschmann et al., 1999; Asimow and Langmuir, 2003]. Parameters such as temperature and pressure certainly vary in natural systems, and the apparent similarities between these studies and the Mariana trough trend may indeed be only coincidental. On the other hand, Asimow and Langmuir  used simple thermodynamic models to propose that adding water to decompression melting regimes at mid-ocean ridges will, seemingly paradoxically, increase total melt production but simultaneously decrease the mean extent of melting. This situation arises when pooling melts from a two-dimensional (2-D) triangular melting regime because low-F, wet melts originate from the large source volume at the triangle's base. Such a geometry can thus lead to a decrease in mean F with increasing H2O in the mantle (Figure 3b, hLKP curve). Although this effect has been documented at hot spot-influenced mid-ocean ridges [Detrick et al., 2002; Asimow et al., 2004; Cushman et al., 2004], it has not been seen in the high-H2O lavas from back-arc basins. Katz et al.  also developed an empirical parameterization of hydrous, adiabatic melting. The relationship between H2O content and extent of melting in their hydrous, adiabatic melting model, however, contrasts with both the observed trend in the Mariana trough and with other efforts to model hydrous, adiabatic melting (Figure 3b, KSL2 curve). Their model produces positive correlations between H2O in the source and F, but the steepness of the trend suggests that H2O addition does not lead to a significant increase in extent of melting, and thus that H2O-fluxed melting contributes volumetrically very little to the final melt produced by adiabatic decompression in this model. For back-arc basins, therefore, we must presently choose between, on the one hand, an unlikely melting process (i.e., flux-induced, isothermal, isobaric melting) that produces trends similar to those observed in nature or, on the other hand, an apparently more realistic melting process (i.e., polybaric, hydrous, adiabatic melting) for which current models do not reproduce observed trends.
 In the work reported in this paper, we studied aspects of the differences between ridge and back-arc melting systematics, focusing in particular on discriminating between the competing effects of H2O, decompression, and mantle temperature on melt production. Using available measurements of the water contents of glasses from several back-arc basins, we first show that the positive H2O-F trend of the Mariana trough found by S&N94 is a general phenomenon in back-arc basin settings. In detail, however, these trends differ in important ways from one back-arc region to another. We then use these differences and their correlations with other geochemical and geophysical parameters and the contrasts with comparable data from mid-ocean ridge basalts to demonstrate the unique way in which water drives melting beneath back-arc spreading centers.
2. Methods and Data Treatment
 In order to test the competing models of wet melting, we must be able to determine and compare the extent of mantle melting (F) and the concentration of H2O in the mantle (H2Oo) over a broad range of mid-ocean ridge and back-arc basin basalt compositions. Here, we present the methods we used to filter and correct the data, to calculate F and H2Oo, and to estimate other relevant factors such as mantle potential temperature (Tp), axial depth, and crustal thickness in a self-consistent manner. Readers more interested in an outline of the methodology than in the details may skip to the methods summary presented in section 2.8.
2.1. Back-Arc Basin Basalt Data
 We compiled a global data set of major element and volatile measurements for 408 glasses and olivine-hosted melt inclusions from six back-arc basin localities (Mariana trough [Volpe et al., 1987; Hawkins et al., 1990; S&N94; Gribble et al., 1996, 1998; Newman et al., 2000], Sumisu rift [Hochstaedter et al., 1990a], Manus basin [Danyushevsky et al., 1993; Kamenetsky et al., 2001; Sinton et al., 2003; Shaw et al., 2004], North Fiji basin [Aggrey et al., 1988; Danyushevsky et al., 1993], Lau basin [Aggrey et al., 1988; Danyushevsky et al., 1993; Sinton et al., 1993; Pearce et al., 1995; Kamenetsky et al., 1997; Peate et al., 2001; Kent et al., 2002; A. J. Kent, unpublished data, 2002; S. Newman, unpublished data, 1994] and East Scotia ridge [Muenow et al., 1980; Leat et al., 2000; Fretzdorff et al., 2002; Newman and Stolper, 1995; S. Newman, unpublished data, 2002]) and three mid-ocean ridge and ridge-like regions (Galápagos spreading center [Cushman et al., 2004], Mid-Atlantic Ridge and Azores platform [Dixon et al., 2002], and Woodlark basin [Muenow et al., 1991; Danyushevsky et al., 1993]).
 Before using these data to model F and H2Oo, we first considered how the composition of each glass may have changed through degassing and crystal fractionation. To assess how degassing may have affected H2O, we examined another volatile species, CO2, which has much lower solubility than H2O in silicate melt and degasses nearly to completion before H2O degassing initiates during open system degassing [Dixon et al., 1995]. The presence of measurable CO2 is thus an indicator that H2O has likely not been significantly affected by degassing, but CO2 data are not published for many of the samples used in this study. The combined concentrations of H2O and CO2 in a melt, however, are pressure sensitive and, in submarine lavas, usually reflect vapor saturation or supersaturation at or near the hydrostatic pressure of eruption [Dixon and Stolper, 1995]. We thus calculated the saturation pressure of each sample with respect to pure H2O (i.e., CO2 = 0 ppm). Glasses with pure H2O saturation pressures equal to or greater than their collection depths probably reached saturation with H2O vapor and experienced some H2O degassing. To account for uncertainties in eruption/collection depth and the chance that lava flowed downhill from the eruption site, we included only those samples with pure H2O saturation pressures at least 30 bars less than the pressure at the collection depth. Exceptions to these criteria were made in the case of basaltic melt inclusions, which are often trapped at high pressure within the magma chamber and, if H2O concentrations are high (e.g., at the Valu Fa ridge), may record H2O saturation pressures much higher than those at the sample collection depth. In these cases, only melts with measured CO2 concentrations >30 ppm were considered undegassed.
2.2. Modeling Mantle Melt Fractions and Water Contents of Mantle Sources
 S&N94 performed a multielement inversion on a suite of Mariana trough glasses to constrain melt fraction and source composition. This inversion was based on the simplifying assumption that variations in Mariana trough basalt chemistry reflect variable extents of melting correlated with mixing of two source components: one similar to the mantle source of normal mid-ocean ridge basalt (NMORB) and the other a water-rich component derived from the subducted slab. They chose the most MORB-like basalt composition and assumed it reflected 5% batch melting of unmodified NMORB source to obtain the composition of this source component. They then used an iterative procedure based on the H2O, TiO2, K2O, Na2O, and P2O5 contents of each glass to solve simultaneously for the composition of the H2O-rich component, the fraction of this component in the source of each sample, and the extent of melting of the source by which each sample was produced. Although this method succeeds for the Mariana trough, the assumptions (1) of a two-component system (requiring that enough data exist to define clear mixing relationships and that additional components are not involved), (2) of a H2O-poor NMORB mantle source and a H2O-rich component that are constant in composition, and (3) of 5% melting to produce the NMORB end-member may not apply to other regions. An alternative approach is therefore necessary because, in many regions, data sets are limited, the compositions of the mantle source and/or slab-derived component may vary regionally, and the extent of melting of the MORB-like end-member is unlikely to be constant for all back arcs.
 Rather than performing a best fit based on several relatively incompatible elements (including some likely present in significant concentrations in the slab-derived components) to constrain F for each sample, we used TiO2 in glasses as a single-element proxy for melt fraction (F). Like any other element that is incompatible during mantle melting, TiO2 decreases monotonically in the melt with increasing F of a single source. While it is difficult to identify a truly “conservative” element in subduction zones (i.e., an element not added from the subducted slab [Pearce and Parkinson, 1993]), TiO2 holds promise in this regard because of its low overall abundance in arc lavas and the possibility that it, like other high field strength elements, may be retained in residual rutile in the slab during dehydration [e.g., Ryerson and Watson, 1987]. We thus adopted the approximation that, except for dilution, the TiO2 content of sources in a given mantle wedge are independent of the amount of slab-derived component they contain. Moreover, systematics of Mariana trough basalts are consistent with low TiO2 in the H2O-rich component (S&N94), as the data show that increasing H2O concentrations correlate with decreasing TiO2 and, by proxy, increasing F (Figure 4a (see also S&N94). This correlation is the starting point of the linear wet melting function and was indeed the observation that led S&N94 to first suspect a positive correlation between the water content and melt fraction of the source of Mariana trough lavas.
|Basin||Region/Segment||Source Modela||f Removed, %||CTio||+b||−b|
|East Scotia ridge||E2–E4||DMM||0||0.133||0.000||0.006|
|North Fiji basin||TJ||Ti/Y||⋯||0.151||0.012||0.012|
|GSC||E||Cushman et al. ||⋯||0.143||⋯||⋯|
|T||Cushman et al. ||⋯||0.108||⋯||⋯|
|N||Cushman et al. ||⋯||0.105||⋯||⋯|
- a DMM source model denotes the use of prior melt extraction to constrain source variation. Ti/Y source model denotes cases where the mantle source is enriched, and the TiO2/Y model is used to constrain source characteristics.
- b Columns denote errors on the value of CTio.
|TiO2, wt %||0.04||0.133|
- a Depleted MORB mantle composition from Salters and Stracke .
 While end-member batch melting is probably not a realistic melting process, it is a useful approximation for determining the bulk F of basaltic partial melts of the mantle. For example, equation (9) provides a fair approximation of the bulk melt fraction (as reflected in incompatible element concentrations) at mid-ocean ridges despite the likely complexity of the melting regime and melting process in this environment [Plank and Langmuir, 1992; Plank et al., 1995]. As a relevant example, the Na8.0 and Ti8.0 variations in mid-ocean ridge basalts are well described by pooling of melts produced by polybaric, adiabatic, fractional melting with Ds that vary as a function of pressure, temperature, composition, and mode (Figure 5 [see also Langmuir et al., 1992]). The Na8.0-Ti8.0 trend, however, is also adequately reproduced with the simplest model (batch melting with constant Co and Ds (Figure 5)). Since back arcs tap mantle similar to MORB, and because we know less about the melting process in these settings, we adopted this simple model as our starting point.
2.3. Partition Coefficients
 The partition coefficients used in the batch melting model impact the results of these calculations. The DTi used here derives from the simplified MORB model above (Figure 5) and describes partitioning between melt and lherzolitic mantle. Published mantle/melt Ds for Ti range up to 0.11 [Kelemen et al., 1993], but a value this high is not permitted in the batch melting model, as it produces negative values for F in high-Ti samples. The value used here (0.04) reflects an average DTi within the range predicted for appropriate variations in pressure, temperature, and melt composition along a polybaric path (e.g., 0.01–0.06 [Langmuir et al., 1992]; <0.01–0.08 [Baker et al., 1995]), and we assess the effect of this uncertainty on the calculations below. In rare cases, extents of melting predicted by the batch melting model exceed 20%. At such high melt fractions, one might expect clinopyroxene (cpx) to become exhausted from the mantle, and the liquid to instead reflect equilibrium partitioning between melt and a two-phase harzburgitic mantle. For the few back-arc samples where cpx may have been exhausted from the mantle (e.g., the Manus basin, based on CaO/Al2O3), we selected a harzburgite/melt DTi of 0.05 (average of Ds reported by Grove et al. , Pearce and Parkinson , and Kelemen et al. ). Because this D is similar to the lherzolite D, the change has a small effect on the calculated F and H2Oo. The used here (0.012) is adopted from S&N94 in order to be consistent with that study. The value is similar to that for the LREE, consistent with variations observed in MORB [Michael, 1988; Dixon et al., 2002]. We evaluate the effect of lowering in section 2.6 below.
2.4. Modeling Depleted Mantle Source Compositions
 The composition of the depleted mantle end-member in the sources of back-arc basin magmas is crucial to the model results, and so we carefully consider here the likely variation of CTio in global back-arc basin and ridge regions. Two variables primarily control the TiO2 concentration of a partial melt of mantle peridotite: the initial concentration of TiO2 in the peridotite and the melt fraction. So while Taylor and Martinez  attribute TiO2 variations in back-arc basins largely to variations in source composition, variations in F would also lead to TiO2 variations for a constant source composition, and the challenge is to distinguish whether a melt with low TiO2 reflects high F, or a highly depleted mantle, or both. The key to doing so is to use not just TiO2, but several elements with different Ds during mantle melting; i.e., although the concentration of a single element in a melt can be modeled by an infinite number of combinations of source concentration and F, the relative abundances of elements with differing mantle/melt Ds can distinguish variations in source composition from variations due to differing extents of melting. For example, source depletion affects highly incompatible elements (e.g., Nb) more than moderately incompatible elements (e.g., Ti (Figure 6a)), while high degrees of melting will affect both elements almost equally provided F ≫ D (Figure 6b). Here, we attempt to account for TiO2 variations in mantle sources using a model based on the systematic variations of a suite of elements in lavas from each basin.
 A complicating factor in separating variations in the MORB-like mantle composition from variations in extent of melting at subduction zones is that there are probably no elements in the mantle wedge that are completely unaffected by the mass flux from the subducting slab. Nevertheless, for back-arc basin lavas, we will assume most trace element enrichments (e.g., LREE) are additions from the slab-derived, H2O-rich component, whereas incompatible element depletion is a feature of the MORB-like mantle. We therefore chose several relatively conservative elements, spanning a range of mantle/melt Ds (Y, Ti, Zr, Nb, and Ta) to set constraints on mantle source variations. These high field strength elements vary systematically during mantle melting at mid-ocean ridges and, unlike the light rare earth elements and Th, are expected to be retained in the slab by residual rutile [Pearce and Parkinson, 1993]. These are thus among the elements in the mantle least affected by addition of slab-derived components.
 Figure 7 illustrates how we determined the composition of the end-member mantle sources for the back-arc spreading centers, to ultimately derive CTio. We did this by fitting the conservative element pattern (rather than the full trace element pattern, most of which is sensitive to slab additions (e.g., Figure 7)) of natural lava samples with a melt removal model to determine the source composition of the “slab-free” mantle end-member for each basin or subregion within a basin. Mantle source variation is expressed as a function of prior melt removal from an average mantle composition. We chose as the starting point the depleted MORB mantle (DMM) composition of Salters and Stracke , which represents an average composition of the mantle that provides the source of MORB. The melt removal model controls the trace element characteristics of the mantle source by removing a specified fraction of melt (f) from DMM using batch melting and the bulk mantle/melt Ds in Table 2. That is, f represents a melt fraction that has been removed from the mantle prior to the melting that takes place within the ridge or back-arc magma source. The removal of f creates depletion of the mantle before it enters into the ridge and back-arc sources. Subsequent melting of these depleted sources, which is the melting step that generates mid-ocean ridge and back-arc basin magmas (F, as defined in section 2.2), employs these same Ds. Source depletion (the removal of f from DMM) has a large effect on the shape of the trace element pattern of a melt (Figure 6a), whereas F controls the absolute abundances of all elements, shifting the whole pattern up or down with a minimal effect on shape (Figure 6b), because f is usually a small value (<3%) and F is a large value (typically 10–20%) with respect to the Ds modeled. Prior melt removal (f) has the largest effect on the most incompatible elements (e.g., Nb and Ta), which may change in source concentration by a factor of 10 with as little as 2.5% melt removed, whereas TiO2 would vary by only a factor of 1.5, using the batch melting model. Removing melt using a fractional melting model would lead to even smaller changes in TiO2 relative to the more incompatible elements, and we thus used the batch removal model because it allows for greater variation of TiO2 in the mantle source. The concentration of Nb or Ta, relative to TiO2 (and other elements), therefore provides a constraint on the amount of depletion necessary in the mantle source of each region. This constraint is a minimum in the sense that Nb and Ta could theoretically be added from the slab, causing the mantle to appear less depleted than it actually is. These constraints are then used to estimate the mantle source composition and CTio for most back-arc spreading segments (Table 1, Figure 7), and we apply a constant source composition to each segment. We unfortunately cannot, in many cases, perform this analysis with the exact samples used to model F and H2Oo because most of these glasses do not have the necessary trace element data. In such cases, trace element data from whole rock samples in the same local area were used to establish regional source characteristics beneath each spreading segment [Hochstaedter et al., 1990b; Nohara et al., 1994; Pearce et al., 1995; Dril et al., 1997; Fretzdorff et al., 2002; Sinton et al., 2003].
 Figure 7 illustrates back-arc regions where the mantle sources were successfully modeled relative to DMM. The conservative elements (CEs) Nb, Ta, Zr, Ti, and Y reflect mantle source characteristics, whereas rare earth elements and Th indicate the extent of geochemical enrichment from the slab. As a general rule, lavas with lower absolute concentrations of CEs (i.e., higher F) show greater absolute abundances in slab-derived elements than low-F lavas from the same regions, suggesting a link between F and the extent of slab-derived input at back-arc basins (such that larger extents of melting are associated with greater slab input of the non-CEs). The mantle depletion model developed here makes a fair approximation of the CE patterns and thus the mantle source characteristics of basins and intrabasin segments tapping variably depleted mantle. In fact, most regions require little to no prior melt removal (f < 0.2%) to explain the CE patterns (e.g., Mariana trough, Sumisu rift, MTJ, ILSC, Manus ER, ESR E2–E6, Woodlark basin NE (Table 1)). The CE patterns are also generally parallel within a given basin spreading segment (F variation) rather than of variable shape (source variation), which supports the assertion that F is the dominant variable controlling CE variation on local scales. A few regions require more depleted mantle (∼1–2.5% f; e.g., CLSC, ELSC-VFR, Manus MSC-ETZ (Table 1)), which relates to low Nb concentrations (<1 ppm).
 We acknowledge that the model curves are not perfect fits to the CE patterns in Figure 7, likely due to variable data quality (particularly for Nb and Ta) and possible additions from the slab in some cases. Conservative trace element variations could, alternatively, arise dominantly or exclusively from variations in mantle source composition. We evaluated this possibility by holding F constant and attempting to fit the CE patterns of lavas only through changing mantle depletion. This model falls short in two ways. First, the extent of prior melt removal necessary to explain variations in the less incompatible elements Zr and Y removes too much Nb and Ta to match the shape of the full CE pattern in multiple samples from a given region (e.g., Figure 7l). Niobium and tantalum could, however, be added from the slab, which would elevate their concentrations above the ambient mantle and explain why the full CE pattern is poorly modeled. Second, the extents of prior melt removal (f) necessary to broadly reproduce the geochemical range recorded, for example, along the Lau basin (Figure 7l) would correlate with variations in H2O concentration along the length of the basin, and indeed in global basins. The Lau basin mantle composition clearly varies along strike regardless of how we model it, but there is no strong argument for why large variations of H2O concentrations in the source regions of arcs and back arcs should correlate globally with the extent of prior mantle depletion [Eiler et al., 2000]. Water concentrations more sensibly correlate with additions of slab-derived components and with F. We therefore elect to constrain variations in the water-poor, MORB-like component of the mantle beneath back-arc basins using the approach described above whereby this component is assumed to have been derived from DMM by variable amounts of prior batch melt extraction, and where the amount of this prior melt extraction is constrained using a fit to the HFSE that assumes they are truly conservative (i.e., uninfluenced by the addition of water-rich, slab-derived components). To the degree that these conservative elements might have been influenced by addition from the slab, the absolute magnitude of their variations in the MORB-like component in the sources of back-arc magmas may require modification, and the source constraints we present (Table 1) would represent the minimum amount of depletion (and therefore the maximum CTio) necessary to explain the geochemistry of these back-arc basins.
2.5. Modeling Enriched Mantle Source Compositions
2.6. Uncertainties and Errors
 The effects of uncertainties in measurements and model assumptions on the final calculations of F and H2Oo require careful consideration. We first addressed the confidence level of each source of uncertainty. For analytical measurements (TiO2 and H2O), we used the standard deviation of replicate measurements on any given sample to reflect the uncertainty in the data (±5% for TiO2, ±10% for H2O). For CTil, both the correction for crystal fractionation and the possibility of slab-derived TiO2 in the melt contribute to errors in this value, and we used an uncertainty of ±20%. Minimum errors in the mantle source composition (CTio) arise from analytical uncertainties in the measurement of the CEs used to constrain the source characteristics. Uncertainties on CTio were thus constrained by allowing 10% variation in all of the CEs in the melt removal model for each region and by constraining the full range of f values (as shown by pattern shapes in Figure 7) permissible by any pair of CEs within this 10% concentration variation (see Table 1). On average, this analysis results in ≤10% error in CTio. We explored the effect of a ±50% variation in DTi (0.02–0.06), which encompasses the range over which the instantaneous value of DTi may vary along a polybaric path (see section 2.3 [Langmuir et al., 1992]). The (0.012) used here originates from S&N94 and is consistent with the DCe used here (Table 2), but recent experiments suggest lower values for both and DCe during batch melting of spinel lherzolite (0.007–0.009 [Aubaud et al., 2004; Hauri et al., 2006]. Studies of MORB and OIB data also suggest a lower value for closer to DLa (0.01 [Dixon et al., 2002]), and we thus also evaluated the effect of lowering in our error analysis but use = 0.012 for the final calculations to remain consistent with S&N94. An additional test of the modeling outcome, using Na2O instead of TiO2 as a proxy for F, is provided in the auxiliary material. Using this alternate proxy for F yields results similar to those for TiO2. Our results are thus not dependent on the use of TiO2 as a proxy for F, nor on factors specific to TiO2 (e.g., the presence of rutile, ilmenite, and Ti-clinohumite in the mantle).
 We used a Monte Carlo error analysis, which allows each parameter to vary simultaneously within its assigned uncertainty during the calculation of F and H2Oo, to evaluate the effects of these uncertainties on the model trends. This technique produces error ellipses around the modeled points in H2Oo versus F, which represent the outcome of 90% of the trial calculations (Figure 9a). Elongation of the ellipses relative to the origin is largely a product of the uncertainties in CTio and DTi, but also serves to emphasize that errors on this diagram are highly correlated. F is used to calculate H2Oo, and any error contributing to the determination of F therefore propagates into error in H2Oo. This analysis results in up to 30% uncertainty in the F-intercept (melt fraction at zero H2Oo) of a regressed line but relatively little variation in the slope (∼10%), which indicates that the slopes of the model trends are more robust than the intercepts.
 Both the S&N94 method and the procedure outlined here result in similar trends despite employing different geochemical constraints and data sets for determining F and H2Oo in the Mariana trough. Figure 9b compares the results from S&N94 with the results from this study. For the two best-fit lines shown in Figure 9b (one regressed through the S&N94 points and the other through the points from this work), the absolute difference in F-intercept is large (3.4 versus 7.0%), owing in part to the extra steps taken here to correct for crystal fractionation, which result in lower TiO2 in the modeled melt compositions. The slopes of the two trends, however, differ by only 28% (1.63 versus 2.08). This difference in slope translates into relatively small differences in H2Oo at a given F (e.g., 0.07 versus 0.10 wt % H2Oo at F = 10%), and is probably within the analytical uncertainty in the H2O measurement. We regard this comparison as a successful reproduction of the original S&N94 trend, using the TiO2 proxy for F.
2.7. Mantle Temperature, Axial Depth, Crustal Thickness, and Melt Production
|Basin||Segment||Dry Samples Only (H2O < 0.5 wt %)||All Samples|
|East Scotia ridge||E2–E4||0.69||0.02||7.48||0.46||2.66||0.13||0.68||0.01||6.62||0.25||2.62||0.07|
|North Fiji basin||N160°||0.73||0.00||8.60||0.00||2.30||0.00||0.67||0.03||6.11||0.57||2.53||0.14|
|East Scotia ridge||whole||0.72||0.01||0.70||0.01|
|North Fiji basin||whole||0.74||0.01||8.59||0.33||2.19||0.03||0.70||0.01||7.97||0.49||2.28||0.07|
|Basin||Segment||Arc Distance, km||1σ||Trench Distance, km||1σ||Axial Depth, m||1σ||CT, km||Mean F||1σ||Mean H2Oo, wt %||1σ||Tp, °C||±||dF/dH2Oo||±||F-Intercept, %||r2|
|East Scotia ridge||E2–E4||200||5||361||4||−3275||73||0.10||0.00||0.08||0.01||1343||12|
|North Fiji basin||N160°||626||30||926||73||−3554||52||0.12||0.03||0.07||0.00||1389||14|
|East Scotia ridge||whole||197||6||356||5||−3363||59||0.09||0.01||0.05||0.01||1348||7||0.32||0.04||5.1||0.848|
|North Fiji basin||whole||623||13||817||42||−2994||227||0.13||0.01||0.05||0.01||1406||9|
 Axial depth and crustal thickness at mid-ocean ridges are also linked to total melt production, reflecting the integrated effects of mantle temperature, wet melting, and melt removal. High mantle temperature and large extents of melting combine to generate thick oceanic crust that, due to isostasy, lies at shallower water depths (i.e., lower axial depth) than regions with thinner crust. Axial depth and crustal thickness relate quantitatively to the extent of melting as reflected, for example, by the correlation of depth with melt fraction proxies (e.g., Na8.0 [Klein and Langmuir, 1987]; see Figure 1). In order to explore the extent to which the chemical and physical relationships observed at mid-ocean ridges extend to back-arc basins, we determined mean axial depths at back-arc basins either from the axial profiles of Taylor and Martinez  for the four basins they examined or from averaging the sample collection depths for the other basins we have examined in our study (see Table 4). We also estimated crustal thickness (see Table 4) from seismic profiles of the few basins where detailed geophysical data exist [Bibee et al., 1980; LaTraille and Hussong, 1980; Ambos and Hussong, 1982; Turner et al., 1999; Crawford et al., 2003; Martinez and Taylor, 2003].
2.8. Summary of Methods
 We have described in detail the several steps in our treatment of glass compositions from back-arc basins, and we summarize them here. The compiled basalt data were first screened to exclude fractionated compositions (MgO < 7.0 wt %) and degassed samples (pure H2O saturation pressure <30 bars from eruption pressure). All remaining glasses were then corrected for the effects of crystal fractionation, adjusting the melt compositions to olivine-enriched compositions that would be in equilibrium with Fo90. The extent of melting of a peridotitic mantle source (F) required to produce each corrected back-arc basin glass composition was calculated based on its TiO2 content relative to its mantle source using the batch melting equation and a constant DTi. The concentration of H2O in the mantle source of each sample was then calculated using this value of F and a constant Note that the calculations of F require knowledge of the TiO2 content of the mantle source (CTio) of each sample prior to melting. We have shown that TiO2 contents of most back-arc mantle sources (prior to addition of slab-derived components) can be modeled using the DMM composition of Salters and Stracke , but in some cases the deviation from this end-member appears to be significant. For mantle lower in TiO2 than DMM, we adjusted CTio for each spreading segment using conservative elements (Nb, Ta, Zr, TiO2, Y), assuming that the concentrations of these elements deviate from DMM due to a previous episode of melt extraction (assumed to be batch melting). For sources enriched in trace elements relative to DMM (again, prior to addition of slab-derived components), we modeled CTio based on their TiO2/Y ratios. The total variation in CTio from region to region is a little more than a factor of 2. A Monte Carlo error analysis reveals uncertainties on the linear regression through the modeled Mariana trough data of ∼30% on the F-intercept and ∼10% on the slope of the line, and the trend of F and H2Oo determined using this procedure is similar to that first shown in this region by S&N94 (see Figure 9b).
 Here we present a summary of the modeling outcome for back-arc basins and mid-ocean ridges. Detailed discussions of the results for each specific region are presented in the auxiliary material. The correlation of TiO2(Fo90) and H2O(Fo90) in the fractionation-corrected glass data illustrate the first-order observations suggesting a relationship between H2O and mantle melting in back-arc basin settings. Most of the back-arc basin data show dominant trends of decreasing TiO2(Fo90) with increasing H2O(Fo90) (Figure 4). Because TiO2 is incompatible during mantle melting, and we assume TiO2 originates only from the mantle, we expect that its concentration in the melt will be progressively diluted as the melt fraction (F) increases. The relationships shown in Figures 4a, 4c, and 4d thus suggest that increasing F correlates with increasing H2O. Using the fractionation corrections and melting model developed here, we find that the maximum H2O concentrations in both the lavas and the mantle at back-arc basins far exceed those at mid-ocean ridges, and the principal relationship between H2Oo and F is positive (Figure 10). Mantle H2O concentrations at back arcs range from MORB-like values (0.01–0.05 wt %), which are present at all basins, to maxima of 0.4–0.5 wt % H2O at the Manus basin and the Valu Fa ridge. Positive trends in H2Oo versus F vary regionally in slope and intercept (Table 4), with the East Scotia ridge segments E2–E4 and the southern Lau basin defining the steepest trends and the Manus and northern Lau basins the shallowest (Figure 11a). The calculated F is <20% in most samples from all back-arc basins, with only a few extreme samples indicating F > 20%. Correcting for mantle source depletion has the largest effect for the Valu Fa ridge, where the mantle is the most depleted relative to DMM (Figure 10e). All arrays defined by back-arc basins indicate finite melt fraction at zero (or low) H2Oo, which strongly implicates decompression melting if we accept that melting in the absence of a flux agent like H2O must be generated by adiabatic decompression. However, the important point in our view is the robust and recurring positive relationship between H2O and extent of melting at back-arc basins.
 The negatively sloping relationship between H2Oo and F proposed for mid-ocean ridges by Asimow and Langmuir  and Cushman et al.  is apparent at four regions (Figure 12): two mid-ocean ridges (GSC, Azores platform), and two spreading centers with distant or past associations with subduction (N. Fiji basin, Woodlark basin). In these regions, melt fraction broadly decreases as a function of increasing H2Oo, although these relationships are much weaker than for back arcs. Maximum H2Oo concentrations reached at these places are low (max. 0.08 wt % H2Oo (Figure 12)) compared to active back-arc basins, and are well within the storage capacity of H2O in nominally anhydrous upper mantle phases such as olivine, orthopyroxene, and clinopyroxene (e.g., 0.12–0.38 wt % H2O at 3 GPa [Hirschmann et al., 2005]). The negatively sloped trends in H2Oo versus F observed at classic mid-ocean ridges (Azores, GSC) are in regions of ridge–hot spot interaction, where constraints on mantle source variation are essential for successful modeling (and, indeed, TiO2 and H2O generally vary with isotope ratios). We are not fully satisfied with any of the approaches for quantifying chemical source variations of the mantle in these regions (including the approach based on TiO2/Y ratios presented here), and consequently the significance of these negative slopes is uncertain. We conclude, however, that such negative slopes are indeed real phenomena, given their persistence at two of three ridges regardless of which approach is taken to constrain variations in source composition and the appearance of such a trend at part of the Woodlark basin. This basic difference in the character of the trend of H2Oo versus F at mid-ocean ridges versus back-arc basins suggests to us a fundamental difference in the role of H2O in the melting processes beneath back arcs and mid-ocean ridges.
4.1. Effects of Variable Mantle Temperature
 Constraining mantle temperature variations beneath back-arc basins is important for understanding subduction zone petrogenesis, structure, and evolution. The 150°C temperature range calculated here (i.e., 1350°–1500°C (Figure 2, Table 4)), using only the driest back-arc basalts, is within the range of global MORBs, which sample upper mantle that spans a ∼250°C range in Tp [Klein and Langmuir, 1987; McKenzie and Bickle, 1988; Langmuir et al., 1992]. Back arcs thus appear to sample mantle of similar temperature to mid-ocean ridges, reflecting normal thermal variations in the upper mantle. The high-T end of the MORB range, however, is due largely to hot spot proximity (e.g., the Mid-Atlantic Ridge in the vicinity of Iceland). Such a hot spot influence at back-arc basins seems unlikely since the slab would generally shield the overlying mantle wedge from the thermal effects of deep upwelling plumes. At the northern segments of the Lau basin, however, infiltration of the Samoan mantle plume through a tear in the subducting plate has been proposed to account for along-strike geochemical variations [Poreda and Craig, 1992] and this could have thermal consequences as well. Among the back-arc basins considered here, the Manus basin taps mantle of the highest Tp; geochemical evidence such as high 3He/4He ratios [Shaw et al., 2004] is also consistent with a hot spot contribution to this elevated Tp. The mantle temperatures calculated by us for back-arc basins also correlate with variations in the S wave velocity structure of mantle beneath four back-arc basins at 40–100 km depth [Wiens et al., 2006]. Specifically, the S wave velocities decrease with increasing temperature, with the Mariana trough as the coldest/fastest and the northern Lau basin as the hottest/slowest, strongly supporting our determination of significant thermal variations in these settings.
 Although back-arc basin basalts thus appear similar to MORBs with respect to mantle Tp, our results demonstrate they are quite different in that they have much higher H2Oo concentrations (approaching 0.5 wt % in some cases) and define positive, linear trends in H2Oo versus F. Moreover, the variations in slope correlate with the Tp variations described above based on independent measures (Na2O and FeO). The relationship between slope (dF/dH2Oo, an expression of wet melt productivity) and temperature (Figure 13) is not an unexpected result, since isothermal-isobaric models predict this effect [S&N94; Hirose and Kawamoto, 1995; G&G98; Hirschmann et al., 1999; Reiners et al., 2000; Katz et al., 2003]. On the basis of our results, melt productivities in the sources of back-arc basin magmas increase from ∼30 to 80%/wt % (i.e., % F per wt % H2Oo) as Tp increases by 150°C; this result is similar to those of MELTS calculations, which predict wet melt productivities of 20–80%/wt % over a 125°C temperature range, although offset to lower absolute temperatures and pressure (1250°–1375°C at 1 GPa [Hirschmann et al., 1999]; see Figure 13). The experimental results of G&G98 indicate melt productivities generally lower than those we have inferred (10–36%/wt % at 1200°–1350°C and 1.5 GPa; see Figure 13) but they overlap with our empirical trend at ∼1300°C.
 The correlation between dF/dH2Oo and Tp has the potential to provide an alternative approach to estimating mantle Tp; this would be particularly useful for regions with H2O concentrations too high to permit successful modeling of Na and Fe variations, in regions at which variations in source composition lead to deviations from the global MORB trend in Fe-Na, and for volcanic arc fronts [Kelley et al., 2003]. At the Valu Fa ridge (VFR), for example, water contents of erupted glasses and melt inclusions do not overlap with MORB, and the relationship between Na and Fe in these samples is disrupted by uniformly high H2O. Samples from the VFR do, however, form a steep linear trend in H2Oo versus F (Figure 12e), indicating less efficient melt productivity, which is consistent with cooler mantle Tp beneath the VFR than the northern Lau basin (Figure 13) and suggests an along-strike thermal gradient in the Lau basin. In principle, the F-intercept of the trend could also provide constraints on mantle Tp, but high errors on the intercept relative to the slope make dF/dH2Oo a more robust indicator.
 Additional factors related to mantle temperature beneath back-arc basins include cooling from the subducting plate, convergence rate, and back-arc spreading rate [e.g., Peacock, 1996; Kincaid and Sacks, 1997; Kincaid and Hall, 2003; England and Wilkins, 2004], and the calculated mantle temperatures for various back-arc basins based on our results can be used to evaluate the effects of these various factors on Tp. For example, in the Lau basin, distance from the spreading axis to the trench (and slab) decreases toward the south (Figure 14), and this may be partially responsible for cooler Tp at the VFR relative to the northern basin. Likewise, convergence rate and back-arc spreading rate are thought to be linked, since fast subduction is expected to drive more rapid wedge circulation and back-arc mantle upwelling, and the fast back-arc spreading will in turn lead to increased relative convergence between the overriding and subducting plates. Our results are consistent with these expectations: convergence rates are fast at the Tonga/Lau and New Britain/Manus (>140 mm/yr) subduction zones, where back-arc temperatures are warmer, and slow at the Mariana (40–70 mm/yr) and South Sandwich/East Scotia (67–79 mm/yr) subduction zones [Taylor and Martinez, 2003, and references therein], where back-arc Tp is cooler.
 An important test of the wet melt productivities calculated here is the effect on the volume of crust created, as recorded in crustal thickness or axial depth (e.g., Figure 15). Extents of melting at back-arc spreading centers are driven higher than MORB by the addition of H2O, and high extents of melting should result in thick crust and shallow axial depth relative to mid-ocean ridges. Axial depth at back arcs varies from ∼1900 to 4300 meters below sea level, within the range of mid-ocean ridges. Geochemical indicators of extent of mantle melting, such as Na8.0, broadly correlate with axial depth at back arcs, as at ridges (Figure 1 [see also Klein and Langmuir, 1987]), although regions with shallow axial depth and high H2Oo (e.g., the southern Lau basin and the Manus basin (Figure 1b, open symbols)) tend to have lower mean Na8.0 than ridges of the same depth. In comparison to the driest melts from each region (H2O < 0.5 wt % (Figure 1b, solid symbols)), however, average back-arc melts (Figure 1b, open symbols) are skewed to low Na8.0 (esp. basins where mean H2Oo is high; Mariana, Manus, southern Lau basins), consistent with high H2O driving higher F and lower Na8.0 (Table 3, Figure 1b).
 We may also compare back-arc mantle Tp and axial depth to that of ridges, which show a positive relationship owing to the greater thermal buoyancy, compositional buoyancy, and crustal thickness of hotter regions (Figure 15 [see also Klein and Langmuir, 1987]). We find that most back-arc spreading axes are at water depths consistent with their mantle temperatures, suggesting that the excess melt produced by high H2O leads to small shifts in axial depth, generally within the range of ridges. For the Mariana trough and the northern Lau basin, the two basins with constraints on both crustal thickness and mantle Tp, we also find that back-arc basins are within the range of normal mid-ocean ridges, albeit plotting toward the high crustal thickness side of the ridge array (Figure 15, inset). Mantle temperature thus appears to be the dominant physical variable contributing to melt generation beneath many back-arc basins. On the other hand, clear excess melt production is present for the most water-rich back-arc segments, where anomalously shallow axial depth results from the excess melt produced by H2O addition (see SLB, NLB, ESR E2-4/E9 and MB ER points in Figure 15). Thus water clearly contributes excess melt production in the wettest regions, whereas lavas from other regions may only reflect high extents of melting of small mantle source volumes and preferentially erupt wet melts.
4.2. Effects of Variable Mantle H2O Concentration
 The H2Oo concentrations at mid-ocean ridges, with few exceptions, do not exceed 0.01–0.05 wt % (max. H2Oo = 0.08 wt % at the Azores platform), which is well below the minimum storage capacity of H2O in nominally anhydrous mantle phases at pressures near the onset of melting (i.e., 0.12 wt % H2O at 3 GPa [Hirschmann et al., 2005]). On the basis of our results, however, the sources of back-arc basin basalts have H2Oo concentrations of 0.01–0.50 wt % (and possibly higher when considering degassed samples (Figure 10)). In many regions, these concentrations clearly locally exceed the minimum storage capacity of nominally anhydrous mantle minerals (i.e., 0.18 wt % H2O at 6 GPa [Hirschmann et al., 2005]). We do note that Hirschmann et al.  report a large range of permissible mantle H2O storage capacities (0.18–0.63 wt % at 6 GPa) and their preferred model indicates a storage capacity of 0.44 wt% H2O at 6 GPa, which would only be exceeded by the wettest local regions indicated by our study. We emphasize, however, that many regions locally exceed the minimum storage capacity, and back-arc basin mantle sources may thus contain some H2O in excess of the nominally anhydrous minerals. As shown in Figure 14, water concentrations in back-arc mantle tend to increase as spreading axes approach the trench. The wettest spreading segments (e.g., Valu Fa, Manus ER, East Scotia E9, Sumisu) are located ∼300 km or less from the trench. Figure 14 shows some back-arc mantle H2O in excess of average MORB up to 400 km from the trench, but the average H2Oo concentrations increase rapidly (fit by a power law) as trench distance decreases below ∼300 km. There is also evidence of even higher H2Oo values beneath the Mariana arc (Figure 14 [Kelley et al., 2003]), suggesting that the trenchward increase in H2Oo defined by back-arc basins may extend to the mantle beneath arcs. At the other extreme, the North Fiji basin has an average H2Oo similar to MORB (0.05 wt % (Table 4)) and is ∼800 km east of the New Hebrides/Vanuatu trench. The distance to the trench in this case is consistent with the low mantle H2O concentrations, and is clearly too far for this ridge to incorporate direct H2O additions from the slab. These relationships strongly suggest that the subducting slab is the ultimate source of elevated H2O at back arcs, as well as at arcs, and provide observational constraints on how H2O may be lost from the slab and transported through the mantle wedge.
4.3. Different Roles of H2O at Ridges and Back-Arc Basins
 On the basis of our results, there appears to be a distinction between basalts from mid-ocean ridges (and spreading centers distant from subduction zones), where increasing H2O is accompanied by decreasing extents of melting (i.e., dF/dH2Oo < 0), and basalts from back-arc basins, where high H2O is associated with high extents of melting (i.e., dF/dH2Oo > 0). How can we explain the different behavior of ridges and back-arc basins during wet melting? Although there are many possibilities, we focus here on the hypothesis that the contrasting trends relate to the relative concentrations of H2O in the two environments. At ridges, water is present in low concentrations, likely dissolved in solid, nominally anhydrous phases such as olivine and pyroxene prior to melting. As such, the shape of the melting regime, and the production of melts and their mixing proportions, are governed to first order by decompression paths along the solid flow field [Langmuir et al., 1992]. At back arcs, on the other hand, H2O added from the subducting plate will, according to our results, at least locally exceed the nominal storage capacity of the mantle. In such cases, excess H2O is supplied to the mantle melting region via fluids or melts, driving high degrees of melting in a process that may be independent of the solid flow field of the mantle. In this final section, we develop these ideas further, and explore some of the consequences of this hypothesis. Figures 16 and 17 portray the different processes that contribute to melting beneath mid-ocean ridges and back-arc basins. Note that these scaled cartoons are designed to be more illustrative than exclusive.
4.3.1. A Back-Arc Melting Model
 In the mantle wedge above subduction zones, P-T conditions experienced by ascending H2O, melt and mantle are unlikely to be adiabatic in the classic sense, in contrast to the conditions beneath a ridge (Figure 16). In particular, the thermal gradient above the slab is influenced by heat flow from the mantle wedge into the cold slab, so as water released from the slab (and any subsequent melt) ascends to lower pressure, its temperature increases as it migrates away from the cold slab and into the warm interior of the mantle wedge (Figure 16e, point 1 [Baker et al., 1994; Hall and Kincaid, 2001; Grove et al., 2002]). Melting under such conditions may also be described as adiabatic if heat is conserved within the system and the ascending material cools as it ascends. However, if the volumes of fluid and melt are small relative to the heat reservoir of the mantle wedge, the impact of H2O transport and melting on the heat budget of the system may be negligible and the early stages of melting may thus be nonadiabatic. Melting initiates once the mobilized H2O crosses the H2O-saturated solidus in the mantle wedge (Figure 16e, point 2). Under the conditions proposed here near the initiation of melting (high pressure and a free H2O-rich fluid phase), the fluid in the H2O-silicate system could instead be supercritical, in which case the concept of H2O-saturated melting would not apply at the earliest stages of melting [Shen and Keppler, 1997; Mibe et al., 2004]. Constraints on the supercritical behavior of basaltic melts and aqueous fluids, however, are still in their infancy and we therefore elect to describe the initiation of melting relative to the H2O-saturated solidus even at these high pressures. The nature of the melt migration process through the mantle wedge is not well known. Reactive porous flow of the H2O-rich melt through the mantle is the most likely mechanism [Davies and Stevenson, 1992; G&G98], but melt and mantle could ascend together as a buoyantly unstable parcel that upwells beneath the arc and back arc (Figure 17a [Davies and Stevenson, 1992; Hall and Kincaid, 2001; Gerya and Yuen, 2003]). The buoyant parcel may follow a path similar to that for diapiric networked flow described by Hall and Kincaid , which exchanges heat as it traverses the hot interior of the mantle wedge. Eventually, the parcel becomes entrained in the adiabatically upwelling paths beneath the back arc (Figure 16e, point 3) that cross the dry solidus (Figure 16e, point 4) and melt further due to adiabatic decompression.
 Other reasonable physical models involve separation of melt and solid flow. If melting is a fractional process, the melt and the mantle will not ascend together as a single parcel. Melt will instead become separated from its mantle source, drawing H2O with it and preventing further H2O-fluxed melting of the mantle source from taking place. In this case, however, if the mantle is resupplied and remelted by a continuous flux of H2O from the slab, then the final pooled melt will reflect the integrated, fractional melting of a single mantle source (Figure 17b). This fractional process would produce melt compositions similar to the final melt of the batch process described above [Plank and Langmuir, 1992]. In this case, the continuous flux of H2O and melt through a single mantle volume could imitate melting under isobaric, isothermal conditions, provided the process is nonadiabatic as described above, since each increment of the H2O/melt flux experiences a similar set of conditions along a path through the mantle wedge. Reactive transport of melt through the mantle wedge [e.g., Kelemen et al., 1997] might also create the appropriate H2O-TiO2 relationships, but quantitative models require better constraints on melt versus solid flow vectors in the mantle wedge.
 The resulting melt fraction, as recorded by the TiO2 concentration of the ascending melt, along the path through the mantle wedge (as illustrated in Figure 16) may be estimated with some simple approximations, borrowing from the melting models developed by Hirth and Kohlstedt  and Katz et al. . Consider mantle with 0.3 wt % H2Oo (near the high end of the back arc spectrum). This water is supplied from the subducting plate, and drives melting in the mantle at the water-saturated solidus (Figures 16e–16f, point 2). The initial H2O concentration of this melt is high (e.g., ∼30 wt % H2O [Grove et al., 2002]), but the melt H2O concentration is continually diluted as melting proceeds. When the parcel reaches pt. 3 in Figure 16e, the activity of H2O in the melt (aH2O) is 0.1, or 10% of saturation (note that the activity curve is schematically located in Figure 16e [Hirth and Kohlstedt, 1996]), and so the H2O concentration of the melt will now be ∼3.5 wt % (H2O sat. = 35% at 4.3 GPa [Katz et al., 2003]). Since melting began in a mantle with H2Oo = 0.3 wt %, we use equation (10) to determine that the melt at pt. 3 reflects ∼8% melting of this mantle (in contrast to a ridge case where, for H2Oo = 0.05 wt %, the amount of melt at this same point reflects only F = 0.04%). As the melting path becomes vertical and mantle parcels ascend adiabatically, melting continues as convective adiabatic decompression melting, with the bulk composition of the source fixed such that H2O concentration (and activity) in the partial melt decrease progressively. Melt productivity in the ascending mantle will continually decrease because the H2O content of the melt is diluted as melting proceeds, moving the effective solidus to progressively higher temperatures. In any case, we assume that melt generation above point 4 occurs at a rate similar to dry systems (∼1% melt per kilobar of ascent), attaining maximum, final melt fractions in excess of 20% [see also Gaetani and Grove, 2003]. The melting path thus reflects a combination of wet, nonadiabatic and wet, adiabatic melting (Figure 16e).
4.3.2. Breakdown of the Melting Regime “Shape” Control
 The driest back-arc basin magmas are more comparable to the mid-ocean ridge environment, where relatively dry mantle undergoes melting largely above the dry solidus, to an extent controlled by mantle Tp. Such compositions define the F-intercept of the wet melting trends characteristic of both back-arc basins and ridges (Figures 16d and 16h). When the water content of the mantle is low enough that all the water can be accommodated in nominally anhydrous mantle phases, melting is “organized” by the 2-D triangular shape of the melting regime, and provided all the melt from the triangle can be pooled, leads to a F versus H2Oo trend with a negative slope [Asimow and Langmuir, 2003; Cushman et al., 2004]. Beneath back-arc basins, the water content is large enough that significant melting takes place at depths well below those at which the shape of the melting regime has any meaning, leading to a quantitatively different set of controls on the extent of melting. Back-arc basins achieve a positive vector of increasing F with increasing H2Oo because high-F, wet melting paths contribute large F before entering the triangular melting regime (Figures 16e–16g). In the ridge case, bulk F is dominated by the large source volume of low F, wet melts. In the back-arc case, the bulk F is dominated by high F, wet melts.
 The unique geometry of plate and mantle juxtaposition at subduction zones also leads to a number of dynamical consequences for both the shape of the melting regime and the interpretation of erupted melt compositions. We examine, for example, the relationship between H2O and melt regime volume. At mid-ocean ridge settings, where H2O is present as a trace element dissolved in solid mantle minerals, the pooling of melt within the triangle leads to a decrease in bulk melt fraction with increasing H2Oo (e.g., Figure 16d [Asimow and Langmuir, 2003]). Water in such a system increases the depth at which adiabatically upwelling mantle intersects the solidus (Po), allowing the production of low-degree, wet melts within the ascending mantle before intersecting the dry solidus (Figures 16a–16d). Increasing H2Oo in this system increases both Po and the volume of the low-F, wet melting region. For the maximum H2Oo in MORB (∼500 ppm), wet melting begins at ∼4.5 GPa (∼150 km (Figure 16a)). This large, low-F, wet-melt volume below the base of the dry-melt triangle skews the bulk melt fraction over the full melting region to much lower values.
 Beneath back-arc basins, however, this relationship may not be so simple. In these settings, the initial depth of melting may be controlled by the water-saturated solidus, which is independent of the normal controls on melting regime shape imposed by mantle Tp, plate spreading, and passive corner flow as at ridges. The addition of water to back-arc mantle does allow a larger mantle volume to experience partial melting than at a dry ridge (Figure 16g), but increasing the flux of H2O into the mantle does not necessarily increase the volume of the wet melting regime. Instead, an increased flux of water effectively breaks the control of the melting regime shape on the depth and extent of melting, allowing for higher extents of melting of the same mantle volume. In this view, F increases with increasing H2Oo. Because H2Oo increases toward the trench (i.e., H2Oo is higher at shallower depths), melting will also take place at progressively shallower depths, although the amount of H2O that can be dissolved in melt at these lower pressures is much less. The depth of melting thus may, in fact, decrease as H2Oo increases in the mantle wedge.
 Another dynamical consequence of subduction zone geometry relates to melt focusing and pooling. Mid-ocean ridge magmas reflect the bulk melt fraction (FB [Plank et al., 1995]) removed from mantle passing through the wide melting region beneath the ridge, but back-arc melts may be biased toward the maximum melt fraction (FMAX). Melt focusing and pooling across the melting regime is an efficient process beneath ridges. Mantle flow beneath back arcs, however, is perturbed by wedge circulation, which deflects flow toward the wedge corner and the slab [Spiegelman and McKenzie, 1987; Conder et al., 2002; Kincaid and Hall, 2003]. This geometry could lead to preferential focusing of low-F melts from the slab side of the melting triangle into the magmatic plumbing system beneath the arc. The effect of such a process would lead to a preferential increase in the bulk F recorded by melts erupted at back arcs, and the magnitude would scale with proximity to the slab, which controls wedge circulation and H2Oo concentration. The active flux of water to the back-arc melting region may also lead to lower viscosity melts that pool more vertically, or even organize flow into vertical instabilities (Figure 17). Thus such melts may not blend as efficiently across the melting region as at ridges. In such a case, the range of lava compositions erupted at back arcs might be greater than at ridges, and we would expect to find dry and wet melts locally erupted, as is the case in the Mariana trough. Alternatively, the positive H2Oo-F trend could instead reflect binary mixing of separate melts from a dry, MORB melting regime and a high-F, wet melting regime, although in this case the initial mantle source composition could be different for each melting end-member. In order to further evaluate the distribution and relative importance of wet and dry melts and their mantle sources on local and regional scales, however, more data are required for more densely sampled back-arc regions.
 The positive relationships between H2Oo and F at back-arc basins derive from several consequences of an active supply of water from the subducting plate. (1) Water concentrations in excess of the minimum solid mantle storage capacity (>0.18 wt %) suggest the presence of free fluid or melt along a significant portion of the back-arc mantle path, rather than incorporation of H2O in solid flow as is thought to be the case at ridges. (2) Because of the inverted thermal gradient imposed by the cold subducting plate, and the small volume of initial melts relative to the mantle, the deepest parts of the melting paths beneath back arcs may not be adiabatic. (3) Melt production beneath back arcs is not governed solely by the shape of the melting regime generated by the solid flow field, but also by the magnitude of the H2O flux from the slab. (4) The extent of lateral pooling beneath back arcs may be less than at ridges, leading to a dominance of vertical pooling and strong local vectors of variability.
 The compiled data and calculations presented here confirm the unique role of H2O in the mantle melting process beneath back-arc basins. The first-order observation of negatively sloping correlations between H2O and TiO2 in erupted back-arc basin basalts suggests a relationship between H2O and extent of melting, since TiO2 is incompatible during melting and is conservative within the subduction zone (i.e., all TiO2 in the magmas is assumed to come from the mantle wedge, not from the slab). Using TiO2 to calculate the mantle melt fraction (F) reveals positive, linear correlations between H2O addition from the slab and F beneath back-arc basins the world over, but with slopes and intercepts that vary regionally. The positive wet melting functions at back arcs contrast with what is observed at mid-ocean ridges, where increasing mantle H2O contents correlate with decreasing F. We conclude that back-arc mantle temperature varies regionally by ∼150°C and plays an important role in melt production in a manner similar to mid-ocean ridges, largely controlling physical variables such as axial depth and crustal thickness, as well as wet melt productivity (dF/dH2Oo). Superimposed on temperature is the effect of H2O on melt production, as high H2Oo correlates positively with high F. The concentration of H2Oo varies in the back-arc mantle as a function of distance from the trench and relates to the orientation (+ or −) of wet melting trends modeled at back-arc basins and mid-ocean ridges. We infer that the presence of the subducting slab in close proximity to back-arc spreading centers initiates a critical change in the role of water during melting, from a relatively passive participant in adiabatic melt generation beneath mid-ocean ridges, to an active fluxing agent that drives melt generation in the back-arc environment.
 Many thanks to M. Hirschmann, R. Katz, C. Langmuir, D. Wiens, B. Taylor, A. Kent, J. Sinton, P. Asimow, G. Hirth, and P. Kelemen for sharing results, unpublished data, and discussion, which were all critical to the successful completion of this study. We also thank E. Klein, J. Dixon, and an anonymous reviewer for careful, thoughtful, and thorough reviews. This work was funded by support from NSF OCE-0001897 and the NSF MARGINS Program as well as by an NSF graduate research fellowship. Development and writing of this manuscript was also supported by a Carnegie Postdoctoral Fellowship.
Auxiliary Material for this article contains detailed information on additional tests of the melting model developed for back-arc basin basalt data, and region-specific discussion of the data and modeling outcome for each back-arc basin and mid-ocean ridge region discussed in the paper.
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|jgrb14517-sup-0002-txts01.txtplain text document, 24 KB||Text S1. This file includes the text that describes the outcome of additional model tests and the discussion of data and modeling for each specific ridge region.|
|jgrb14517-sup-0003-fs01.epsPS document, 139.7 KB||Figure S1. This figure is referred to in section A of the file 2005JB003732-txts01.txt, and shows the outcome of additional modeling tests compared to the method used in the paper.|
|jgrb14517-sup-0004-t01.txtplain text document, 1.4 KB||Tab-delimited Table 1.|
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|jgrb14517-sup-0006-t03.txtplain text document, 2.1 KB||Tab-delimited Table 3.|
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