A Reactive Porous Flow Control on Mid-ocean Ridge Magmatic Evolution

Mid-ocean ridge basalts (MORB) provide fundamental information about the composition and melting processes in the Earth’s upper mantle. To use MORB to further our understanding of the mantle, is imperative that their crustal evolution is well understood and can thus be accounted for when estimating primary melt compositions. Here, we present the evidence for the occurrence of reactive porous ﬂow, whereby migrating melts react with a crystal mush in mid-ocean ridge magma chambers. This evidence comprises both the textures and mineral major and trace element geochemistry of rocks recovered from the lower oceanic crust, and occurs on a range of scales. Reaction textures include dissolution fronts in minerals, ragged grain boundaries between different phases and clinopyroxene–brown amphibole symplectites. However, an important ﬁnding is that reaction, even when pervasive, can equally leave no textural evidence. Geochemically, reactive porous ﬂow leads to shifts in mineral modes (e.g. the net replacement of olivine by clinopyroxene) and compositions (e.g. clinopyroxene Mg–Ti–Cr relationships) away from those predicted by fractional crystallization. Furthermore, clinopyroxene trace elements record a progressive core–rim over-enrichment (relative to fractional crystallization) of more-to-less incompatible elements as a result of reactive porous ﬂow. The fact that this over-enrichment occurs over a distance of up to 8mm, and that clinopyroxenes showing this signature preserve zoning in Fe–Mg, rules out a diffusion control on trace element distributions. Instead, it can be explained by crystal–melt reactions in a crystal mush. The data indicate that reactive ﬂow occurs not only on a grain scale, but also on a sample scale, where it can transform one rock type into another [e.g. troctolite to olivine gabbro, olivine gabbro to (oxide) gabbro], and extends to the scale of the entire lower oceanic crust. Melts undergoing these reactive processes change in composition, which can explain both the major element and trace element arrays of MORB compositions. In particular, reactive porous ﬂow can account for the MORB MgO–CaO–Al 2 O 3 relationships that have previously been interpreted as a result of high-pressure (up to (cid:2) 8 kbar) crystal fractionation, and for over-enrichment in incompatible elements when compared with the effects of fractional crystallization. The ﬁnding of a signiﬁcant role for reactive porous ﬂow in mid-ocean ridge magma chambers ﬁts very well with the geophysical evidence that these magma chambers are dominated by crystal mush even at the fastest spreading rates, and with model predictions of the behaviour of crystal mushes. Together, these observations indicate that reactive porous ﬂow is a common, if not ubiquitous, process inherent to mushy magma chambers, and that it has a signiﬁcant control on mid-ocean ridge magmatic evolution.

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INTRODUCTION
Mid-ocean ridge basalt (MORB) is the most abundant volcanic rock on Earth. Critically, MORB magmas provide the geochemist with a window into the upper mantle: because they are formed directly by decompression melting of the mantle and do not traverse thick, older crust, their compositions are considered to directly reflect the composition and melting processes of their mantle source (e.g. Klein & Langmuir, 1987). This approach, however, requires that the crustal evolution of MORB can be corrected for. This is conventionally done by assuming that the crustal evolution is predominantly controlled by fractional crystallization. Given that fractional crystallization of MORB is well constrained (e.g. Grove et al., 1992), this assumption has allowed MORB compositions to be parameterized in terms of degree and depth of melting, as well as source compositions (Langmuir et al., 1992). However, a substantial range of data collected over the last decades has provided evidence indicating that the crustal evolution of MORB is complex, involving more than fractional crystallization alone. This evidence comes from both MORB itself as well as mid-ocean ridge plutonic rocks. From a MORB perspective, open-system processing has long been established to play a role [e.g. Dungan & Rhodes, 1978;Rhodes et al., 1979; see Shorttle (2015) for a recent perspective]. Furthermore, the observation initially made in the 1970s that mid-ocean ridge basalts are enriched more strongly in incompatible trace elements with decreasing MgO or Mg# than predicted by fractional crystallization (Bryan & Moore, 1977;White & Bryan, 1977;Dungan & Rhodes, 1978) has been highlighted again in recent years (O'Neill & Jenner, 2012;Lissenberg et al., 2013). Similar observations have been made in Iceland (Eason & Sinton, 2009). This signature has been variably interpreted as reflecting replenishment cycles (O'Neill & Jenner, 2012), in situ crystallization (Coogan & O'Hara, 2015) or melt-rock interaction (Eason & Sinton, 2009;Lissenberg et al., 2013) in oceanic magma chambers. Whichever model is correct, it demonstrates that crustal processing may exert a strong signature on the erupted lavas. This is further highlighted by the occurrence of ultra-depleted, high-Al melt inclusions in MORB phenocrysts, which result from the interaction of MORB with lower crustal lithologies (Danyushevsky et al., 2003;Kamenetsky & Gurenko, 2007;Laubier et al., 2012). Plutonic rocks recovered from the lower oceanic crust also record complex histories. Complex zoning patterns, reaction textures, as well as mineral compositions and modes that do not conform to conventional phase equilibria, all indicate that fractional crystallization is not the only process controlling their formation (Meyer et al., 1989;Coogan et al., 2000;Dick et al., 2002;Ridley et al., 2006;Gao et al., 2007;Lissenberg et al., 2013). Similar observations have been made for ophiolitic magma chambers (Bé dard, 1991;Bé dard et al., 2000;Sanfilippo et al., 2015b).
In summary, the available data indicate that crustal processing of MORB is complex. Hence, if we want to understand the mantle, it is imperative that we first understand the overprint imparted by the crust. As part of this effort, in this contribution we present the textural and geochemical evidence for reactive porous flow (RPF) in mid-ocean ridge magma chambers, and discuss its link to the observed array of MORB compositions. We conclude that reactive porous flow is a very common-if not ubiquitous-process in oceanic magma chambers, and that it plays a significant role in modifying MORB.

THE RECORD OF REACTIVE POROUS FLOW IN PLUTONIC ROCKS
In this section, we review the evidence for reactive porous flow in plutonic rocks from the grain scale to the lower crustal scale. We focus predominantly on plutonic rocks from three locations in the ocean basins: Hess Deep, the Kane Megamullion and Ocean Drilling Program (ODP) Hole 735B. Hess Deep exposes a lower crustal section through 1Á2 Ma lower crust formed at the East Pacific Rise (Francheteau et al., 1990;Rioux et al., 2012) and represents fast-spreading lower crust (spreading rate $130 mm a -1 ). An extensive sample collection (93 gabbroic rocks) was recovered during expedition JC-21, ranging from primitive gabbroic rocks intercalated with peridotites at the base to evolved oxide gabbros and gabbronorites near the base of the sheeted dyke complex at the top . As such, the Hess Deep JC-21 samples are the only suite representing a more or less complete stratigraphic section of the lower oceanic crust anywhere in the oceans. The Kane Megamullion (23 N, Mid-Atlantic Ridge) exposes the plutonic foundation of a 50 km long, second-order, slow-spreading (23 mm a -1 ) ridge segment, which was extensively mapped and sampled during expedition KN180-2 . Plutonic rocks formed in a series of magmatic centres surrounded by weakly magmatic peridotite-dominated areas Xu et al., 2009), and span the entire compositional spectrum of oceanic plutonic rocks, from olivinerich troctolites to oxide gabbros . ODP Hole 735B drilled 1508 m into gabbroic rocks unroofed at the Atlantis Bank core complex on the Southwest Indian Ridge, recovering a plutonic section dominated by series of generally coarse-grained olivine gabbros cross-cut by more evolved rocks (gabbronorites, oxide gabbros) and subordinate troctolite (Dick et al., 2000). It formed at a spreading rate of 15Á7mm a -1 (Baines et al., 2007), which is transitional between slow and ultraslow (Dick et al., 2003). With >20 000 electron microprobe analyses available (Dick et al., 2002), it is the bestdocumented section of oceanic lower crust. The combined sample sets from Hess Deep, the Kane Megamullion and ODP Hole 735B cover the three main ocean basins, and encompass nearly the full spreading rate spectrum; hence, they provide a relatively rigorous picture of the nature of the lower oceanic crust. Although ophiolitic plutonic sections also contain abundant evidence for melt-rock reaction (Bé dard, 1991;Bé dard et al., 2000;Sanfilippo et al., 2015b), they commonly contain rocks of different parentage (e.g. MORBlike, fore-arc basalt, island-arc tholeiite, boninite). In this setting, melt-rock reaction may be enhanced by the increased differences in major element compositions and water contents between different magma batches and their crystallization products; hence, this may not directly inform inferences about mid-ocean ridge magmatic evolution. We have therefore excluded from this study observations made in ophiolites, with one exception (trace element distributions in the Oman ophiolite lower crust).

RPF at the grain scale Textures
Reactions between melts and crystals commonly leave behind textural evidence. Arguably the most common is the presence of dissolution fronts in plagioclase (Fig. 1a). Widely described, these comprise irregular contacts between zones of different anorthite content. The difference in anorthite contents of the different zones indicates that different parental melts were involved in crystallization of the crystal, with the morphology of the contact providing evidence of a reactive origin. Dissolution fronts can be distinguished from other forms of anorthite zoning (e.g. oscillatory and continuous zoning), which do not require reaction, by the contact between the different zones being irregular and discordant to the crystallographic axes (Fig. 1a). This commonly results in embayed habits. Dissolution fronts in plagioclase do not in themselves require RPF; they are common in phenocrysts in MORB where they result from the incorporation of earlier-formed crystals in new magma batches (e.g. Dungan & Rhodes, 1978). In this scenario, disequilibrium between the crystals and the carrier melt may result in dissolution. Evidence that at least some plagioclase dissolution fronts result from RPF comes from plutonic rocks in which the dissolution process was 'frozen in'. An example of this was presented by Lissenberg & Dick (2008), who described centimetre-wide channels of coarse-grained, poikilitic  Lissenberg et al. (2013), showing dissolution fronts (blue arrows) in plagioclase in gabbro from Hess Deep (Pacific Ocean). (b) Plagioclase dissolution textures in a clinopyroxene oikocryst from a Kane Megamullion gabbro (Lissenberg & Dick, 2008). Dissolution results in irregular, embayed crystals with grain boundaries that are discordant to the crystallographic axes (highlighted by 1), and locally dissolution has proceeded the extent that parts of originally millimetre-sized grains become very thin ($100 lm; location 2). Some grains have become elongate in the direction of the a-orb-axis as a result of dissolution (sub)parallel to the c-axis ( gabbro in a medium-grained troctolite host rock from the Kane Megamullion (23 N, Mid-Atlantic Ridge). These channels formed by the percolation of clinopyroxene-saturated melts through the troctolite, which led to the melt reacting with olivine, plagioclase and Cr-spinel in the troctolite to yield clinopyroxene and lower-anorthite plagioclase in the reaction [modified from Lissenberg & Dick (2008) to incorporate the dissolution of spinel]: The dissolution of the plagioclase is captured by the plagioclase chadacrysts enclosed in the clinopyroxene: plagioclase chadacrysts have highly irregular shapes, with curved grain boundaries discordant to the crystallographic axes (Fig. 1b). Competition during cocrystallization of plagioclase and clinopyroxene can be ruled out as a cause of these textures, because plagioclase (An 65-67 ) is not in equilibrium with clinopyroxene (Mg 86-87) (Lissenberg & Dick, 2008). In places, dissolution has proceeded to the extent that only very thin (100 lm) plagioclase relics remain of what otherwise were millimetre-sized crystals. Remarkably, some plagioclase crystals were dissolved (sub)parallel to their albite twins (i.e. a-toc-axis, depending on crystal orientation in the thin section), resulting in grains that are now elongated perpendicular to their twins (i.e. along their shorter a-o rb-axes; Fig. 1b); hence, plagioclase morphology can become disconnected from its usual crystal habit. Similar textures to the ones described here have been found in other oceanic gabbro studies. Blackman et al. (2006) described rounded and resorbed plagioclase chadacrysts in pyroxene oikocrysts from Intergrated Ocean Drilling Program (IODP) Hole U1309D (30 N, Mid-Atlantic Ridge), and corroded plagioclase inclusions in clinopyroxene oikocrysts occur in gabbros recovered from IODP Hole 1256D in the equatorial Pacific Ocean (Teagle et al., 2006). Where the reactive melt is more evolved and saturated in Fe-Ti oxides, a distinct texture of irregularly shaped, resorbed plagioclase 'islands' in Fe-Ti oxides may develop ( Fig. 1c and d). The resorbed plagioclase shares many characteristics with its clinopyroxene-hosted counterparts described above: curved grain boundaries discordant to the crystallographic axes, grains elongated along a-t o b-axes, and the presence of narrow relicts of former grains ( Fig. 1c and d).
Clinopyroxene also preserves textural evidence for reaction with melts. In gabbroic rocks from ODP Hole 735B (Southwest Indian Ridge), complexly intergrown, ragged clinopyroxene-clinopyroxene grain boundaries are commonly present ( Fig. 2a and b). Furthermore, cumulus clinopyroxene crystals commonly contain zones with small ($10-100 lm) blebs of brown amphibole ( Fig. 2c and d). These zones can occur throughout the clinopyroxene grains, including areas apparently far from grain boundaries. The example shown in Fig. 2c and d occurs within a large ($2 cm) cumulus clinopyroxene grain. Their brown color, high Ti contents and their association with other magmatic phases such as Fe-Ti oxides, indicate a magmatic, not hydrothermal origin for the amphibole (e.g. Coogan et al., 2001). The brown amphibole blebs are associated with recrystallized clinopyroxene, which indicates that the following reaction was responsible for their formation: The same reaction is marked by clinopyroxeneamphibole symplectites that are common in both 735B gabbros and high-level gabbros from Hess Deep. These symplectites form at the expense of original cumulus clinopyroxene, invading the pre-existing clinopyroxene from their grain boundaries ( Fig. 2e-h); this is a form of so-called hydration crystallization reactions (Beard et al., 2004). It is important to note, however, that RPF does not necessarily leave any textural evidence: it may be cryptic, with extensive modifications in mineral chemistry in texturally pristine cumulates. A case in point is the deepest and one of the most primitive olivine gabbros recovered from Hess Deep (Fig. 3). This olivine gabbro shows a classic equilibrated texture of cumulus olivine, plagioclase and clinopyroxene (Fig. 3a). Grain boundaries are sharp and commonly straight, and there is no textural evidence for the presence of a trapped, evolved melt (e.g. no interstitial brown amphibole and Fe-Ti oxides) or any reactions in the form of dissolution fronts, symplectites or complex plagioclase zoning. A Ti-Cr element map ( Fig. 3b; see Supplementary Data for method), however, reveals that all clinopyroxene crystals are zoned, with Cr-rich cores giving way to Tirich rims. In principle, the presence of Cr-Ti zoning is in itself consistent with fractional crystallization. However, as we will discuss below (in the section on mineral trace elements), this kind of Cr-Ti zoning is an excellent indicator of core-rim incompatible trace element enrichment owing to RPF. Hence, even in rocks lacking any textural evidence for the process, RPF may be pervasive.

Mineral major and minor elements
Because the compositions of mineral phases reflect the evolution of the melt from which they crystallize, they form a solid line of descent to complement the melt's liquid line of descent. Such a solid line of descent is readily observable in global compilations of mineral compositions (Coogan, 2014), and, in clinopyroxene, is characterized by an exponential decrease in Cr 2 O 3 and increase in TiO 2 with decreasing Mg#. However, there are some significant deviations from these overall trends, leading to Mg-Ti-Cr relationships that appear contradictory to well-established phase equilibria. One of these is the occurrence of clinopyroxene with unusually high Mg#. At lower oceanic crustal pressures ( 2 kbar), MORB is not predicted to crystallize clinopyroxene until after significant olivine and plagioclase have crystallized (Grove et al., 1992). As a result, the Mg# of the melt has already dropped significantly by the time clinopyroxene saturates, with experiments providing an average Mg# of 83 for the first clinopyroxene (Grove & Bryan, 1983;Tormey et al., 1987;Grove et al., 1990Grove et al., , 1992Yang et al., 1996). Clinopyroxene with higher Mg#s, which have commonly been found in oceanic gabbros (e.g. Elthon et al., 1992), may represent formation at higher pressures (P > 5 kbar), where clinopyroxene saturation precedes that of plagioclase (Grove et al., 1992). However, the high-pressure hypothesis is inconsistent with the rock record. In a case study on the Kane Megamullion gabbros, Lissenberg & Dick (2008) found that both the textures and mineral chemistry of the high-Mg# clinopyroxene (Mg# 86-91) require crystallization at low pressure from already evolved melts. Texturally, high-Mg# clinopyroxene encloses plagioclase or occurs as an interstitial phase between olivine and plagioclase, which indicates that the melt followed the normal low-pressure liquid line of descent, with olivine and plagioclase preceding clinopyroxene. Compositionally, the TiO 2 contents of the high-Mg# clinopyroxenes extend to very high values (1Á46%), which indicates crystallization from evolved melts (Lissenberg & Dick, 2008). This is inconsistent with the early saturation of clinopyroxene required by highpressure models. These observations can be reconciled by a model in which high-Mg# clinopyroxene forms as a result of reaction between migrating melts and a primitive olivine þ plagioclase matrix [reaction (1) above; Meyer et al., 1989;Lissenberg & Dick, 2008]. Because diffusive Fe-Mg exchange between olivine and melt is rapid (Chakraborty, 1997), melts migrating through a matrix containing primitive olivine will be buffered for Fe and Mg (Meyer et al., 1989). Hence, upon crystallization, their clinopyroxene Mg# will be high, and exceed the Mg# expected on the basis of its actual degree of differentiation as indicated by TiO 2 . Alternatively, gabbro assimilation may also produce melts with elevated Mg# (Kvassnes & Grove, 2008;Leuthold et al., 2015). However, this would not produce the high TiO 2 observed, and is therefore unlikely to be important here.
Similarly complex relationships can be observed for clinopyroxene Cr 2 O 3 , which is high (up to 1Á39%) in the Kane Megamullion samples, despite the fact that the same clinopyroxene TiO 2 indicates crystallization from melts with TiO 2 contents typical for moderately evolved MORB (Lissenberg & Dick, 2008). MORB Cr reaches a plateau at about 500 ppm, for which the equilibrium clinopyroxene contains $0Á5% Cr 2 O 3 [for D ¼ 5Á9, calculated for a primitive MORB composition using equation (627) of Bé dard (2014)]. Hence, such high clinopyroxene Cr 2 O 3 cannot be explained by fractional crystallization from MORB. The fact that the troctolite matrix in which these clinopyroxenes crystallized contains Cr-spinel, but that Cr-spinel is absent in the gabbroic bands with high-Mg#, high-Cr 2 O 3 clinopyroxenes, suggests that Cr-spinel was removed by reaction during formation of the bands. This is in keeping with the predicted phase equilibria for MORB, which show that Cr-spinel is no longer on the liquidus when clinopyroxene saturates; hence, clinopyroxene-saturated melts are undersaturated in Cr-spinel. It follows that clinopyroxene-saturated melt flowing though a troctolite matrix would not only acquire a high Mg# but also dissolve its Cr-spinel, enriching the melt in Cr. The clinopyroxene crystallizing from the reacted melts will thus have high Mg# and Cr, with only its TiO 2 content reflecting the true degree of differentiation of its parental melt.
The high-Mg, high-Cr signature of the Kane clinopyroxene can be readily observed elsewhere. In Fig. 4,w e show clinopyroxene Mg#-Cr 2 O 3 -TiO 2 relationships for gabbroic (sensu lato) rocks from IODP Hole U1309D (Mid-Atlantic Ridge; data from Miller et al., 2009). There is a significant population of high-Mg#, high-Cr 2 O 3 clinopyroxenes (Fig. 4a). These clinopyroxenes form a distinct array in Cr-Ti space (Fig. 4b), maintaining high Cr 2 O 3 concentrations at increasing TiO 2 , even when TiO 2 concentrations increase to $1%, which would suggest crystallization from a highly evolved melt ($2Á4% TiO 2 assuming D ¼ 0Á42 [D calculated from Bé dard (2014) using mean composition of high-Mg#, high-Cr 2 O 3 clinopyroxenes from Lissenberg & Dick (2008)]). Hence, although one might presuppose from the Mg#-Cr data that these clinopyroxenes represent grains crystallized from very primitive melts, their Cr 2 O 3 -TiO 2 relationships reveal that in fact the melts from which they formed were moderately to highly evolved. These relationships are the same as those in the well-studied Kane Megamullion sample of Lissenberg & Dick (2008), and we interpret the U1309D data in similar terms: melts that evolved to clinopyroxene saturation percolated through, and reacted with, a primitive olivine-and Cr-spinel-bearing matrix, leading to Mg#-Cr-Ti relationships unlike those expected in normal crystallization scenarios. This interpretation fits well with the fact that some of the high-Mg#, high-Cr 2 O 3 clinopyroxenes occur in olivine-rich troctolites, which have previously been interpreted as hybrid rocks formed by melt percolation into peridotites (Suhr et al., 2008;Drouin et al., 2009Drouin et al., , 2010. However, they are also abundant in rock types that form major building blocks of the lower oceanic crust (troctolite, olivine gabbro and some gabbro; Fig. 4).
Hence, we conclude that mineral major and minor element relationships may be significantly shifted away from those predicted by conventional models (i.e. those based on crystal-melt equilibrium) as a result of RPF. In the case of clinopyroxene, this results in the formation of what would commonly be interpreted as primitive and high-pressure crystals at low pressures and from evolved melts.

Mineral trace elements
Mineral trace elements are sensitive tracers of crystallization processes. Progressive fractional crystallization will lead to enrichment in incompatible trace elements, coupled with a decrease in compatible trace elements in both the melt and its crystallization products. The zoning patterns in crystals can be readily compared with fractional crystallization scenarios provided that accurate partition coefficients are available. In oceanic gabbros, mineral trace element studies to date have made a number of significant observations. First, clinopyroxene is commonly strongly zoned in trace elements. However, the core-rim enrichment in incompatible elements does not generally fit fractional crystallization models: highly incompatible trace elements are enriched beyond what is predicted by fractional crystallization relative to less incompatible trace elements (Coogan et al., 2000;Gao et al., 2007;Lissenberg et al., 2013). There is a systematic relationship between the degree of this over-enrichment and the degree of incompatibility of a trace element in a gabbroic system . A prominent example is the over-enrichment of Zr to Nd: because the bulk partition coefficient of Zr in a gabbroic system is markedly lower ($0Á06, reflecting the low Zr D in plagioclase) than that of Nd (bulk D of $0Á15), Zr is enriched more quickly than Nd, leading to an increase in Zr/Nd with progressive crystallization. This increase is greater than predicted by fractional crystallization, but can be reproduced by combined assimilation-fractional crystallization (AFC) models (Coogan et al., 2000;Lissenberg et al., 2013). Hence, the grain-scale over-enrichment in incompatible trace elements has been interpreted to result from dissolution-reprecipitation reactions between migrating melts and a crystal mush (Coogan et al., 2000;Gao et al., 2007;Lissenberg et al., 2013).
Recently, Coogan & O'Hara (2015) argued that, instead of a reactive origin, the trace element distributions in oceanic clinopyroxene are controlled by diffusion. They envisaged that these crystals become initially zoned through crystallization of evolved trapped melts, and that the zoning patterns are then modified by diffusion to lead to the observed trace element fractionation. The diffusion of Zr, for example, was assumed to be significantly slower than Nd, leading to the increased Zr/Nd signature in the clinopyroxene rims that is so often observed (Coogan et al., 2000). To test the reactive vs diffusion hypotheses for trace element zonation, we have acquired a detailed (170 points) laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) core-rim traverse across a large clinopyroxene grain from an olivine gabbro from ODP Hole 735B ( Fig. 5 and Supplementary Data Table 1; see Supplementary Data for analytical procedures; all sup plementary data are available for downloading at http:// www.petrology.oxfordjournals.org). This sample is typical of the dominant olivine gabbro lithology that forms the bulk of the 735B section, with a coarse-grained, granular texture (Fig. 5a). The selected clinopyroxene grain provides an ideal test case for the role of diffusion: it is sufficiently large ($1Á5 cm) that diffusion cannot realistically have modified the trace element distributions across most of the crystal given the diffusion rates in clinopyroxene (e.g. Van Orman et al., 2001) and the cooling rates prevalent in the lower oceanic crust (Coogan et al., 2007). Moreover, an Fe-Mg-Na element map reveals that the grain is zoned in Fe-Mg ( elements (Dimanov & Wiedenbeck, 2006;Mü ller et al., 2013), the preservation of Fe-Mg zoning provides a strong indication that the incompatible trace elements should preserve their original magmatic distributions. Hence, if the trace element distributions are controlled by RPF (see Lissenberg et al., 2013) they will show the over-enrichment associated with this process. On the other hand, if the over-enrichment that is generally observed is produced by a diffusive overprint of enriched rims formed by fractional crystallization (Coogan & O'Hara, 2015), the trace element distributions in the 735B grain studied here should, in the absence of significant diffusion, follow a fractional crystallization pathway.
In Fig. 5c we show the core-rim distribution of selected trace elements (Cr, Ti, Y, Yb, Nd, Zr, Ce and La) in an $8 mm core-rim traverse across the 735B clinopyroxene. These distributions are presented as enrichment factors: the concentration of an element at a given step relative to its concentration in the core. The grain is strongly zoned, with the enrichment in La, Zr and Ce reaching a factor of $30. In terms of absolute (c) Enrichment factors (¼ concentration at given step divided by the core concentration) of Cr, Ti, Y, Yb, Nd, Zr, Ce and La. Irregular peaks, best displayed in Ti (e.g. at 4Á7 mm and 6Á3 mm), result from the beam overlapping minor inclusions, but do not appear to have a major effect on the overall profiles of the trace elements. Dark grey band outlines data point taken to represent the core; light grey band marks data points taken to represent enrichment prior to saturation of trace phases such as ilmenite. (d) Enrichment factor for the Ce/Y ratio. abundance, the core has a composition close to that of clinopyroxene in equilibrium with MORB (mean La ¼ 0Á17 ppm for the first four points), whereas the rim composition, which peaks at $4Á6 ppm, indicates growth from a strongly enriched melt. There is a significant difference in enrichment between La, Zr and Ce on the one hand and Y and Yb on the other (Fig. 5c). As a result, the Ce/Y ratio [the most precisely measured proxy for the degree of light to heavy rare earth element (LREE/HREE) fractionation in clinopyroxene owing to the high absolute concentrations of Ce and Y relative to the other LREE and HREE respectively] increases significantly from core to rim, showing an enrichment factor of $4 ( Fig. 5d). Zr/Nd increases to a maximum of $1Á9, although it decreases near the rim, where Zr concentrations show a slight dip. Ti shows a slight decrease in the second half of the profile, probably reflecting ilmenite saturation, which, along with the decrease in Mg# towards the rim, indicates that the melt that formed the rim was evolved beyond the point of oxide saturation.
Consistent with the presence of Fe-Mg zoning, we find no evidence for diffusion of the trace elements. There is a strong correlation between the enrichment of elements with different diffusion coefficients [e.g. Zr vs LREE vs middle REE (MREE)], such that increases and decreases in enrichment occur in the same place for these different elements [as also observed by Gao et al. (2007)]. Diffusion would lead to significant offsets in enrichment profiles between elements with different diffusivities. Furthermore, there is no decrease in La near the clinopyroxene rim, which would be predicted to occur if diffusion operated (Coogan & O'Hara, 2015). Hence, the data demonstrate that the trace element distributions are primary magmatic features. They do not, however, fit fractional crystallization trends. A fractional crystallization model for the interval of the grain that represents crystallization along the three-phase olivineplagioclase-clinopyroxene cotectic (i.e. prior to ilmenite saturation; 0-3Á9 mm), derived using cotectic proportions of olivine þ plagioclase þ clinopyroxene (0Á075-0Á435-0Á49, respectively) and the partition coefficient compilation of Bé dard (2001) is shown in Fig. 6. We first fit a fractional crystallization model to the measured Ce enrichment for this interval, and then examine whether the model fits the other elements. We find that, to match the Ce enrichment, 79% mineral fractionation (i.e. F ¼ 0Á21) is required. It is clear, however, that the fractional crystallization model fails to provide a match for Y, which is lower than predicted (Fig. 6a). Similar to Zr/Nd, this is another example of the over-enrichment of more incompatible elements (Ce) relative to less incompatible ones (Y): the 79% fractional crystallization scenario only achieves a Ce/Y enrichment factor of 1Á20, well short of the observed factor of $1Á7 ( Fig. 6b). Hence, fractional crystallization cannot explain the trace element distributions in the first 3Á9 mm of the profile. Moreover, fractional crystallization cannot, under any circumstances, produce the Ce/Y enrichment factor of >4 observed towards the clinopyroxene rim: even 99Á9% fractionation (F ¼ 0Á001) only increases the Ce/Y ratio by a factor of 2Á3 ( Fig. 6b). We therefore conclude that, although diffusion may play a role in small, slowly cooled grains, the over-enrichment in incompatible elements is a primary signature of a magmatic process that is more efficient than fractional crystallization at fractionating trace elements. Coogan et al. (2000) and Lissenberg et al. (2013) successfully modelled the incompatible trace element over-enrichment using AFC models. Given that crystalmelt reactions are likely to operate by dissolutionreprecipitation (Liang, 2003), there is some justification for this approach. However, AFC models do not take into account the second significant finding of trace element studies of oceanic gabbros: that clinopyroxene cores  as well as plagioclase  and olivine (Drouin et al., 2009;Sanfilippo et al., 2014) may be strongly depleted in trace elements compared with what is expected of crystallization from MORB, although it should be pointed out that this depletion is not universal (e.g. the clinopyroxene core in Fig. 5 is in equilibrium with MORB). Because the degree of depletion in plagioclase (and to a certain extent olivine) correlates with partition coefficients, but  (2001). It should be noted that fractional crystallization fails to reproduce the observed enrichments, even after 99Á9% fractionation (F ¼ 0Á001). not diffusion coefficients , the process governing these distributions appears to be a magmatic one. Lissenberg et al. (2013) proposed that the depleted cores, where present, represent the residue of the reactions that generated the trace element enriched melts from which the clinopyroxene rims crystallized: as such, the enriched clinopyroxene rims are the trace element enriched counterpart to the depleted cores. If so, zone refining, a process by which a passing melt front depletes a solid framework in its impurities (i.e. incompatible elements) through (partial) melting (Pfann, 1952;Harris, 1957;McBirney, 1987), may be a more appropriate model to apply to oceanic gabbros. We model zone refining using the equation from (Harris, 1957): where C L is the concentration of an element in the liquid after zone refining, C 0 is the initial concentration of that element in the liquid, D is its partition coefficient, and l is the number of equivalent volumes of solids processed by the liquid. However, the choice of appropriate values for these input parameters is not straightforward; there is significant uncertainty on both l and the mineral modes and any potential modal changes associated with zone refining, which makes it difficult to select appropriate partition coefficients. We have therefore modelled three scenarios, covering different l and different mineral modes (Fig. 7). To test whether zone refining may explain the trace element enrichment observed in the 735B clinopyroxene from Fig. 5 we compare the enrichment in trace elements (i.e. C L /C 0 )of the zone refining models with the clinopyroxene data (Fig. 7). As before, we have taken the enrichment in the analysed clinopyroxene crystal to the point of saturation of trace phases (outlined by the grey box in Fig. 5) to focus on melt evolution in a cotectic olivineplagioclase-clinopyroxene system. Despite the uncertainty relating to l and phase proportions during zone refining, the correlation between zone refining and the natural clinopyroxene data is significant in all models (R 2 ¼ 0Á83-0Á95; Fig. 7). Hence, the over-enrichment of trace elements in clinopyroxene relative to fractional crystallization (as illustrated in Fig. 5) is similar to that expected to develop during zone refining of a gabbroic system. This is consistent with the hypothesis that RPF in oceanic magma chambers occurs though a process akin to zone refining . In summary, the crystal-scale distributions of trace elements in oceanic gabbros appear to be controlled by a type of reactive process that redistributes trace elements, over-enriching the melts in incompatible elements relative to fractional crystallization.

Sample scale
Oceanic gabbroic rocks are commonly complex on a sample scale. Excellent examples are provided by cores recovered by ocean drilling, which commonly contain different gabbroic rock types with complex relationships on a small (centimetre to decimetre) scale. Element mapping is an excellent tool to investigate such complexities, and we here present two examples from Hole 735B ( Fig. 8; see Supplementary Data for method). The first is from a fine-grained troctolite unit, which contains strings of medium-grained olivine gabbro ( Fig. 8a and b). The contact between the two lithologies ranges from diffuse to moderately sharp. The Fe-Mg-Na element map of a thin section containing a troctolite-olivine gabbro-troctolite profile reveals that there is a continuous gradation in Fo content of the olivine from the troctolite (Fo 80 ) to the olivine gabbro (Fo 70 ). Furthermore, the An content of plagioclase in the troctolite (An 72 ) is higher than that of the olivine gabbro (as low as An 54 ). Critically, some plagioclase crystals in the olivine gabbro preserve resorbed cores of higher An plagioclase that is similar to that of the host troctolite, and small, high-Mg# clinopyroxene grains (Mg# 87) occur in the top left corner of the troctolite. The occurrence of high-Mg clinopyroxene in the troctolite indicates that the olivine gabbro is unlikely to simply be a vein in the troctolite, even if Fe-Mg diffusion during and/or after intrusion is invoked to produce the Fo gradient. This is because, like their Kane counterparts, the high-Mg# clinopyroxene occurs together with olivine and plagioclase, and therefore cannot have formed by fractional crystallization, requiring formation through reaction with the troctolite olivine instead (see above). Together, the observations imply that a three-phase saturated melt percolated through the troctolite, resorbing the anorthitic plagioclase of its host, and crystallizing lower-An plagioclase, lower-Fo olivine and clinopyroxene. Percolation of small volumes of intergranular melt into the troctolite matrix formed the small high-Mg clinopyroxene crystals. Fe-Mg diffusion between the percolating melt and the olivine of the troctolite lowered the Fo contents of the troctolite olivine, generating the observed Fo gradient. Hence, the olivine gabbro strings formed through reactive porous flow of a more evolved and clinopyroxene-saturated melt through the troctolite. This is consistent with the irregular nature of the strings as revealed by core observations (Fig. 8a).
A second example of complex sample-scale relationships is provided in Fig. 8c and d. This medium-grained olivine gabbro contains a narrow (0Á5-1 cm) oxide gabbro mylonite band: one of the hallmarks of the 735B section (Dick et al., 2000;Natland & Dick, 2001). The contact in hand specimen appears to be sharp (Fig. 8c). An Mg-Fe-Na-P element map (Fig. 8d) reveals that the oxide gabbro contains markedly lower An plagioclase and clinopyroxene Mg# (An 25 , Mg# 71) compared with its host (An 43 , Mg# 78), which is consistent with its high mode of Fe-Ti oxides and apatite. However, the oxide gabbro contains relict resorbed cores of plagioclase with An contents similar to that of the olivine gabbro. Furthermore, the cumulus clinopyroxene in the olivine gabbro is zoned in Fe-Mg: low Mg# rims (Mg# 74), which are invaded by small brown amphibole blebs similar to those shown in Fig. 2d, are intermediate between the core (Mg# 78) and the clinopyroxene in the oxide gabbro (Mg# 71). These relationships require that a highly evolved melt infiltrated the olivine gabbro and reacted with its constituent minerals to produce the oxide gabbro. The integrated melt flux was high in the centre of the sample, leading to an evolved, Fe-Ti oxide-and apatite-rich oxide gabbro with completely re-equilibrated clinopyroxene, and low towards the edges of the sample, leading to zoning of cumulus clinopyroxene, with the formation of low-Mg#, amphibole-bearing reaction rims, plus An zoning of cumulus plagioclase (Fig. 8d). Similar to the example of the olivine gabbro string in the troctolite ( Fig. 8a and b), porous flow of melt through a plutonic rock has fundamentally changed its mineralogy and composition.
These two examples illustrate that RPF may be responsible for the evolution of plutonic rocks, at least on a sample scale. In both cases, it has transformed one rock type into another, and was the dominant control on the An-Fo-cpx Mg# relationships. By extension, it would have had a significant effect on the compositions of the melts involved. Literature data suggest that these cases are far from unique. Other well-described examples include the following: (1) the formation of olivine-rich troctolites by the infiltration of migrating melts into the olivine framework of mantle peridotites in both oceanic (Suhr et al., 2008;Drouin et al., 2009Drouin et al., , 2010Sanfilippo et al., 2015a) and ophiolitic sections (Sanfilippo et al., 2014); (2) the transformation of troctolite into gabbro in rocks from the Kane Megamullion (Lissenberg & Dick, 2008).

Lower crustal scale
To constrain the length scale over which RPF operates we examine the clinopyroxene trace element distributions within two stratigraphic sections through the lower crust. Because only one more or less complete section through lower crust is available in the oceans (Hess Deep; Lissenberg et al., 2013), we also include a section through the lower crust of the Oman ophiolite (Wadi Abyad;MacLeod & Yaouancq, 2000;Coogan et al., 2002b;Thomas, 2003). This section samples gabbroic rocks that formed during the main axial stage of crustal growth (Geotimes unit), whose magmas, with the exception of elevated water contents, were MORBlike (Godard et al., 2006;MacLeod et al., 2013). Although the nature of the reaction processes may be influenced by the elevated water contents of the magmas, our purpose in this section is to examine the scale, not the exact nature, of RPF. Given that the physical parameters that govern melt migration and mush compaction (melt fraction, permeability, viscosity, buoyancy of melt relative to solid) are likely to be similar between Oman and a mid-ocean ridge magma chamber, we Trace element enrichment in clinopyroxene is taken for the interval of the grain that represents crystallization along the three-phase olivine-plagioclase-clinopyroxene cotectic (i.e. prior to ilmenite saturation, outlined by the grey box in Fig. 5). Partition coefficients used in the zone refining model are from the compilation of Bé dard (2001).
consider using Oman as a second case study for the scale on which RPF operates, to be justified. The stratigraphic variation of clinopyroxene chondritenormalized (Anders & Grevesse, 1989) Ce/Y ratios is illustrated in Fig. 9. Although there is considerable complexity at any given level owing to large grain-scale variations in trace element ratios (see mineral trace element section above), there appears to be an overall increase in clinopyroxene Ce/Y between different stratigraphic levels. It is low (averaging $0Á2 at Hess Deep and $0Á15 in Oman) in the lower half of the crust, where primitive layered gabbros are exposed in both sections (MacLeod & Yaouancq, 2000;Lissenberg et al., 2013;Gillis et al., 2014). The ratio then increases, particularly at Hess Deep, in the overlying gabbros, which generally exhibit a marked foliation that is steeply dipping both in Oman  and Hess Deep (ODP Hole 894G; MacLeod et al., 1996). Another step increase in clinopyroxene Ce/Y (to $0Á35 at Hess Deep and $0Á25 in Oman) occurs in the top few hundred metres, where evolved, isotropic gabbroic rocks are exposed in both Oman (MacLeod & Yaouancq, 2000;Coogan et al., 2002b)a n d Hess Deep . Hence, both sections show an up-section increase in clinopyroxene Ce/Y by a factor of around 1Á6-1Á7. We note that this is a minimum: at least at Hess Deep, the common occurrence of apatite in the isotropic gabbros indicates that melts at this level reached apatite saturation, which would have decreased Ce/Y, accounting for the lower end of the Ce/Y range observed at this level.
The up-section increase in clinopyroxene Ce/Y could be due to either variations in the degree of LREE depletion of the parental melts to the sections (i.e. a mantle signature) or crustal-level differentiation processes, and the same is true for the grain-scale variations in trace element ratios (Fig. 5d) diagrams (e.g. Ce/Y vs Mg#; Fig. 10). In this scenario, magma mixing during cumulate formation may result in cumulates with intermediate trace element signatures, as well as cumulate grains zoned in trace elements. However, there are three arguments against this scenario. First, there is no evidence of distinct series of cumulates (Fig. 10). Instead, the data show that Ce/Y increases with decreasing Mg# (Fig. 10). This inverse correlation covers a large range of Mg#, and is present both on a grain scale (Mg# 84-70: Fig. 5) as well as a stratigraphic scale (e.g. Hess Deep, Mg# 88-65: Figs 9 and 10). Second, rims are systematically more enriched than cores, which would not be expected if the trace element zoning was due to mixing: mixing would occur in both directions (i.e. N-MORB rims on E-MORB cores and vice versa), which is not observed. Third, there is no apparent reason why melts with higher Ce/Y ratios should be emplaced systematically higher in the crust, and that this pattern would be present at Hess Deep as well as Oman. Hence, the data do not support a mantle control on incompatible trace element distributions. Instead, the fact that the enrichment develops upwards through the lower crust and is coupled with decreasing Mg# provides strong evidence that it is a differentiationcontrolled feature. However, the data indicate that this differentiation process is not fractional crystallization.
As shown above, fractional crystallization is not very efficient in fractionating Ce from Y. We model the upsection Ce/Y fractionation at Hess Deep by taking the average anorthite content of plagioclase from the deep (>1800 m below dyke-gabbro transition; Fig. 9a) and shallow (<250 m) levels of the Hess section (An ¼ 76Á6 and 52Á7, respectively; data of Lissenberg et al., 2013), and relating these to melt mass of a fractional crystallization path of a primary East Pacific Ridge (EPR) magma. The latter was derived by regression of the PetDB EPR dataset (Lehnert et al., 2000), and is provided in Table 1 (see Supplementary Data for details). The fractional crystallization path, modelled using MELTS (Ghiorso & Sack, 1995) at pressure of 1Á5 kbar, oxygen fugacity of QFM -1 (where QFM is quartz-fayalitemagnetite buffer) and an assumed H 2 O content of 0Á15 %, indicates that the difference in plagioclase anorthite content between the deep and shallow levels at Hess Deep records 50Á4% mineral fractionation. Assuming Ce and Y bulk D values of 0Á12 and 0Á23, respectively  Lissenberg et al.,20 13 ). Samples from expedition JC-21 presented here are consistent with the observations in the drill holes, and define three levels with markedly different mineral compositions . The mean clinopyroxene Ce/Y shown here therefore uses this three-fold subdivision. Data points represent single spot analyses, and are taken from Lissenberg et al. (2013) (Hess Deep) and Coogan et al. (2002b) and Thomas (2003) (Wadi Abyad). of plagioclase yields a Ce/Y fractionation factor of 1Á13. Although there is inherent uncertainty in these models, both factors fall well short of the observed fractionation factor of 1Á6-1Á7. Hence, the trace elements in the lower oceanic crust are controlled by a differentiation process that is more effective than fractional crystallization at fractionating trace elements.
Similar to the grain-scale zoning presented above (Fig. 5), the ratio of Ce/Y examined here reflects a broader observation: that any incompatible element is enriched up-section more at a given amount of fractionation relative to less incompatible elements compared with fractional crystallization models . In other words, more-to-less incompatible elements in the Hess Deep and Oman gabbroic rocks are systematically over-enriched up-section. Because the same enrichment signature is present from core to rim, Lissenberg et al. (2013) argued that the same process was responsible for both the core-rim and up-section distribution of trace elements. The arguments presented by Lissenberg et al. (2013), and reiterated above, indicate that this process was RPF. Hence, the fact that the incompatible trace element ratios increase throughout the entire lower crust, and that this observation holds for both Hess Deep and the Oman ophiolite, indicates that RPF occurred on the scale of the entire lower crust.

THE LINK TO MORB
If RPF occurs on a lower crustal scale, this raises the question of whether it plays a role in the petrogenesis of MORB. The major element perspective of this question was addressed by Lissenberg & Dick (2008). Their detailed study of the Kane Megamullion samples (see section on 'textures') indicated that the generation of gabbroic bands in troctolite is governed by the reaction of melt with olivine, high-An plagioclase and Crspinel to generate clinopyroxene þ low-An plagioclase [reaction (1) above]. The element map showing the transformation of a Hole 735B troctolite into olivine gabbro ( Fig. 8a and b) is fully consistent with this reaction: clinopyroxene precipitates in the olivine gabbro band, and relatively anorthitic plagioclase is resorbed, being replaced by lower-An plagioclase. Reaction (1) is not the only reaction occurring in gabbroic crystal mushes, as evidenced, for example, by the clinopyroxeneamphibole symplectites [reaction (2)]. However, the symplectites appear to occur mainly on a grain scale (Fig. 2) and may result from local reaction of evolved melt at relatively small melt fractions. In contrast, reaction (1) occurs in channels, and extends to relatively large scales (at least outcrop scale; Lissenberg & Dick, 2008, fig. 12). Furthermore, its hallmark signature (high-Mg# clinopyroxene) is a common constituent in oceanic gabbros (e.g. Fig. 4). Hence, it is likely to be an important reaction in oceanic magma chambers during melt transport.
Because plagioclase occurs on either side of this reaction (albeit with a different composition), the net modal change effected by the transformation of troctolite into olivine gabbro is the replacement of olivine by clinopyroxene. The effect of this reaction on the full major element inventory of the melt was modelled by Lissenberg & Dick (2008); Cr was not included, because the small proportion of spinel assimilated means that it does not significantly affect the major elements. The main findings were that the melt shifts in composition to lower CaO and higher Al 2 O 3 , and that melt MgO increases. Combined, this leads to a compositional shift away from the low-pressure liquid line of descent that is very commonly observed in MORB: a shift towards higher MgO at a given CaO (e.g. Lissenberg & Dick, 2008, fig. 10). Previously, this spread was interpreted to represent a difference in the pressure of fractional crystallization (Grove et al., 1992;Danyushevsky et al., 1996;Michael & Cornell, 1998;Herzberg, 2004 Fractional crystallisatio n Fig. 10. Relationship between clinopyroxene Mg# and chondrite-normalized (n) Ce/Y ratio for the lower crustal section exposed at Hess Deep. Also shown is a fractional crystallization pathway (red) for clinopyroxene in equilibrium with MORB, with a primitive Hess Deep clinopyroxene core as the starting composition. The fractional crystallization trend was derived from a MELTS model of the primary EPR MORB presented in Table 1. Mineral modes along the liquid line of descent predicted by MELTS were used to calculate bulk D values for Ce and Y at each step, allowing the Ce and Y evolution of the melt to be determined. Clinopyroxene Ce/Y values were then calculated from melt Ce/Y using the partition coefficients of Bé dard (2001). Data from Lissenberg et al. (2013). 2007): at elevated pressures, the clinopyroxene stability field expands relative to that of plagioclase, leading to earlier clinopyroxene fractionation and hence a CaO decrease at relatively high MgO. Hence, the MORB liquid lines of descent were parameterized for pressure of fractionation, showing that pressures of up to 8 kbar are common (Grove et al., 1992;Danyushevsky et al., 1996;Michael & Cornell, 1998;Herzberg, 2004;Villiger et al., 2007). According to these parameterizations, a large majority (72%) of glasses from the Mid-Atlantic Ridge would have last crystallized in the upper mantle prior to eruption, with a large peak at $4 kbar or $12 km, resulting in an average of 17-19% gabbroic (P < 5 kbar) and ultramafic (P > 5 bar) cumulates in the upper mantle . There are a number of problems with this interpretation. First, it is inconsistent with the rock record. Mantle sections, where recovered, do not typically show a large proportion of cumulate rocks. Furthermore, olivine melt inclusion CO 2 -H 2 O relationships indicate that the deepest crystallization occurs at $9km ($3 kbar) below the seafloor at slow (Wanless et al., 2015) and even ultraslow-spreading ridges (Shaw et al., 2010), where crystallization would be predicted to be deepest. Finally, at oceanic core complexes, which represent melt-poor lithospheric accretion along slowspreading ridges, and which in at least some cases comprise gabbroic plutons embedded in mantle peridotites (e.g. Kelemen et al., 2004), crystallization depths have been shown to be $6-8 km, equivalent to $2-3 kbar (Grimes et al., 2011;Schoolmeesters et al., 2012;Lissenberg et al., 2016). Second, is not clear how melts would be erupted from depths of up to $25 km, as implied by the pressure calculations, without further increments of crystallization or mixing. On the basis of these arguments, and because the shift in melt composition during reactive formation of clinopyroxene-rich lithologies from olivine-rich ones matches the shift in MORB compositions, Lissenberg & Dick (2008) proposed that the MORB array reflects, at least in part, RPF in lower crustal magma chambers. The common occurrence of high-Mg# and high-Cr clinopyroxene (Fig. 4), and the fact that the troctolite-to-olivine gabbro reactions have now also been observed in the Hole 735B section (Fig. 8), lend further support to this contention.
Regarding trace elements, we have shown above that RPF produces an over-enrichment of more relative to less incompatible elements when compared with fractional crystallization predictions, and that this signature occurs both on a grain scale (Fig. 5) and on a lower crustal scale (Fig. 9). O'Neill & Jenner (2012) presented the trace element distributions of a global suite of ocean floor basalts, and similarly found that incompatible trace elements are more enriched and fractionated than can be accomplished by fractional crystallization. Lissenberg et al. (2013), focusing on Ce and Y, demonstrated that this is also the case for the PetDB EPR dataset (their fig. 9).
Here, we explore to which extent the incompatible trace element enrichment in the lower crustal rocks matches that observed in MORB. To this end, we compare the enrichment in the detailed core-rim profile in the Hole 735B olivine gabbro (Fig. 5) with the global ocean floor basalt trace element distributions (O'Neill & Jenner, 2012). These trace element distributions reflect the crustal evolution of mantle melts. The parameterization of a large suite of trace elements versus MgO provided by O'Neill & Jenner (2012) allows the crustal evolution of ocean floor basalts to be calculated. Using this parameterization, we calculate the enrichment in the global trace element dataset between 8Á6 and 5Á6wt % MgO, which represents the window in which the O'Neill & Jenner (2012) model to account for the trace element distributions reaches steady state. It should be noted that the result of our comparison is independent of the chosen MgO window: it is the slopes of the trace element data versus MgO that are relevant for comparison with the clinopyroxene data. For the 735B clinopyroxene profile, we calculate the enrichment to be from the crystal core to the point of saturation of Fe-Ti oxides (light grey box in Fig. 5), to focus on melt evolution in a three-phase saturated system and to avoid the uncertainties introduced on the partition coefficients by the saturation of trace phases such as ilmenite. The results are shown in Fig. 11. The correlation between the trace element enrichment in the 735B clinopyroxene and that observed in ocean floor basalts is very strong (R 2 ¼ 0Á97), which demonstrates that the trace element distributions in ocean floor basalts are consistent with an origin by RPF in the lower crust.

How common is reactive porous flow?
Above, we have shown that RPF can play an important role in the evolution of oceanic plutonic rocks, and that the resulting major and trace element distributions are similar to those in MORB. To assess whether RPF represents a bona fide candidate for controlling MORB compositions we need to establish not only its scale (Fig. 9), but also its extent. In Fig. 12, we compile the existing trace element data for clinopyroxene from the lower oceanic crust. Focusing once again on Ce-Y relationships during differentiation, in Fig. 12 we show the global array in clinopyroxene Ce-Y, as well as fractional crystallization and zone refining predictions for comparison. The data reveal two important observations. First, the global clinopyroxene array shows much stronger enrichment in Ce relative to Y than fractional crystallization can account for, mimicking the grain-scale observations in Fig. 5. In contrast, zone refining can generate the observed over-enrichment in Ce relative to Y, with additional fractional crystallization of resulting melts required to reproduce the evolved end of the global data array. Second, the observation of Ce overenrichment holds for samples from the three main ocean basins (Pacific, Atlantic and Indian Oceans). Hence, the signature of RPF is a general feature in the lower oceanic crust. The observation that trace element fractionation correlates inversely with Mg# (Fig. 10) indicates that RPF is an inherent part of the differentiation process in oceanic magma chambers.
An important role for RPF fits well with theoretical considerations on crystal mush evolution. Recently, Solano et al. (2014) developed a quantitative model of a crystal mush undergoing compaction, which included heat, mass and major and trace element transport and reaction. They made two significant findings that are relevant here. The first is that melt migrating through a compacting crystal mush will react with the mush. Critically, they found that melts migrating through a homogeneous mush column, as well as melts in sill-like bodies cooled from above and below, acquire an enriched trace element signature. Similar to the observations in gabbros , the enrichment in incompatible elements exceeds that predicted by conventional models. The second finding is that melt migration through a crystal mush may lead to the formation of high-porosity melt layers. This provides a mechanism for reacted melts to concentrate and, owing to the instability of melt-rich zones in a compacting mush, to escape upwards. An additional mechanism of extracting reacted interstitial melts from the crystal mush is its destabilization by small amounts (10-20%) of partial melting (Huber et al., 2011). Given that the emplacement of hot, primitive melt into crystal mush is likely to be a common process at mid-ocean ridges, partial melting and the resulting unlocking of the surrounding crystal mush could potentially occur. In conclusion, the available models for crystal mush evolution indicate that crystal mushes are inherently reactive, and that reacted melts may be extracted from them.
The parallels between these physico-chemical models of crystal mush evolution and the pervasive reaction in oceanic magma chambers revealed by the natural data are striking. The model predictions of trace element enrichment and the fact that these enrichments are indeed found in oceanic gabbros together indicate that upward reactive flow of interstitial melt in crystal mushes is a generic process that is expected to operate in any magma chamber in a mushy state. This is further supported by the fact that RPF is common in layered intrusions (Irvine, 1980;Bé dard et al., 1988;McBirney & Sonnenthal, 1990;Mathez, 1995;Boudreau, 1999;Namur et al., 2013;Leuthold et al., 2014). Hence, RPF appears to be the norm, not the exception, in mushy magma chambers.

The compositions of reactive melts
The available data enable us to place some constraints on the compositions of the melts responsible for the observed reactions. In some samples [e.g. the primitive olivine gabbro from Hess Deep (Fig. 3) and the 735B troctolite-olivine gabbro ( Fig. 8a and b)], the reaction  Fig. 10, with a starting composition of Ce N ¼ 0Á66 and Y N ¼ 4Á9. Two zone refining models are shown, which were calculated using equation (1), using a cotectic assemblage (model 1) and an assemblage of 80% clinopyroxene-20% plagioclase (model 2). It should be noted that the global array shows over-enrichment of Ce relative to Y compared with fractional crystallization, and that this holds true for samples from the three main ocean basins (EPR, East Pacific Rise; MAR, Mid-Atlantic Ridge; SWIR, Southwest Indian Ridge). Zone refining can generate the observed Ce over-enrichment, with additional fractional crystallization of the resulting melts required to reproduce the evolved end of the global data array. Data are from Coogan et al. (2000Coogan et al. ( , 2002a, Gao et al. (2007), Drouin et al. (2009) and Lissenberg et al. (2013).
Core-rim enrichment factor 735B clinopyroxene  products are olivine, plagioclase and clinopyroxene, suggesting that the reactive melts were relatively hightemperature, cotectic melts. Because their Mg# may have been buffered by reaction with the matrix (Lissenberg & Dick, 2008), using clinopyroxene Mg# or Fo contents of olivine as a tracer of the degree of evolution of these melts is problematic. Plagioclase anorthite contents are more reliable in this respect, because buffering is unlikely owing to the slow coupled NaSi-CaAl diffusion (Morse, 1984), although the reaction may modify the composition of the plagioclase in equilibrium with the reactive melt to some degree (Lissenberg & Dick, 2008). Plagioclase in the element maps of the primitive olivine gabbro from Hess Deep (Fig. 3) shows only minor zoning, with many rims maintaining An contents similar to the cores (An 79 ), indicating crystallization from primitive melts. Although still on the threephase olivine-plagioclase-clinopyroxene cotectic, plagioclase in the olivine gabbro channel in the 735B troctolite-olivine gabbro, as well as the gabbro channel in the Kane troctolite (Lissenberg & Dick, 2008), has lower An contents (An 54 and An 67 , respectively), indicating that the reactive melts became more evolved. To investigate just how much more evolved these melts were, we ran a fractional crystallization model for the primary melt of Dick et al. (2000) using MELTS (Ghiorso & Sack, 1995), assuming 0Á15% H 2 O, oxygen fugacity of QFM -1 and a pressure of 2 kbar. This primary melt composition was derived for the Southwest Indian Ridge; however, because its Na 2 O contents are at the lower end of the Southwest Indian Ridge array, and are typical of Atlantic MORB, this melt is a reasonable approximation for both the Southwest Indian Ridge and Mid-Atlantic Ridge samples. The results are shown in Fig. 13, and indicate that melts crystallizing An 67 (Kane) are basaltic, with an Mg# of $56 (i.e. they are typical MORB). The An 54 in the 735B olivine gabbro channel would have formed from more evolved MORB (Mg# $40). Plagioclase extends to still lower An contents in some samples, indicating that reactive melts can reach highly evolved compositions (see below).
TiO 2 may be the best indicator of melt evolution in clinopyroxene, provided that the melt has not yet reached Fe-Ti oxide saturation; it is not a major constituent in olivine, plagioclase and clinopyroxene, and, being moderately (rather than highly) incompatible, is not very sensitive to the incompatible trace element over-enrichment induced by RPF. Figure 4 shows that the group of high-Cr clinopyroxenes that we attribute to reactions of melts with a primitive gabbroic matrix have TiO 2 contents of 0Á3-1Á1 wt %, indicating that these crystals formed from melts with $0Á7-2Á4 wt % TiO 2 [for D ¼ 0Á45, calculated from equation (606) of (Bé dard, 2014) using typical oceanic clinopyroxene compositions]. The clinopyroxene in the 735B olivine gabbro channel (Fig. 8b) falls within this range as well, with a clinopyroxene TiO 2 of 0Á86% indicating crystallization from a MORB melt with $1Á9% TiO 2 . The global correlation between TiO 2 and Mg# in MORB indicates that the lower end of this TiO 2 range is typical for primitive MORB, with the higher end reflecting evolved MORB (Mg# < 50).
There are several observations that indicate that reactive melts can extend to highly evolved compositions: (1) evidence for saturation in trace phases; this evidence comes directly from petrographic and element map observations (e.g. the common occurrence of accessory apatite and zircon, as well as quartz, in the upper, most reacted parts of the Hess Deep section and the abundance of Fe-Ti oxides and apatite in Fig. 8d), and from clinopyroxene trace element data, which show decreasing Ti, P and Zr towards the rim in some crystals, reflecting saturation of Fe-Ti oxides, apatite and zircon, respectively; (2) the low An content of plagioclase in some reacted domains (e.g. An 25 in the oxide gabbro of Fig. 8d); (3) the common association of reacted domains with brown amphibole (e.g. Fig. 2), indicating significant fractionation of MORB to reach elevated water activities. The fractional crystallization model for slowspreading MORB compositions (Fig. 13) indicates that apatite saturates with $12% melt mass remaining, when the melt has reached an Mg# of $19, and is andesitic (SiO 2 $ 60%). This provides a minimum degree of differentiation for the reactive melt forming the apatite-rich oxide gabbro in Fig. 8d. Its An 25 plagioclase indicates the melt was in fact even more evolved (dacitic, with SiO 2 $ 67%; Fig. 13).
In summary, the data indicate that reactive melts range in composition from primitive (basalts) to highly evolved (dacites), which implies that RPF occurs over the full temperature spectrum of evolution of oceanic plutonic rocks.

Testing competing models for MORB evolution
There are currently four competing hypotheses for the differentiation process of MORB: (1) fractional crystallization, which is the traditional model for MORB  Fig. 13. Compositions of olivine, plagioclase, clinopyroxene, low-Ca pyroxene and melt as a function of melt mass remaining during differentiation of slow-spreading MORB. Primary melt composition was taken from Dick et al. (2000), and was modelled using MELTS (Ghiorso & Sack, 1995)a tP ¼ 2 kbar and QFM -1. Star marks apatite saturation. evolution, and relies on the instantaneous separation of saturated phases from the melt; owing to extensive phase equilibia studies, this can be predicted with reasonable accuracy (e.g. Grove et al., 1992); (2) RepTapFrac, which describes a magma chamber that goes though cycles of replenishment (Rep) followed by melt extraction (Tap) and then fractional crystallization (Frac) (O'Hara, 1977;Albarè de, 1985;O'Neill & Jenner, 2012); (3) in situ crystallization in a replenished magma chamber, during which a fractionating magma reservoir receives a contribution of enriched melt extracted from the underlying crystal mush (Langmuir, 1989;Coogan & O'Hara, 2015); (4) RPF, which posits that MORB includes a component of melts that evolved through reaction within a crystal mush . Contamination by assimilated hydrothermally altered crustal rocks (Coogan et al., 2003;Wanless et al., 2010), or partial melts thereof (France et al., 2014), may add to the complexity, and appears to be particularly relevant for dacitic lavas (Wanless et al., 2010). Any successful model for the evolution of MORB needs to fulfil three criteria: (1) it needs to reproduce the compositional array of MORB; (2) it needs to be consistent with the rock record; (3) it needs to be compatible with available constraints on the nature of midocean ridge magma chambers. The first of these criteria only partly discriminates between the four models for MORB evolution. As shown previously, fractional crystallization cannot reproduce the trace element distribution patterns of MORB (Bryan & Moore, 1977;White & Bryan, 1977;Dungan & Rhodes, 1978;O'Neill & Jenner, 2012;Lissenberg et al., 2013), and thus fails the first test. RepTapFrac and in situ crystallization can both successfully reproduce the MORB trace elements (O'Neill & Jenner, 2012;Coogan & O'Hara, 2015), and we have shown in this study that the same is true for RPF (Fig. 11).
The second of the three criteria is that the proposed mechanism is compatible with the rock record. As outlined above, this is not the case for fractional crystallization: it requires a high proportion of mineral fractionation at high pressures, which is not compatible with existing constraints on the crystallization depths of plutonic rocks, and cannot reproduce the trace element distributions in the gabbroic rocks. Only RPF can account for the depletion in clinopyroxene cores, plagioclase and olivine: in fractional crystallization, RepTapFrac and in situ crystallization models, crystallization is governed by equilibrium partitioning at the crystal-melt interface during crystal growth, which would prevent the formation of highly depleted crystals from melts with MORB compositions. This does not, however, rule out RepTapFrac and in situ crystallization models, as RPF could, in principle, represent an overprint on cumulates produced in RepTapFrac or in situ magma chambers, although the fact that reactions are also found in gabbroic xenoliths in axial lavas (Gurenko & Sobolev, 2006;Ridley et al., 2006) indicates that reactions occur at least in part beneath the ridge axis.
The third criterion is that the model needs to be compatible with the constraints on the nature of mid-ocean ridge magma chambers, which we briefly review here. At the magmatically most robust spreading ridges such as the East Pacific Rise, seismic data have identified a melt lens at the base of the sheeted dykes, which is present along much of the ridge axis (Harding et al., 1989;Kent et al., 1990Kent et al., , 1993Vera et al., 1990;Carbotte et al., 2013). An important, but generally neglected, observation is that the melt lens is composed of crystal mush (<40% melt) along substantial proportions of its length (80-90% at 14 S, >75% at 9 N), with only 2-4 km sections containing high (>70%) melt fractions (Singh et al., 1998;Xu et al., 2014). This kilometre-scale petrological segmentation is superimposed on small-scale (hundreds of metres) variations in crystal content (Marjanovi c et al., 2015). The variation in crystallinity is most probably the result of the very short time scales (a few decades) of cooling of melt to mush in an axial melt lens (Singh et al., 1998). The melt lens overlies a large region characterized by low seismic velocities interpreted as a crystal mush with a small (<15%) average proportion of melt (Crawford et al., 1999;Vera et al., 1990;Dunn et al., 2000;Crawford & Webb, 2002), which contains sills with higher melt fractions Marjanovic et al., 2014).
At slow-spreading ridges (away from hotspots) the magmatic system is less robust, and melt-rich bodies are scarce , with the Lucky Strike segment the only segment documented to date with an axial melt lens (Singh et al., 2006;Combier et al., 2015). It overlies a lower crustal low-velocity zone that may contain a small (1%) portion of melt (Seher et al., 2010). Along the rest of the Mid-Atlantic Ridge, no melt-rich bodies have been found: where present, melts occur in small proportions (most probably a few per cent) in low-velocity zones occupying the deeper (2-10 km) parts of the crust and uppermost mantle (Canales et al., 2000;Dunn et al., 2005). The scarcity of magma-rich bodies at slow-spreading ridges is consistent with microearthquakes generally extending to 5-8 km (Toomey et al., 1985;Kong et al., 1992;Wolfe et al., 1995;Barclay et al., 2001), indicating that the crust is characterized by a relatively cool thermal structure (Dusunur et al., 2009). It is also consistent with ridge axis thermal models (Sleep, 1975;Chen, 2004). Together, a picture emerges of a relatively cool ridge axis with episodic emplacement of melts, which then cool quickly to a mush before complete solidification. It is these constraints that models for MORB evolution must take into account.
One of the main distinguishing features between the RPF model on the one hand, and the RepTapFrac and in situ models on the other, is the nature of the magma chamber. RPF requires a crystal mush to operate, whereas RepTapFrac and the in situ crystallization model require a long-lived and melt-filled magma chamber. The RepTapFrac parameterization indicates that as many as several hundred cycles are required to explain the abundances of incompatible trace elements such as La at 5Á6% MgO (the limit of the steady-state operation of RepTapFrac;O'Neill & Jenner, 2012) The in situ crystallization of Coogan & O'Hara (2015) is proposed to occur in similarly replenished magma chambers. As discussed above, the geophysical constraints indicate that crystal mush is the norm in oceanic magma chambers, and that melt turns into mush quickly. This is true even for the melt lens at fastspreading ridges; at slow-spreading ridges, there is a near absence of melt-filled magma chambers. These constraints pose a serious challenge to models that depend on the presence of long-lived, melt-rich magma chambers. In contrast, the common occurrence of crystal mush provides favourable conditions for RPF to operate. Because the over-enrichment is observed in lavas across the spreading rate spectrum, but long-lived melt-rich magma chambers apparently are not, we argue that RPF is the most viable mechanism to explain the MORB array.

SYNTHESIS AND OUTLOOK
The data presented here demonstrate that RPF is a common-if not ubiquitous-process in oceanic magma chambers. It changes both major and trace elements in the crystal mush, and leads to the formation of melts with compositions that do not match conventional crystallization models. Both the occurrence of RPF and the resulting changes in melt composition are predictable consequences of the mushy state of magma chambers (Solano et al., 2014), and similar features are also present in layered intrusions on the continents (e.g. Irvine, 1980). Together, this suggests that reactive porous flow is intrinsic to large mafic magma chambers.
The apparent ubiquity of RPF in mid-ocean ridge magma chambers, coupled with the excellent fit between the trace element distributions caused by RPF and those observed in ocean floor basalts (Fig. 11), leads us to posit that RPF has a major control on the evolution of MORB. We contend that if the trace element evolution in the plutonic rocks matches that in the volcanic rocks, the likelihood is that the same process is responsible for both. It would be highly fortuitous if the trace element distributions in erupted lavas matched those in their crystal residues but they result from different processes. RPF can account not only for the observed trace element over-enrichment in plutonic and volcanic rocks, but also the apparent high-pressure signal in both MORB (shifts in MgO-CaO-Al 2 O 3 ) and gabbroic rocks (high-Mg# clinopyroxene). Our model for the evolution of MORB is thus a holistic one, tying together the evolution of the plutonic and volcanic components of the system.
We envisage the following general scenario for MORB evolution. Primary melts are emplaced as meltrich bodies in the lower crustal crystal mush (fastspreading ridges and magmatically robust slow-spreading ridge segments) or in already cooled lower crust or upper mantle (magma-poor slow-and ultraslow-spreading ridge segments). The high crystallization rate over a limited temperature interval after plagioclase saturation (Kelemen & Aharonov, 1998) rapidly leads to the formation of a crystal framework. Owing to the buoyancy of the interstitial melt the mush compacts, leading to melt migration by porous flow and the associated reactions described here. Because porous flow leads to the formation of melt-rich layers in the crystal mush (Solano et al., 2014), melts with an RPF signature (over-enriched trace elements and/or modified MgO-CaO-Al 2 O 3 ) are extracted from the crystal mush and concentrated. This facilitates upward transport of these melts, either to feed eruptions, or to feed into melt-rich bodies further up-section. In addition, the crustal-scale over-enrichment in trace elements (Fig. 9) indicates that there is a pervasive low-volume flux of reactive melt, which may mix into eruptible reservoirs . The end product is a plutonic section and overlying volcanic rocks that both carry the distinct signature of RPF.
Our understanding of the RPF process is only in its infancy. A number of different approaches would improve this. One of these is experimental studies, which would allow reconstruction of the rates, mechanisms and chemical consequences of melt-crystal reaction (e.g. Kvassnes & Grove, 2008;Leuthold et al., 2015). Physico-chemical models have the potential to shed further light on the conditions required for RPF, the percolation rates and potential length scales involved, the extraction mechanisms of melts from crystal mushes, and, if phase diagrams are included (see Solano et al., 2014), the chemical consequences of RPF. Stable isotope constraints (e.g. Pogge von Strandmann et al., 2015) have the potential to provide information on the time scales involved. Finally, the rock record can be mined to build up a database of relevant observations, which serve as a benchmark for the experimental and modelling studies. In particular, the detailed study of samples taken from a well-defined field context has the potential to add significantly to our understanding of RPF.

FUNDING
This work was supported by the Natural Environment Research Council NERC Grant NE/I001670/1 to C.J.L. and used samples and/or data provided by the Ocean Drilling Program (ODP). ODP is sponsored by the US National Science Foundation (NSF) and participating countries under management of Joint Oceanographic Institutions (JOI), Inc.

SUPPLEMENTARY DATA
Supplementary data for this paper are available at Journal of Petrology online.