Investigating solid mantle upwelling rates beneath mid-ocean ridges using U-series disequilibria, 1: a global approach

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Earth and Planetary Science Letters 157 (1998) 151–165

Investigating solid mantle upwelling rates beneath mid-ocean ridges using U-series disequilibria, 1: a global approach C.C. Lundstrom Ł , Q. Williams, J.B. Gill Earth Sciences Board, University of California, Santa Cruz, CA 95064, USA Received 10 July 1997; revised version received 20 January 1998; accepted 12 February 1998

Abstract U-series disequilibria in MORB produce trends of (230 Th)=(232 Th) as a function of (238 U)=(232 Th) for given lengths of ridge often defined by first-order segmentation. These trends are most easily explained as mixing between melts derived from chemically heterogeneous mantle sources. We propose that the slopes of these disequilibria trends provide a method for constraining solid upwelling rates beneath mid-ocean ridges that may avoid difficulties in interpreting absolute disequilibria. Melting models based on melt ascent under both equilibrium and disequilibrium transport conditions are used to explore the effect of solid upwelling rate variations on the slope of such trends. Solid upwelling rate variations have no effect on the slope of the disequilibria trends in near-fractional melting models in which melting only begins in the presence of garnet. If the high (238 U)=(232 Th) melt is derived from melting spinel peridotite, then near-fractional models can produce an upwelling rate dependence. Equilibrium porous flow models have a greater dependence of slope on upwelling rate. This dependence occurs irrespective of whether or not the high (238 U)=(232 Th) melt comes from a garnet-bearing source. We regress all available U-series data from individual areas of ridge for both the slopes of the trends and the corresponding errors. The slopes of all trends except one decrease as spreading rate decreases, consistent with the prediction of our modeling. The sole exception is the trend of data from the northern MAR which produces a well-defined mixing trend with samples from Sao Miguel (Azores) suggesting it is influenced by plume-type melting. The dependence of disequilibria slopes on spreading rate suggests that melting rate variations are recorded by 230 Th excess variation. This mutual variation is most easily explained as a direct relation between spreading rate and solid upwelling rate. The close correspondence between the observed dependence of slope on spreading rate and the modeled dependence of slope on upwelling rate is consistent with purely passive plate driven flow of the solid mantle beneath ridges.  1998 Elsevier Science B.V. All rights reserved. Keywords: mantle; mid-ocean ridges; U-238=Th-230; convection

1. Introduction Mid-ocean ridges play a major role in both the plate tectonic cycle and the geochemical and thermal Ł Corresponding

author. Present address: Department of Geological Sciences, Brown University, Providence, RI 02912, USA. Fax: C1 (401) 863-2058; E-mail: [email protected]

evolution of the Earth. Yet, despite an abundance of diverse constraints on their chemistry and dynamics, a unified understanding of how ridges operate remains elusive. Although it is agreed that melting results from pressure release in an upwelling column of mantle material, the rates of melting and melt movement, the distribution of melt, and the style of mantle melting and upwelling remain controver-

0012-821X/98/$19.00  1998 Elsevier Science B.V. All rights reserved. PII S 0 0 1 2 - 8 2 1 X ( 9 8 ) 0 0 0 3 8 - 7

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sial. Because the observed fractionations of elements within the uranium series decay chain (U-series disequilibria) most likely result from differential flow of melt and solid, they yield insight into specific aspects of melt generation. When coupled with an appropriate flow model, a range of properties including the manner of melt transport and the rate of solid upwelling may be constrained. Therefore, U-series disequilibria provide a critical link between the observed chemistry, geophysical models, and observations of sub-ridge seismic anomalies. U-series disequilibria were first suggested as a probe of solid upwelling and melting rates beneath ridges by McKenzie [1] but subsequent work [2,3] concluded that no relationship between spreading rate and disequilibria existed. Here, we approach the problem differently by considering the U-series observations on a local scale with particular attention to seeing through the effects of source heterogeneity. We examine a series of numerical models that assume a heterogeneous mantle and show that a relation between the upwelling rate beneath a ridge and the disequilibria is expected. We then analyze MORB U-series data as a function of spreading rate and find that the available data are consistent with a direct relation between half-spreading rate and the solid upwelling rate.

2. General observations of U-series disequilibria in MORB The most fundamental observation regarding the 238 U–230 Th systematics of MORB is the consistent correlation between (238 U)=(232 Th) and (230 Th)=(232 Th). This correlation is discussed in the majority of MORB U-series studies to date [4–9] and is illustrated for individual areas of ridge in Fig. 1. The choice of samples and segments shown in Fig. 1 is discussed in Section 4. The correlations in Fig. 1

show that the amount of 230 Th excess is a function of Th=U and that a large range in zero-age 230 Th excesses occurs within single lengths of ridge. Prior evaluations of a spreading rate dependence [2,3] simply averaged the disequilibria for a given length of ridge; by so doing, these treatments ignored an important observation – the ubiquitous correlation between 230 Th excess and Th=U. Furthermore, these treatments produced error bars around each average value that were much larger than the analytical error for the individual data points. The simplest explanation for the correlation between 230 Th excess and Th=U is that both Th=U variation and radioactive disequilibria reflect fractionation by changes in the degree of melting (F). However, the experimentally constrained partition coefficients for Th and U between mantle minerals and melt [10–12] are so similar and small that extremely small degrees of melting are required to produce the disequilibria. These small melt fractions are inconsistent with the stable trace element systematics of MORB in general and for the samples with U-series measurements in particular. This inconsistency is exacerbated when (226 Ra)=(230 Th) or (231 Pa)=(235 U) are considered. Similarly, it could be postulated that the trends observed are analogous to ‘local trends’ [13], representing melts from different depths within a polybaric near-fractional melting column with the highest Th=U and high (230 Th)=(238 U) representing deep, low degree melts. This explanation is unlikely for two reasons. First, given the small values for their partition coefficients, Th and U are effectively removed from the solid within the first 0.5% fractional melting [3], implying that melts from shallower in the melting column have virtually no leverage with which to create the observed mixing array. For example, the U concentration in the source decreases by 7 orders of magnitude and Th=U decreases by 4 orders of magnitude during only 4% near-fractional

Fig. 1. The trends of MORB U-series data for differing sections of mid-ocean ridge (A–H) produced by both mass spectrometry and alpha spectrometry. Reported 2¦ errors are shown except in H which shows 1¦ . Samples with measured 226 Ra excesses are solid while open symbols denote .226 Ra/=.230 Th/ D 1:00 or the existence of no data. York linefits [31,32] are given. For each area of ridge, good correlations are seen between (238 U)=(232 Th) and (230 Th)=(232 Th) that are most easily explained as mixing between melts derived from enriched and depleted sources. (A) Gorda Ridge: sample from Escanaba Trough omitted from regression because of contamination. (B) 9–10ºN EPR: only zero age samples used [7]. (C) Juan de Fuca: two samples from axial seamount omitted. (E) NMAR: highest (238 U)=(232 Th) sample omitted because of contamination. (H) two samples (not shown) omitted because of contamination.

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Fig. 2. The decrease of U and Th=U in the solid source with progressive near-fractional melting. This calculation uses the dynamic melting model of Ref. [17] and a mode of 12% garnet and 8% cpx, Rm of 0.4%=km, max of 0.15% for a 45-km-long melting column, although only the first 10 km (4% melting) are shown. Note how quickly the U-series elements are stripped from the residue such that only the initial ¾0.5% melting contributes to excesses, in agreement with previous conclusions [3]. Because of this rapid depletion, the observed trends are unlikely to represent mixing of melts from different depths in a near-fractional melting column. Retained melt cannot slow the elemental depletion rate in the solid because  required by the disequilibria is so small.

melting (Fig. 2). While it cannot be wholly excluded that depleted melts within the melting column might approach such compositions, the observed concentrations and Th=U in all MORB ever sampled must be dominated by the initial melt of the column. Second, the observed trends show no relation to Na8.0 – Fe8.0 systematics of the samples, and the majority of U-series data come from either Pacific ridges or the Azores and 33ºS regions of the Mid-Atlantic Ridge where no clear local Na8.0 –Fe8.0 trends exist. Instead, differences in Th=U in MORB probably reflect differences in Th=U of the sources within the melting region [14], as do ratios of other highly in-

compatible elements. If so, then the observed trends imply that the amount of disequilibrium depends on how different source materials melt. Mixing of melts, sources, or both must account for the trend observed in each data set (Fig. 1). Here, we explicitly assume that Th=Umelt D Th=Usource and that the observed trends result from mixing. The observed variation in disequilibria of three parent–daughter pairs (226 Ra–230 Th, 231 Pa–235 U and 230 Th–238 U) as a function of Th=U [4,9] supports these assumptions. Because wide variations in Th=U and 230 Th excess can occur in spatially proximate basalts, the mixing trends may reflect the effect of enriched mafic veins within the peridotite source [4,15]. Geochemically, these veins may not differ substantially from OIB source material, although volumetrically they are likely to be minor relative to peridotite. Because the concentrations of U-series nuclides often differ greatly between enriched MORB (EMORB) and primitive depleted MORB (Th concentrations of EMORB are 40–60 times those of depleted MORB in the Siqueiros Transform [16]), any enriched veins in the source can contribute significantly to the U– Th budget of normal MORB (NMORB) while not affecting the crustal production rate. Thus, most of the 230 Th excess in NMORB may reflect a volumetrically small, but chemically significant (for incompatible elements), pollution of peridotite-derived melt (tholeiite) by a melt derived from a trace elementrich mafic vein source. 2.1. A method for seeing through source heterogeneity If mixing between melts from heterogeneous sources occurs, then most geochemical probes are limited in their usefulness for investigating the melting process. U-series disequilibria are unique in that all source materials, regardless of differences in Th=U and fertility, are in secular equilibrium prior to melting with identical parent–daughter activity ratios of 1.0. Therefore, the endmembers of the mixing trend still provide a great deal of information about the melting process [9]. However, despite equal starting conditions in the differing sources, greater 230 Th excesses are usually observed in EMORB (higher Th=U) relative to NMORB (lower Th=U). This is consistent with enriched sources having more gar-

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net and=or beginning to melting at greater mantle depths. Although the observed fractionations between very incompatible U-series nuclides cannot be reconciled with variations in degree of melting, many numerical treatments [1–3,17–20] have demonstrated that the observed disequilibria can result from twophase flow during melting. That is, despite degrees of melting that eventually remove all U-series nuclides from the solid residue, differential flow between melt and solid creates disequilibria that ‘ingrow’ during melting through elements having different residence times in the melting column. As melting occurs and melts move relative to the surrounding solid, the rate of elemental transfer from solid to melt depends on the melting rate of the source which itself is a function of the solid upwelling rate. Thus, the amount of disequilibrium in the endmembers of the mixing array should reflect differences in the solid upwelling rate. The goal of our modeling is to evaluate whether variations in this ingrowth process for two representative depleted and enriched sources can simulate the observed slopes of the trends as a function of differences in upwelling rate. Ingrowth models show that several factors affect the amount of disequilibria produced by melting. First, increasing the depth of melt initiation can produce greater 230 Th excesses [10]. Therefore, increased mantle potential temperature or regional water contents will produce greater 230 Th excesses at any particular Th=U [22]. Second, the average Th=U for each area in Fig. 1 varies considerably indicating that the characteristics of the different sources such as fertility are probably region specific. Therefore, the absolute position of the trends both horizontally and vertically may reflect important influences that cannot be easily constrained (Fig. 3A). Consequently, absolute disequilibria are unlikely to be useful in determining relative or absolute upwelling rates. However, if the generation of (230 Th)=(238 U) in the endmember melts depends on upwelling rate, then the slopes of the trends should rotate systematically regardless of the vertical position of the trend (Fig. 3A). Slope variation provides the first-order observation that can see through the effects of ubiquitous source heterogeneity in MORB and examine upwelling rate variations.

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3. Modeling U-series disequilibria in a heterogeneous mantle There are two endmember models for U-series ingrowth during melting. First, melt transport can occur in chemical equilibrium with the surrounding solid, here referred to as equilibrium porous flow (EPF) [17]. Alternatively, melt transport can be chemically isolated, here referred to as dynamic melting (DM) [1,18]. As originally demonstrated by Spiegelman and Elliott [17], equilibrium porous flow produces greater U-series disequilibria than does dynamic melting for a given set of parameters. Changes in the melting column length affect EPF and DM models differently. Table 1 gives a series of models that show how different mineral modes and melting column lengths affect excesses in the two types of models. Because both U and Th are readily stripped from the solid residue during nearfractional melting (D DM) (Fig. 2), changes in the melting column length in dynamic melting models produce no change in disequilibria [9]. In contrast, greater 230 Th excesses are produced by an increased melting column length in EPF models [10]. The increase in 230 Th excess with EPF melting column length occurs for two reasons. First, residence time differences (between U and Th) are increased. This effect is greatest at slow upwelling rates and becomes unimportant at fast upwelling rates. Second, for one-dimensional models, longer melting columns with higher degrees of melting produce greater melt velocities in the upper column reducing the amount of 230 Th decay. Note that greater excesses result from simultaneously increasing both mode and melting column length than would be predicted by simply increasing the individual parameters independently. The relation we assume below between the fertility of the source (i.e. mode of garnet) and the depth of initial melting is consistent with the observation that mafic source materials have lower solidi [15]. EPF models with variable melt initiation depths provide quantitatively better explanations than do DM models for observations from the Juan de Fuca [9] and Mid-Atlantic Ridges [21], and for a suggested global relation between ridge depth and 230 Th excess [22]. The inability of dynamic melting models to explain these observations suggests that portions

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C.C. Lundstrom et al. / Earth and Planetary Science Letters 157 (1998) 151–165 Table 1 Effect of column length and mineral mode on EPF and DM models

230 Th

excesses in

Ws (m=yr)

max a (%)

Initial depth (km)

gt=cpx mode

(230 Th)=(238 U) EPF b

DM b

0.01 0.01 0.01 0.01 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1

0.23 0.23 0.30 0.30 0.23 0.23 0.30 0.30 0.23 0.23 0.30 0.30

70 70 100 100 70 70 100 100 70 70 100 100

0.12=0.08 0.30=0.20 0.12=0.08 0.30=0.20 0.12=0.08 0.30=0.20 0.12=0.08 0.30=0.20 0.12=0.08 0.30=0.20 0.12=0.08 0.30=0.20

1.22 1.31 1.33 1.47 1.14 1.25 1.19 1.33 1.10 1.19 1.11 1.21

1.12 1.24 1.09 1.19 1.05 1.13 1.05 1.13 1.03 1.07 1.03 1.07

cpx=l D cpx=l D Th D 0:015, U D 0:01 gt=l D D 0:015 [12]; bulk D U Th;U D

[10]; gt=l DTh D 0:0015; 0:001 in sp lherz. (makes D 0:4%=km; final depth 25 km;

upper melt column inert). Rm gt–sp lherz transition D 60 km. a max scaled to reflect same permeability in all models. b Both models use equations from Ref. [17].

of the chemical signature of MORB reflect continuous re-equilibration of ascending melts with the surrounding mantle. However, this conclusion conflicts with the most commonly suggested models of MORB production and extraction which postulate rapid transport without chemical equilibration and pooling of near-fractional melts from different depths in the melting column [13,23]. The conflict between the U-series data and other geochemical probes may reflect the presently incomplete understanding of the chemistry and physics of melt extraction and the role of chemical heterogeneity in the mantle. However, it could also mean that different geochemical probes give information about

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different depths in the melting column. For instance, the 230 Th disequilibria data could reflect chemical equilibrium within the deepest portion of the melting column, while the abyssal peridotite data [23] could reflect shallower loss of equilibrium. These two possibilities are not mutually exclusive, but we will hereafter ignore whether MORB equilibrates in the upper melting column (¾50–25 km depth) because equilibration there has relatively little impact on the (230 Th)=(238 U) of the melt [17]. For simplicity, we adopt a simple treatment of mantle chemical heterogeneities; clearly, significant work remains which will further refine and distinguish endmember processes. There is considerable uncertainty in the precise mineral modes, source lithologies, and mechanisms of reactive flow as a function of depth in the melting column. The productivity (% melting=km decompression) during melting also may change as a function of depth [24] or even source fertility. Nevertheless, as long as melting rate remains a function of upwelling rate, the slopes of the 230 Th excess trends should record variations in the solid upwelling rate. We simplify the problem by using the same EPF model as in [9] and compare this to a DM model where transport times are accounted for [17], with all other parameters held the same. Therefore, the essential physical contrast between the two models becomes apparent without introducing ill-constrained complexity. The EPF model intends to examine the endmember process that occurs in a locally equilibrated vertical melt column above a melting heterogeneity. We do not imply that equilibration of all melts occurs with all sources in the melt column because this would erase the effects of the heterogeneities and is inconsistent with the modeled meter per year rates of melt ascent [25,26].

Fig. 3. An equiline diagram showing the slopes of mixing lines between melts created by equilibrium porous flow (solid lines) and dynamic (dashed lines) models as Ws (solid upwelling velocity) is varied. Black squares denote initial composition in all models. Arrows show projected ingrowth during melting. (A) schematic diagram indicating the likely effects of mantle temperature variations, source fertility variations and upwelling rate variations on the positions and slopes of hypothetical mixing lines (gray fields). (B) Mixing of enriched and depleted melts derived from two garnet-bearing sources. No dependence of slope on upwelling rate is seen for the dynamic model, while the equilibrium porous flow model shows an upwelling rate dependence. Models using an intermediate composition (dots and pluses) do not necessarily lie on the mixing trend of the endmembers, indicating that mixing of sources does not necessarily create linear trends. The decrease in 230 Th excess in the slowest Ws EPF model reflects the stronger effect of transport in the spinel peridotite field. (C) Mixing between modeled enriched melts and a depleted melt that has .230 Th/=.238 U/ D 1:0. In this case, dynamic melting models produce some slope dependence, but the dependence is not as great as equilibrium porous flow models.

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For the models, we assume a range in (238 U)=(232 Th) based on the spread typically observed in MORB. Because the enriched component appears to dominate the (230 Th)=(238 U) of MORB due to concentration differences, discerning the (230 Th)=(238 U) in the depleted (high (238 U)=(232 Th)) endmember is not simple. Almost all MORB have 230 Th excess, so a logical conclusion would be that both endmember melts are derived from garnet-bearing sources. However, the observed mixing trends could as well reflect garnet pyroxenite-derived melts with high 230 Th excess and high Th concentrations dominating over spinel peridotite-derived melts that have either no excess 230 Th or excess 238 U. We cannot distinguish these possibilities so we examine two types of depleted endmember melts both having a (238 U)=(232 Th) of 1.4. In Model 1 (Fig. 3B), the melt reflects a melting model calculation using a source with 8% cpx and 12% garnet that begins to melt at 70 km. In Model 2 (Fig. 3C), the depleted endmember melt is assumed to be in (230 Th)=(238 U) equilibrium. In all models, we assume that the enriched source material contains 12% cpx and 20% garnet, begins to melt at 110 km depth and has a (238 U)=(232 Th) of 1.0. The trends formed by mixing of melts from these depleted and enriched sources at various solid upwelling rates are presented in Fig. 3. In both EPF and DM models, melts from enriched source materials are displaced more from the equiline than are melts from depleted materials because of both higher garnet modes and longer melting columns. Particularly in EPF models, a slower solid upwelling rate accentuates the production of disequilibria in melts from the enriched endmember, thereby producing a shallower slope for the predicted mixing trend than for a fast upwelling rate. A decrease in the productivity of the enriched source might also produce shallower slopes. However, enriched materials, such as pyroxenites, are expected to have greater melt productivities [15] than depleted materials resulting in steeper slopes. EPF disequilibria trends flatten with decreased upwelling rate regardless of the depleted endmember. In contrast, the slopes of DM models do not vary with solid upwelling rate if a garnet-bearing depleted source is used (Fig. 3B) and show less sensitivity to upwelling rate if the depleted endmember

has .230 Th/=.238 U/ D 1:0 (Fig. 3C). The result of melting an intermediate source composition (90 km depth, 16% garnet and 10% cpx; Fig. 3B) shows that melting a spectrum of sources does not necessarily produce linear trends. This lack of linearity results from the differing effects of transport through spinel peridotite for melts from the enriched and depleted members as a function of melt flux (upwelling rate). The decrease in modeled excess of the depleted endmember at the slowest upwelling rate also shows this effect (Fig. 3B). Whether this variation actually occurs depends critically on the degree of interaction of ascending melts with spinel peridotite.

4. Comparison to observed U-series data 4.1. Assessing the slopes of disequilibria trends in MORB Although it has been over 15 years since the first studies of U-series disequilibria in MORB, there is still not a sufficiently large and precise set of data to rigorously assess their geodynamic implications. Here, we use all currently available U-series data for MORB, including alpha spectrometry studies in which precision is significantly worse and the possibilities of contamination are greater. We also include a number of two- or three-point trends determined by mass spectrometry. The slopes of these trends are more susceptible to analytical error or unconstrained age. Our conclusion depends in part on segment definition and sample selection (e.g. judgment about sample age and freshness, and exclusion of samples from seamounts) which are discussed next. The first uncertainty concerns segment definition. We define most of the data sets by first-order ridge segmentation (JDF, Gorda, 9–10ºN EPR, 11–13ºN EPR, and 21ºN EPR) or, more generally, latitude (20–27ºS EPR). In part, the grouping also reflects the coherence of the U-series trends. For example, the southern JDF is spatially closer to the Gorda Ridge than it is to the Endeavour segment, so treating the JDF Ridge (>300 km in length) as a single system might not be justified. However, the difference in U–Th trends [7] and in average axial depths between the JDF and Gorda Ridges favors separating data for the two at the Blanco Transform. The FAZAR

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data [21] are not broken down by segments because the data have an estimated age uncertainty of š30 ka. The individual segments all produce slopes >1 (consistent with our single regression for all the data), but the age uncertainty results in too great an uncertainty in slope for sample subsets to warrant separate treatment. Second, many of the samples lack age control. Large (226 Ra)=(230 Th) disequilibria are common in recent MORB [27,28] and any such disequilibrium constrains the eruption age to be <8 ka. Consequently, in Fig. 1, we use closed symbols to indicate samples known to have such disequilibria. Unfortunately, most MORB analyzed by mass spectrometry do not have 226 Ra results and therefore are not well age-constrained. We only use data from 9 to 10ºN EPR that are zero-age according to the dating methods of Goldstein et al. [8], and for most other studies we use only on-axis samples [4,7,29]. Third, alteration and assimilation will affect results and mask melting-related traits. Because of the large sample size required, alpha spectrometry data

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are especially susceptible to contamination by MnO2 [5] which increases scatter and can systematically steepen slopes because added 230 Th has more effect on depleted (high (238 U)=(232 Th)) samples. For this reason we excluded: the datum from the Escanaba Trough on the Gorda Ridge because its anomalous Th isotopic composition, along with other geochemical signatures, was attributed to turbidite sediment assimilation [7]; two data from 21ºN EPR study claimed by the authors to be contaminated [29]; and the 238 U excess sample of Ref. [6] also claimed to be contaminated. Finally, we excluded data from seamounts (i.e. two data points from Axial Seamount in Fig. 1C) because we believe that a seamount which rises 800 m above the surrounding ridge is unlikely to reflect the normal melting process beneath that segment. For each data set filtered, using the principles above, we utilize a York weighted linear regression (Model 2 in isoplot for all fits except for 21ºN EPR where Model 1 was used [30,31]) to obtain a slope with an error (Table 2). Despite the age uncertainty

Table 2 Regression analysis of all available U-series data

* Symbol used in Figs. 2, 4 and 5. # Mass (M) or alpha (A) spectrometry. error on slope by York regression [30].

**

Number of data and

226 Ra

constrained data.

%

Slope and

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and low precision on many samples, most of the regressions show significant correlations (in Fig. 1, R for regressions A–E >0.77). Because the slopes of some regressions (e.g. 9ºN EPR and 20–27ºS EPR) are heavily weighted by single points, we have tested their slope by regressing the data sets without the most depleted sample (highest (238 U)=(232 Th)) from 20–27ºS EPR, and without the most enriched sample from 9ºN EPR. The new regressions are 0.80 and 0.56, which are almost identical to the full regressions, but with larger errors. Although most of the data from 20–27ºS EPR lie within error of (230 Th)=(238 U) equilibrium, all have significant 226 Ra excess, which indicates that their original slope must have been similar to the equiline slope. Consequently, data for the youngest and freshest samples from all conventionally defined ridge segments for which U-series data have been published show the previously noted correlation between excess 230 Th and Th=U ratio. We show below that the slope of these trends positively correlates with spreading rate. Further studies will determine how robust this relationship is. 4.2. Slope dependence on spreading rate We believe that the regression values in Table 2 are an accurate representation of the slope for each data set. Because slopes rather than absolute disequilibria can see through the effects of source heterogeneity and mantle temperature variations, we plot the regressed slopes to rotate about a common point (Fig. 4). The trends of all the data sets except one indicate that an increase in the slope of the trends occurs as the half-spreading rate increases. The lower (238 U)=(232 Th) end of individual trends generally have higher 230 Th excesses and higher trace element concentrations. The sole exception to this, and also to the spreading rate–slope correlation, is the data set from the northern Mid-Atlantic near the Azores mantle plume where the most enriched samples in terms of concentration have higher (238 U)=(232 Th)) and greater 230 Th excesses. Fig. 1E includes data from Sao Miguel (Azores) [32] and shows the good correlation along and adjacent to this length of ridge for MORB data (FAMOUS and FAZAR [6,21]) and for OIB. Even within the samples from Sao Miguel [32], the most MORB-like

Fig. 4. The slopes of trends from Fig. 1 (except G) plotted on an arbitrarily scaled equiline diagram. The y-intercepts are changed such that the trends rotate around a common point. Symbols used to identify segments given in Table 2. The plate rates shown are from Refs. [7,49]. A decrease in slope is seen as a function of decreasing spreading rate excepting the Azores influenced NMAR. An absolute š0.2 slope error is shown on the NMAR slope to illustrate typical uncertainties (see Table 2 for specific errors on each slope).

samples (in terms of 206 Pb=204 Pb) have the greatest 230 Th excess, indicating the low (238 U)=(232 Th) endmember produces the least disequilibria. One speculative explanation for this non-typical behavior involves the effect of water on productivity and melting rate. Productivity likely increases with water content [33], reducing the ingrowth of 230 Th excess during melting. The Azores have been suggested to be a mantle wet spot [34] so that lower 230 Th excesses might be expected in the low (238 U)=(232 Th) endmember in this case. The increase in melting rate with added water could also explain the lower (230 Th)=(238 U) at axial seamount along with lower (230 Th)=(238 U) in the most highly enriched EMORB (in terms of K=Ti or Zr=Nb) from the Endeavour segment of the Juan de Fuca relative to less enriched EMORB on that segment (Fig. 1C). 4.3. Implications for melting models In Fig. 5, we combine our modeling results with the regressed slopes and errors (Table 2). The slopes of the disequilibria trends that are age-constrained by 226 Ra data correlate well with the half-spreading rate of a ridge. The slopes from studies without 226 Ra

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Fig. 5. The slopes of disequilibria trends versus the observed half-spreading rate. Error bars are 1¦ . Only the data from northern MAR, influenced by the Azores mantle plume, are not consistent with the existence of a spreading rate dependence of the slope. The predicted slopes of mixing lines in both equilibrium porous flow and dynamic models are shown. Model 1 refers to Fig. 3B, while model 2 refers to Fig. 3C. Dynamic melting models of two garnet-bearing sources (Model 1) are inconsistent with the observed relation, while dynamic Model 2 does show an upwelling rate dependence on the slope. Equilibrium porous flow models better match the observed relation and suggest a near one-to-one relation between model upwelling and half spreading rate, consistent with passive flow upwelling.

constraint are also consistent with this correlation, despite age uncertainties. Even slopes from ridges with limited data are consistent with a spreading rate dependence. Only the Azores-influenced MAR is inconsistent and may reflect a different style of melting or upwelling encountered at isolated melting loci. The slopes of trends created in both DM and EPF models are shown as a function of the modeled solid upwelling rate. A robust, model-independent conclusion is that dynamic melting of two garnet-bearing sources (Model 1) cannot reproduce the slope dependence that current U-series data sets imply. The slope dependence of DM models when the depleted melt has no 230 Th excess (Model 2) is less than the observed dependence, although a lowering of the enriched endmember’s melt productivity might account for this discrepancy. For the EPF models, the predicted slopes for both models (1 and 2) as a function of the solid upwelling rate generally agree well with the observations at the corresponding half-spreading rate. Given the many parameters involved, this may be fortuitous. Nevertheless, this successful match of

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theory and observation using physically reasonable values for the parameters is encouraging. Global U-series data have also been used to suggest a relation between 230 Th excess and axial depth, possibly indicating mantle temperature variations [22]. The relation that we observe does not specifically contradict this model. We use the slopes of trends, rather than absolute disequilibria, to discern differences in upwelling rate in order to specifically avoid effects like mantle temperature variations. Comparison of the Juan de Fuca and Gorda Ridge trends shows the two ridges have non-overlapping trends with similar slopes consistent with having similar upwelling rates. At the same time, the JDF data are offset to higher 230 Th excess at a given Th=U consistent with greater depths of melt initiation for the JDF relative to the Gorda and accounting for the differences in average 230 Th excess as a function of average axial depth [22]. Thus, differences in temperature could explain some differences between the absolute disequilibria of ridges. However, the axial depth correlation [22] subordinates local variability and increases scatter beyond analytical error, similar to previous spreading rate assessments [2,3]. For example, segments with mass spectrometry data are characterized by standard deviations as large as for segments with only alpha spectrometry data. This scatter does not reflect age. Data from 33ºS MAR [35] further test this correlation as three nearly adjacent segments (2, 4 and 5) have dramatic differences in average axial depth (Fig. 6). However, the average disequilibria for these three segments show no variation ranging from 1.140 to 1.153. The individual data from 33ºS widen the swath forming the axial depth correlation such that (230 Th)=(238 U) varies between 0.9 and 1.25 at ¾3500 m depth, a range which encompasses most MORB. Removing ridges influenced by hot spots (Fig. 6), the axial depth correlation is much less predictive than the method proposed here because it ignores the fundamental observation of the local 230 Th excess trends such that segment averages depend heavily on the randomness of sampling. If hot spot-influenced ridges are to be included, then a better test of the global axial depth correlation should come from hot spot-influenced ridges, such as Kolbeinsey, where a wide spectrum from depleted to enriched melts is found.

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Fig. 6. (230 Th)=(238 U) versus axial depth. Figure reproduced from Ref. [37] with 33ºS MAR data [35] added. Solid symbols for 33ºS data denote samples age constrained by the measurement of 226 Ra excess. When the FAZAR data (shaded field) are omitted, the global relation with axial depth loses much of its predictive ability. The data from 33ºS show no relation to axial depth on either an individual basis or as segment averages and expand the observed range in (230 Th)=(238 U) for a given depth. At ¾3500 m depth, (230 Th)=(238U) can vary from 0.90 to 1.25, a range that encompasses most MORB. The large spread in data at each area of ridge results from the coherent trends of 230 Th excess as a function of Th=U and suggests that ‘average’ disequilibria for a given location are, to some extent, dependent on the sampling.

Because 231 Pa also has a half-life long enough to sample the entire melting column (33 ka), it too should depend on differences in solid upwelling rate. Because of its shorter half-life and the probable greater difference of its partition coefficient relative to its parent, modeled (231 Pa)=(235 U) are even more sensitive to both solid upwelling rate and porosity variations than are (230 Th)=(238 U). The limited (231 Pa)=(235 U) data available appear to show this variation. Zero age (231 Pa)=(235 U) in N-MORB from the fast-spreading 9–10ºN EPR [8] vary between 2.76 and 2.60 at essentially constant (230 Th)=(238 U). However, zero-age (231 Pa)=(235 U) from the slowspreading 33ºS MAR are significantly lower in the one segment suggested to have active upwelling relative to adjacent segments [35] consistent with upwelling rate sensitivity. More data are clearly needed to assess the ability of 231 Pa to monitor upwelling rate variations, but it ultimately could provide the most robust constraints on the melting process. 4.4. Passive upwelling beneath the Pacific? Few relations have been found between spreading rate and MORB geochemistry. Spreading rate

is inversely correlated with geochemical variability [13,36] and positively correlated with abyssal peridotite depletion [37]. The correlation between spreading rate and (230 Th)=(238 U) systematics discussed above suggests that U-series disequilibria are influenced by the solid upwelling rate. In purely passive upwelling driven by the separation of two flat plates, upwelling rate should be proportional to the half-spreading rate [38], although others have argued that the average upwelling rate across the melting region may remain relatively constant through a range of spreading rates [2,3]. In detail, the similarity between EPF models and observations in Fig. 5 is consistent with the former, showing a direct relation between half-spreading rate and solid upwelling rate. However, we note that the majority of segments making up the trend (and the most constrained slopes) come from the Pacific ridges. Results for surface wave velocity reductions from the MELT experiment imply that melt is broadly distributed along the southern EPR [39], which may also indicate passive upwelling. If Fig. 5 is confirmed, then U-series disequilibria can be used to quantify solid upwelling rates and to constrain the style of solid upwelling in the sub-ridge environment.

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Considerable numerical modeling has been devoted to examining solid mantle flow beneath ridges considering the effects of melt retention, matrix depletion, and viscosity on the style of upwelling [40–43]. Empirical constraints on the problem include the variability of crustal thickness in the global ridge system [38,44,45], the narrowness of the zone of accretion [46], gravity signatures [47] and the chemistry of erupted basalts [13,48]. Fig. 5 illustrates that U-series disequilibria could discriminate between different upwelling styles. The deviation between the observed 230 Th disequilibria trend and the trend predicted based on the half-spreading rate of a ridge will reflect the amount (or percent) of rapid upwelling present beneath a given ridge segment. However, if melt productivities of enriched sources vary, then it may be difficult to distinguish increases in solid upwelling rate from increases in productivity. The degree to which spreading rate correlates with the slope of disequilibria is entirely testable with further data. However, many criteria should be considered in collecting future U-series data. First, high quality mass spectrometry data are required from a suite of samples possessing a great range in Th=U. This is best accomplished by emphasizing samples not erupted on axis, as crustal magma chambers appear to efficiently homogenize the melting regime [16]. Second, these data must be age-constrained for 230 Th excess by measurement of 226 Ra excess, submersible observation, or other technique. Presently, less than half of the mass spectrometry data meet this requirement. Lastly, 231 Pa data may also provide important information for constraining solid upwelling rates.

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upwelling rate variations beneath ridges. However, melting models demonstrate that these mixing trends can record upwelling rate variations through variation of their slopes and therefore can be used to constrain solid upwelling rates beneath ridges. The available U-series data sets are evaluated for the slope of the mixing line. All sets of data, but one, suggest that the slope of the trend decreases with decrease in half-spreading rate, consistent with the prediction of the above models. The one exception is the data set from northern MAR which is shown to have a good mixing relation with an enriched component from the Azores. The dependence of the disequilibria slopes on spreading rate suggests that melting rate variations are recorded by 230 Th excess variation. This mutual variation is most easily explained as a direct relation between spreading rate and solid upwelling rate. The close correspondence between the observed dependence of slope on spreading rate and the modeled dependence of slope on upwelling rate is consistent with purely passive plate driven flow of the mantle beneath ridges.

Acknowledgements This work has greatly benefited from reviews by A. Lenardic, K. Sims, M. Spiegelman, T. Elliott, M. Hirschmann, C. Langmuir, and several anonymous reviewers. We thank the reviewers for constructive criticism. This work is supported by a NSF-RIDGE post-doctoral fellowship to C.C.L. and N.S.F. grants to Q.W. and J.G. [CL]

References 5. Conclusions U-series disequilibria, when examined on a segment scale basis, produce trends that show good correlation between the amount of 230 Th excess and Th=U. As Th=U is most likely an indicator of chemical heterogeneity in the melting region, the observed trends reflect mixing of melts derived from heterogeneous sources and imply that how the mantle melts depends on source variations. Thus, absolute disequilibria are unlikely to be useful in discerning solid

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