Spiegelman et al.: Channel induced chemical variation 1

Extreme chemical variability as a consequence of channelizedmelt transport

Marc Spiegelman

Lamont-Doherty Earth Observatory of Columbia University, Palisades, New York

Peter B. KelemenWoods Hole Oceanographic Institute, Woods Hole, Massachusetts

(accepted Geochem. Geophys. Geosys. 2002)

Abstract. The spatial and temporal variability of chemical signals in lavas, residuesand melt inclusions provides important constraints on source heterogeneity, theefficiency of convection, and melt transport processes in the mantle. The pastdecade has seen an impressive increase in the number, precision and spatialresolution of chemical analyses. However, as resolution has increased, the pictureof variation that emerges has become increasingly difficult to understand. Forexample, mid-ocean ridge basalts can display large variations in trace-elementconcentration on scales from 1000 km of ridge to melt inclusions in 500 microncrystals. These observations suggest that melt transport processes do not readilyhomogenize partially molten regions. While some of the observed variability isdue to source variations, a large proportion could be the consequence of magmatransport in channelized systems.We present results of numerical models that calculate the trace element signaturesof high porosity dissolution channels produced by reactive fluid flow. These modelswere originally developed to explain the organization of melt transport networks,based on observations of “replacive dunites” found in ophiolites. Channelizedflow can produce orders of magnitude variation in the concentrations of highlyincompatible elements, even for idealized systems with a homogeneous source,constant bulk partition coefficients and equilibrium transport. Most importantly,the full range of variability may be found in each channel because channelizationcan transpose the chemical variability produced by melting throughout the meltingcolumn into horizontal variability across the width of the channel. The centers ofchannels contain trace element enriched melts from depth, while the edges of thechannels transport highly depleted melts extracted from the inter-channel regionsat shallower levels. As dunite channels may be spaced on scales of 1–100 m in themantle, this mechanism allows highly variable melt compositions to be deliveredto the Moho on small length scales. The chemical variation produced in the modelsis consistent with that seen in melt inclusion suites, lavas and residual mantleperidotites dredged from the ridges and sampled in ophiolites.

1. Introduction

The natural variation of chemical composition of prim-itive melts, melt inclusions and residual mantle peridotitesis one of the primary sources of information on convec-tion, melting, and melt transport processes in the mantle.The past decade has seen a significant increase in the num-ber, precision and spatial resolution of chemical analyses.However, as we sample at smaller and smaller scales, thecompositional variability of mantle materials does not seemto diminish. For example, the trace element variability inlavas erupted over 1000 km of ridge axis is comparable tothat seen in suites of melt inclusions within individual hand-samples. The observation of large chemical variability atsmall scales implies that melt transport in partially moltenregions is inefficient at mixing melts. One possible explana-tion is that melt transport occurs in a channelized networkthat limits interaction between melt and solid. While thisassumption is implicit in many commonly used geochemi-cal models (reviewed below), these models do not explicitlyaccount for the mechanism of melt transport. Thus the phys-ical mechanisms of network formation and melt transport,and their effect on chemical variation, remain poorly under-stood.

This paper explores the chemical consequences of newphysical models of channelized melt transport [Spiegelmanet al., 2001]. Significant compositional variability can beproduced by the melt extraction process alone, even for ide-alized homogeneous systems. These models are consistentwith observations, producing extreme chemical variabilityon very small length scales. These results are a natural con-sequence of melt transport processes and provide physicalexplanations for some of the least understood observationsof chemical variability.

1.1. Evidence for channelized flow: Compositionalvariability in mid-ocean ridge melts

Melt inclusion studies Chief among the puzzling newobservations are the results of melt inclusion studies [e.g.Sobolev and Shimizu, 1993; Nielsen et al., 1995; Sobolev,1996; Shimizu and Grove, 1998; Shimizu, 1998; Saal et al.,1998; Sours-Page et al., 1999; Sobolev et al., 2000; Slateret al., 2001]. These studies show extreme variability in bothtrace elements and isotope ratios in individual hand samplesand in some cases between inclusions within the same crys-tal. Figure 1, for example, shows a summary of rare earthpatterns from melt inclusions trapped in high Mg olivinephenocrysts from three hand-samples from the Mid-AtlanticRidge. These inclusions show 1–2 orders of magnitude con-centration variation in La and about a factor of 2 variationin Yb. These samples include distinct, “ultra-depleted” melt

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Figure 1. Chemical variation observed in melt inclusionsfrom single hand samples; summary of results from Shimizu[1998] and Sobolev and Shimizu [1993] for samples from theMid-Atlantic Ridge.

inclusions with compositions that are not found among theerupted host lavas [Sobolev and Shimizu, 1993]. Similar re-sults for Iceland [Slater et al., 2001] also show large vari-ability of melt inclusions within individual flows from The-istareykir shield volcano. The most trace-element enrichedinclusions are ∼ 2–4 times more enriched than their hostlavas. The Iceland data also show a distinct tail of very de-pleted inclusions.

Olivine hosted melt inclusions are thought to be trappedduring crystallization in the crust at moderate to low pres-sures [e.g. Sobolev, 1996]. If so, then the large variabilityin hand samples implies that melts found near the Moho areheterogeneous on small length scales. This requires somemechanism for delivering melts to the Moho without signif-icant homogenization during melt transport. The reductionin variability between melt inclusions and host lavas wouldarise from crustal processes such as mixing in magma cham-bers and flow in dikes.

Variability in MORB lavas Larger scale samplingalso yields compositionally variable lavas over short spa-tial scales. For example, at 12◦N on the East Pacific Rise[Reynolds et al., 1992; Reynolds, 1995; Reynolds and Lang-muir, 2000] lavas with compositionally distinct parentalmagmas can be sampled within 500m of each other withinthe axial summit graben. Other studies at 9◦N EPR [e.g.Perfit et al., 1994a, b; Perfit and Chadwick Jr., 1998] showmore modest variations and the overall variability of melt

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Spiegelman et al.: Channel induced chemical variation 3

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Figure 2. Chemical and spatial variation of MORB glasses with MgO > 7% from 8–15◦N EPR. (a) Variability of traceelement concentrations for off-axis melts (black) and on-axis melts (red). The data sources are as reported by PetDB [Lehnertet al., 2000] with most of the off-axis analyses from Niu and Batiza [1997]. (b) A map showing log 10 Ba concentration as afunction of sample position. Red points are high Ba and blue points are low Ba. Note that the seamounts tend to be somewhatmore depleted than the axial melts but in general the correlation between composition and location is poor.

compositions varies significantly along the ridge axis. Nev-ertheless, the variability in trace element chemistry of theNorthern EPR is comparable to that seen in melt inclusionsuites from individual hand-samples.

Figure 2 summarizes the composition and spatial dis-tribution of samples from 8–15◦N on the EPR. Figure 2a,compares trace element variation in off-axis lavas, includingseamounts [Niu and Batiza, 1997], to variation in on-axissamples. All samples are basalt glasses with greater than 7wt% MgO. The overall variation in highly incompatible ele-ments (e.g. Ba, Th, U) is approximately two orders of magni-tude in concentration while the rare-earth elements (REE’s)show variability similar to that seen in melt inclusions (Fig.1). Moreover, the range of composition of melts erupted onaxis is similar to that seen in the seamounts, although theseamounts demonstrate a slightly wider range of variationwith a larger population of more depleted compositions.

Figure 2b shows a map of sample locations, with differ-ent colors corresponding to different Ba concentrations. Itsuggests that there are no spatial domains in which com-position varies smoothly. In many cases, trace element en-riched samples are adjacent to very depleted samples. Morequantitative measures of spatial coherence, such as two point

correlation functions, also show that the correlation betweencomposition and distance is low with no systematic changeas a function of length scale. As might be expected frommelt inclusion data, there is as much variability in samplesfrom some individual dredge hauls (less than about 1 km onthe seafloor) as there is in the entire data set.

Taken together, Figures 1–2 suggest that partially moltenregions in the mantle beneath oceanic spreading ridges canpreserve significant chemical variability at all scales. Whilesome of this variability reflects source heterogeneity, it is un-certain how much of this variability arises as a result of melt-ing and melt transport. To answer this definitively requiressystematic measurement of long-lived radiogenic isotopeson samples with known major and trace element composi-tions to investigate the correlations between trace elementcontents of lavas and isotopic variability. Given the observedlack of spatial correlation, comparing isotopes and trace el-ements from different samples in the same area is problem-atic. Surprisingly, there are relatively few areas along theglobal mid-ocean ridge system where isotope and trace ele-ment analyses have been made on the same samples. Wherefull data sets are available, the degree of correlation betweentrace element enrichment and isotopic enrichment is variable

Spiegelman et al.: Channel induced chemical variation 4

(see discussion). In any case, regardless of the source ofvariability, the preservation of heterogeneity on small scalessuggests that melt transport processes in the mantle do notreadily homogenize melt compositions.

Other evidence for channelized flow Perhaps the mostdirect evidence for channelized flow comes from studies ofophiolites and abyssal peridotites which show evidence for“replacive dunites” embedded in residual mantle harzbur-gites [e.g. Boudier and Nicolas, 1972, 1977; Dick, 1977;Boudier, 1978; Quick, 1981; Kelemen et al., 1992; Kele-men and Dick, 1995; Kelemen et al., 1995a, 2000; Suhr,1999]. Geochemical arguments and field relations demon-strate that mantle dunites were channels for chemically iso-lated transport of melt, partly or entirely via porous flow.Several models for flow localization have been developed,ranging from mechanical instabilities driven by shear in vari-able viscosity solids [Stevenson, 1989; Richardson, 1998;Hall and Parmentier, 1998; Connolly and Podladchikov,1998; Phipps Morgan and Holtzmann, 2001] to physico-chemical instabilities in which high porosity dissolutionchannels form via reactive melt transport in compactible me-dia [Kelemen et al., 1995b; Aharonov et al., 1995; Spiegel-man et al., 2001]. To date, these models have focused on themechanics of flow localization and channel formation. Herewe explore the observable chemical consequences of theseprocesses. We first review the chemical variability expectedfrom commonly used geochemical models that do not in-clude melt transport, then compare this behavior to that ofthe reactive flow models.

1.2. Variability expected of standard melting models

A simple melting model for a mid-ocean ridge, is thesteady-state, 1-D near-fractional melting column model [e.g.Langmuir et al., 1977; Johnson and Dick, 1992; Sobolev andShimizu, 1992; Slater et al., 2001] illustrated in Figure 3.These “dynamic” melting models assume that batch meltingoccurs up to a threshold porosity φ0. Any melt producedabove this threshold is then extracted instantaneously andassumed to have no further interactions with the solid. The“instantaneous” melts produced at each depth are assumedto be in chemical equilibrium with their host. In the limitφ0 → 0, this model is identical to fractional melting.

These models do not include physical mechanisms ofmelt transport. Nevertheless, they commonly include theassumption that instantaneous melts are mixed efficientlyso that at any depth there are only two melt compositions:the instantaneous melt produced at that depth and the com-plete mixture of all instantaneous melts produced up to thatdepth. If melts are sampled only from the top of the column,the bulk of the melts will therefore be the column aggre-gate which shows no variability. Moreover, the aggregated

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Figure 3. 1-D near-fractional melting column model. (a)Cartoon of a melting column upwelling at solid velocityW0 with linearly increasing degree of melting F (z). Ateach level the instantaneous melt composition for trace el-ements relative to source are cf (z)/cs

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/(Fmax−φ0), where Fmax is the max-imum degree of melting at the top of the column. (b) Traceelement patterns for a 1-D column model with Fmax = 10%and φ0 = 0 (pure fractional melting). Black lines are instan-taneous melts shown for melting increments dF = 0.5%,the red line is the mean composition after complete mixing.(c) “Dynamic” melting with Fmax = 10% and φ0 = 1%.Instantaneous melts shown for dF = 0.45%. As discussedin Spiegelman and Elliott [1993], φ0 is not necessarily thephysical porosity, rather it is the fraction of melt that is al-lowed to equilibrate with the solid residue.

Spiegelman et al.: Channel induced chemical variation 5

melt composition for a range of values of retained porosityis nearly indistinguishable from an accumulated fractionalmelt with the maximum degree of melting of the column.

To produce significant variability from these models re-quires that instantaneous melts be extracted from all depthswithout mixing or interacting with other instantaneousmelts. Figure 3b,c shows the column aggregate and distri-bution of instantaneous melts from two models with differ-ent values of retained melt fraction φ0. For simplicity, bothcalculations assume constant bulk partition coefficient and auniform source.

Figure 3b shows the solutions for pure fractional meltingφ0 = 0 while Fig. 3c has a retained melt fraction φ0 = 1%.The aggregate melts from both calculations are nearly iden-tical and show constant concentrations relative to sourceof ≈ 1/Fmax for all elements with partition coefficientsD ∼< Fmax. In contrast, the instantaneous melts from eachcalculation show quite different distributions. For pure frac-tional melting, the instantaneous melt compositions show astrong peak in concentration for elements with D ∼ F . El-ements with crystal/liquid distribution coefficients that aresmaller than the degree of melting F become extremely de-pleted, while elements with D’s much greater than F areenriched relative to source by a factor of about 1/D. Thesefractional instantaneous melt patterns are distinctly differentfrom the compositions of melt inclusions and lavas whichare nearly parallel to the mean concentrations (Figures 1–2).As discussed by Slater et al. [2001], this shows that meltinclusions are not trapped fractional melts.

Instantaneous melts produced by dynamic melting with1% retained melt (Figure 3c) are more similar to observedmelt compositions. However, with 1% retained melt, themost enriched instantaneous melts are more enriched thanobserved, while calculations for U-series disequilibrium[McKenzie, 1985; Williams and Gill, 1989], which are verysensitive to the value of φ0, produce excesses that are smallerthan are observed in mid-ocean ridge basalts. When φ0 wasused as a fitting parameter to model variability in melt inclu-sions and lavas, Slater et al. [2001] found that φ0 = 4–6% isrequired for Iceland and the mid-Atlantic Ridge [Shimizu,1998]. These best-fit values of φ0 produce negligible U-series excesses in dynamic melting models, and Slater et al.[2001] show that they still don’t fit the trace element datawell.

More complex two-dimensional models that approximatethe melting region as an integrated set of 1-D columns ofdifferent heights (i.e. a “triangular” melting region) [e.g.Plank and Langmuir, 1992; Langmuir et al., 1992; McKen-zie and O’Nions, 1991; Kinzler and Grove, 1992a, b; Shenand Forsyth, 1995] produce variability similar to the 1-D col-umn models but also predict a systematic spatial distribution

of melt compositions, where more enriched, smaller degreemelts are found preferentially off axis. Aggregate melts pro-duced in all of these models are similar to mean melt com-positions at mid-ocean ridges. Moreover, dynamic meltingmodels can also reproduce the observed range in composi-tion, if large values of φ0 are assumed. However, like the1D models, the 2D models do not account for large compo-sitional variations in a small area (e.g., melt inclusions). Nordo they explain relatively large U-series excesses in MORB,or the lack of correlation between location and lava compo-sition on the ridge segment scale.

To summarize, the overall variability of mid-ocean ridgemelt compositions is better modeled by dynamic melting ascompared to fractional melting. However, to interpret meltinclusions as instantaneous, dynamic melts that are trappedin olivine near the Moho, requires a physical system that ex-tracts melts from each specific depth without allowing themto mix with melts from any other depth during transportthrough the mantle. To date, it has been difficult to imag-ine a physical mechanism for this process, although it doesimply some form of channel network. In this paper, we showthat, when the physics of melt extraction is included, chan-nelization itself can provide the mechanism.

2. Geochemical consequences of reactive meltchanneling

This section presents results of a simple model for re-active flow and chemical transport that demonstrates howchannelized flow can produce orders of magnitude varia-tion in the concentrations of highly incompatible elements,even for idealized systems with a homogeneous source, con-stant bulk partition coefficients and equilibrium transport. 1

This example is meant to be illustrative, rather than “realis-tic”. The discussion considers additional geologically rele-vant processes and future work.

The model is described in Spiegelman et al. [2001]. Itconsists of a two-dimensional domain, in which the solidis upwelling vertically and melting by adiabatic decompres-sion. In addition, melt can dissolve solid material duringascent, increasing the porosity. Without reactive dissolu-tion, this is the classic 1-D, steady-state melting column, forwhich there are analytic solutions for porosity and chemicalcomposition with depth [e.g. Ribe, 1985; Spiegelman and El-liott, 1993; Spiegelman, 2000]. In particular, for equilibrium

1“Equilibrium transport”, assumes that trace elements maintain chemi-cal equilibrium between the melt and solid at all times. In contrast, “dis-equilibrium transport” assumes that instantaneous melts are produced inequilibrium with their local solid source but do not equilibrate with the solidduring transport. Disequilibrium transport is essentially the same as frac-tional melting.

Spiegelman et al.: Channel induced chemical variation 6

transport, the trace element composition of the melt at anydepth z is identical to that of a batch melt with degree ofmelting F (z). This result is independent of the value of theretained porosity. Likewise, disequilibrium transport pro-duces compositions identical to an accumulated fractionalmelt.

Figures 4a,c show the numerical solutions for porosityand chemical composition for equilibrium transport. Theporosity evolves to a 1-D steady state, which depends onthe permeability. The permeability in this particular solutionis specified using the constraint that the maximum melt ve-locity at the top of the column is 50 times faster than thesolid upwelling velocity. Conservation of mass in steadystate then requires that the maximum porosity at the top ofthe column is φ0 = Fmax/50 = 0.2% [see Spiegelman andElliott, 1993]. The same solution would be found by specify-ing a permeability that varies as kφ = k0φ

2 with a prefactor

k0 =50W0µ

φ0∆ρg.

For φ0 = 0.002, upwelling velocity ∼ 3 cm yr−1 and meltbuoyancy ∆ρg/µ = 5000 (ms)−1, the maximum perme-ability is ∼ 2 × 10−14 m2. This compares very well withestimates of mantle permeabilities by Von Bargen and Waff[1986]. For example, using their formulas for permeabilitywith φ = 0.002, grain diameter d = 3mm and a dihedralangle θ ∼ 35◦ (∆q ∼ .35) yields kφ ∼ 3 × 10−−14.

The composition of the “erupted melts” at the top of thecolumn in Fig. 4a matches the analytic, batch melting solu-tion to within 1 part in 10−3. Unlike the dynamic meltingcolumn in Fig. 3, equilibrium transport, without channels,produces a single melt composition at any depth with themost depleted melt being the melt at the top of the column(here a batch melt of 10%). Thus, without channels, the so-lution is rather dull and produces no variability at the topof the melting column. When reactive dissolution is added,however, all hell breaks loose. (Figure 4b,d).

To model the effects of reactive dissolution, we followSpiegelman et al. [2001] and assume that the solid is com-posed of two phases, which can be considered to be equiva-lent to pyroxene and olivine. Mantle melts produced at depthbecome undersaturated in pyroxene as they decompress adi-abatically. Where undersaturated melts react with mantleperidotite, they dissolve pyroxene, producing a larger massof melt, and precipitating a small amount of olivine [e.g.Kelemen, 1990; Kelemen et al., 1990; Daines and Kohlstedt,1994; Kelemen et al., 1995b]. As a first approximation, theequilibrium solubility of pyroxene is a smoothed ramp thatvaries from ∼ cf

min = 1 to cfmax = 1.2 over z0 ≤ z ≤ 1.

Equilibrium solubilities greater than 1 imply incongruent re-actions, in which pyroxene dissolution produces both melt

and olivine; this is a more appropriate formulation than thatused by Spiegelman et al. [2001].

Because additional melt is produced in this reaction, itcauses a local increase in porosity and permeability, which inturn results in a larger flux of undersaturated melt. This feed-back between melt flux and dissolution leads to localizationof porous flow into high-permeability dissolution channels[Kelemen et al., 1995b; Aharonov et al., 1995; Spiegelmanet al., 2001]. Figure 4a,b compares a calculation without re-action to one with well-developed dissolution channels. InFig. 4b, reaction causes the flow to localize into porous chan-nels separated by low-porosity, “inter-channel” regions. Thelow-porosity regions form because the solid matrix is de-formable and the lower pressure in the channels sucks meltfrom the inter-channel regions, causing them to compact [seeSpiegelman et al., 2001].

The behavior of trace elements is readily calculated giventhe flow and melting rate fields. For clarity, we consideridealized tracers which have a constant bulk partition coef-ficient D and a homogeneous source. We also assume thatthe tracer remains in chemical equilibrium with the solid atall times, and neglect diffusion/dispersion. These assump-tions permit solution for the natural log of the concentration,rather than the concentration itself. This technique is dis-cussed in Spiegelman [1996] and is significantly more ac-curate in numerical models when concentrations vary overmany orders of magnitude.

Figure 4d shows the chemical variation produced in thechannelized run (Figure 4b) at t = 50 and demonstratesseven orders of magnitude variation in incompatible elementconcentration. Melts range from 3-4 times more enrichedthan the mean to ultra-depleted melts a few orders of mag-nitude more depleted than the mean. The distribution isskewed, with a much larger range of incompatible elementabundance below the mean, compared to the range abovethe mean. The mean composition of erupted melts is similarto the output of a 1-D column model with the same Fmax.However, the distribution of individual melt compositionssampled at the top of the model domain is dramatically dif-ferent.

The source of the large compositional variation in Figure4d is clear when we consider the spatial distribution of fluxand composition. Figure 5 compares profiles of vertical meltflux and melt concentration as a function of distance acrossthe top of Figure 4b at t = 50. The channels have largepeaks in flux, flanked by compacted regions with negligi-ble flux. They also show strong peaks in trace element con-centration. However, the compositional peaks are narrowerthan the flux peaks, with the width of the concentration pro-file dependent on partition coefficient. Highly incompati-ble elements (e.g. D = 0.0001) have narrower peaks than

Spiegelman et al.: Channel induced chemical variation 7

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Figure 4. Evolution of porosity and chemical signatures of two upwelling models, with and without reactive dissolution.Distances are scaled to the height of the melting column and dimensionless time is scaled to the time it takes melt to cross thecolumn at the melt reference velocity w0 (a) Solid decompression melting but no reaction (Da = 0 [see Spiegelman et al.,2001]). The porosity rapidly evolves to a steady state with uniform porosity at any height z and maximum porosity φ max =0.002. The maximum degree of melting is 10% and the maximum ratio of melt velocity to solid velocity is w 0/W0 = 50 (b)The same problem but with reactive flow (Da = 320, P e = 160). For this problem quasi-steady-state channels form rapidlywith maximum porosity ∼ 0.008. The porosity between the channels, however, has compacted to a very small value ∼ 0.0002making the inter-channel region nearly impermeable to deeper melts. (c) Chemical signature of trace elements sampled atthe top of the column with no reaction (Fig. 4a) at time t = 50. The black lines show concentration of each tracer relative tosource for each melt that exits the box (they’re all the same in this problem). The red dashed line is the analytic solution fora 10% batch melt. (d) Chemical signature of channelized flow. The blue curves show the distribution of melt concentrationsproduced by the run in Figure 4b at t = 50. These curves have been sampled out of the probability distribution determinedby the melt flux (i.e. compositions with large fluxes are sampled more often than those with small fluxes). The black curveis the mean of all compositions at the top of the box and the red dashed curve is the analytic solution calculated for the meandegree of melting at the top of the box (here around 14%). (Because of reactive dissolution, the maximum degree of meltingfor this problem is greater than the 10% in Figure 4a). Note that while the mean concentration is similar to that in Figure 4a,the range of compositional variation is extreme.

Spiegelman et al.: Channel induced chemical variation 8

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Figure 5. Comparison of variation in melt flux and varia-tion in composition at the top of a channelized run. The bluecurve shows the vertical melt flux φw at the top of the boxshown in Figure 4b at time t = 50. The red curve shows theconcentration of a very incompatible tracer (D = 0.0001) inthe melt relative to source (cf/cs

0). The green curve showsmelt concentrations normalized to source for a moderatelyincompatible tracer with D = 0.1. Note that the composi-tional peaks are narrower than the flux peak due to lateral ad-vection of depleted melt from the inter-channel regions intothe channels. Highly incompatible elements show larger de-pletions between the channels and have sharper peaks. Notethat the concentration at the center of the channel is moreenriched than the mean concentration for the same element(here cf/cs

0 ∼ 7).

moderately incompatible elements (D = 0.1). This pro-duces chemical distributions across the channels in whichthe channel centers have a large flux of enriched melts (withconcentrations ∼ 3–4 times the mean concentration) whilethe channel edges have a significant flux of extremely de-pleted melts.

The presence of depleted melts within the channel edgesis a natural consequence of channel formation in com-pactible material. Figure 4b shows that channel forma-tion is accompanied by inter-channel compaction such thatinter-channel regions have low porosity (here ∼ 0.02%) andtherefore low permeability. As a result, the inter-channel re-gions almost completely exclude the ascent of deeper melts.Nevertheless, the solid is undergoing decompression melt-ing everywhere. Melts produced between the channels havecompositions similar to instantaneous fractional or dynamic

melts, and become highly depleted at shallow depths. Shal-low, ultra-depleted melts are drawn into the channels by thelower melt pressure in the channels. This advection of inter-channel melts toward the channels produces channel edgesthat are extremely depleted in highly incompatible elements.

The consequence of this process is that every channelcontains a full spectrum of concentrations from extremelydepleted to moderately enriched. In effect, the vertical distri-bution of instantaneous melt compositions due to polybaricdecompression melting has been transposed into horizontalchemical structure across each channel. The centers of thechannels preserve mixtures of enriched melts produced atdepth while the edges preserve depleted instantaneous meltsfrom shallower depths. In classical dynamic melting mod-els, all of these melts are assumed to be homogenized intoa single “aggregate melt” composition. However, when thefluid mechanics of flow in porous media is considered, muchof the chemical variability produced by melting can be pre-served by slow laminar flow. Moreover, because dunitechannels in the mantle may only be 1–100 m in width andspaced 1–1000 meters apart, [Kelemen et al., 1995a; Kele-men and Dick, 1995; Kelemen et al., 2000; Braun and Kele-men, 2002], this implies that large ranges of compositionalvariation can be produced and preserved by melt extractionprocesses over small length scales.

This mechanism may explain how crystals within a singlepillow lava can trap variable melt inclusions. If the channelsdeliver melts across the Moho with highly variable concen-trations on the 10 m scale, it becomes straightforward forcrystals formed near the Moho to capture this variability. Atshallower depths within the crust, mixing in melt lenses anddikes reduces the variability of erupted lavas.

This model demonstrates that several orders of magni-tude of variation in incompatible element concentration canbe generated just by incorporating the physics of channel-ized flow in a homogeneous, near steady-state, 1-D modelof a melting column. Figure 6 shows some additional, time-dependent behavior. Most notably, small changes in the con-figuration of the channel network can result in significantchanges in composition at a single point along the top of themodel over time scales smaller than the melt extraction time(e.g., 24,000 years for melt traveling 50 times faster than thesolid, solid upwelling over a distance of 60 km, and a solidupwelling rate of 0.05 m/year). Temporal changes in thiscalculation, however, could be on time scales longer thansingle eruption events lasting a few years to tens of years[Reiners, 2002]. As a result of this time dependence, indi-vidual channels can change their mean compositions fromenriched to depleted when and where they become sepa-rated from deep sources. Thus time dependence introducesanother, larger scale of spatial variability, equivalent to the

Spiegelman et al.: Channel induced chemical variation 9

a

t=0.00

0 0.1 0.20

0.1

0.2

0.3

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0.5

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1t=10.00

0 0.1 0.20

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0 0.1 0.20

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1

b0 0.05 0.1 0.15 0.2

0

5

10

15

20

25

30

35

Distance x/h

Flux and concentration at t=50.00

D=0.0001 Melt flux

0 0.05 0.1 0.15 0.20

5

10

15

20

25

30

35

40

Distance x/h

Flux and concentration at t=30.00

D=0.0001 Melt flux

mean concentrationmean concentration

distance x/h distance x/h

t=50t=30

Figure 6. Time-dependent evolution of porosity and composition in channels. Animations of this and other runs can be foundat the G3 web-site. (a) Evolution of porosity. While there are always approximately three channels near the top of this model,their depth extent and positions change over time. This can lead to temporal variation in flux and chemistry at any point alongthe top of the model. (b) Flux and composition for an element with D = 0.0001 at the top of the column showing the threechannels at times t = 30 and t = 50 in Fig. 6a. In particular, note the left most channel at t = 30 extends to relatively greatdepth and has a large flux of enriched material. At time t = 50 however, this channel has become connected to three otherchannels carrying more depleted material, producing a large flux of depleted material at the same location. Despite this localchange from enriched to depleted melts, the overall variability at the top of the entire model domain is nearly constant, andcomparable to Fig. 4d.

channel spacing, that may account for some of the variabil-ity seen in erupted lavas on intermediate length scales. Tem-poral variation of lava composition at a given eruptive siteis an important qualitative feature of volcanic systems thatis difficult to understand if we only consider the flow of theupwelling, solid mantle. However, the addition of a physi-cally consistent plumbing system provides a framework forunderstanding these features.

3. Discussion

3.1. Controls on variability

The calculated variability in Fig. 4b is considerably largerthan that seen in natural systems (Figs. 1-2). Questions re-main as to what accounts for the differences and what it maytell us about the behavior of partially molten systems.

Sensitivity to channel structure One possibility is thatthe variability is sensitive to the depth and efficiency of chan-neling. Figure 7 shows three high-resolution, single-channelcalculations that have all the same parameters as Fig. 4b ex-cept for the “compaction porosity,” φc which controls thebulk viscosity (ease of compaction) of the matrix at smallporosities [e.g. see Spiegelman et al., 2001, Eq. (12), andFig. 6]. Systems that compact easily produce smaller innerchannel porosities, more flow localization and deeper chan-nel initiation. All of these effects lead to larger variabilityin highly incompatible elements (Fig. 7a). Systems withshorter channels and larger inter-channel porosities have

smaller variability.

Figure 7 shows that small changes in the channel structurecan lead to orders of magnitude differences in chemical vari-ability even though the mean melt composition in all of thesecalculations is similar. Moreover, while the distributions ofincompatible elements are qualitatively similar to those pro-duced by dynamic melting models, the physical parametersrequired to produce them are significantly different. For ex-ample, the maximum porosity in all of these models is stillless than 1%, and the interchannel regions have porosities aslow as 0.04% (Figure 7a) to 0.08% (Figure 7c), yet the modelresults show variability similar to dynamic melting modelsthat retain more than 1% melt everywhere in the meltingcolumn. Even very small inter-channel porosities producemelt compositions that are sub-parallel to the aggregate meltand do not resemble pure fractional melts (Fig. 3b). Fur-thermore, unlike the large retained melt fractions required toproduce such melt compositions in dynamic melting mod-els, these small inter-channel porosities are consistent with areactive flow origin for the U-series disequilibrium observedin MORB Jull et al. [2002].

In general, these calculations suggest that the observeddistributions of chemical variability as a function of compat-ibility could be a sensitive probe of the structure of partiallymolten regions. Future work will map out, and attempt toparameterize, the relationship between variability and chan-nel structure.

Spiegelman et al.: Channel induced chemical variation 10

a

t=0.00 [ 1 1 ]

0 0.050.10

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cf /cs 0

Mean concentration12.95% Batch melt

b

t=0.00 [ 1 1 ]

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10−4

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cf /cs 0

Mean concentration13.61% Batch melt

c

t=0.00 [ 1 1 ]

0 0.050.10

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0 0.050.10

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1t=70.00 [ 0.39338 3.05936 ]

0 0.050.10

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1

10−4

10−2

100

10−3

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10−1

100

101

102

Bulk partition coefficient D

cf /cs 0

Mean concentration14.42% Batch melt

Figure 7. Chemical variability in three high-resolution(257×641 grid points), single channel calculations, in whichchannels extend to different depths within the melting col-umn. These calculations have the same parameters as Fig.4b except for the compaction porosity φc which controls thebulk viscosity of the matrix at low porosities [see Spiegel-man et al., 2001]. Results can be understood in terms ofthe parameter φc/φ0, which is the compaction porosity rel-ative to the reference porosity at the top of the domain inthe absence of channels. Figure 4b has φc/φ0 = 0.1. (a)φc/φ0 = .2 The channels begin about halfway up the boxand the minimum inter-channel porosity is .22φ0 producing∼ 4 orders of magnitude variation in highly incompatible el-ement concentration. (b) φc/φ0 = 0.3, producing 2 ordersof magnitude variation in highly incompatible element con-centration. (c) φc/φ0 = 0.4. Brackets above each porosityimage give [φmin/φ0φmax/φ0] at the top of the column.

Diffusion/Dispersion Another possibility for reducingmodel variance is molecular diffusion and/or hydrodynamicdispersion. While the models presented in this paper includediffusion in the reactive “major elements”, they do not, atpresent, incorporate diffusion of trace elements. However,the consequences of diffusion/dispersion can be estimated.

Using an argument similar to that of Spiegelman andKenyon [1992], we can estimate a diffusive Damkohler num-ber which considers the importance of diffusion across thechannels relative to advective transport along the channels.The Damkohler number

DaD =Deff l

w0d2(1)

is the time it takes for a tracer to be transported a distance lalong the channel at speed w0 divided by the time it takesto diffuse across a channel of width d given an effectivediffusivity Deff .2 The effective diffusivity includes molec-ular diffusion and hydrodynamic dispersion. Systems withDaD ∼< 0.1 have negligible dispersion [Spiegelman andKenyon, 1992]. Rearranging Eq., (1) we can estimate thewidth of channels that can preserve their internal chemicalstructure and will not be homogenized by diffusion and dis-persion. This width is

d ≥√

10Deff l

w0(2)

If we assume that the melt velocity is approximately 50times the solid upwelling velocity (i.e w0 ∼ 1.5 m yr−1=5×10−8 m s−1), use values of molecular diffusivity for rareearth elements in Jadeite/Diopside melts of Dm ∼ 10−11 m2

s−1[Nakamura and Kushiro, 1998] and assume that meltshave traveled at least 30 km (10 kb) in channels, then Eq.(2) suggests that channels wider than ∼ 10 m will be able topreserve their internal variability against diffusion. A similarresult is reported by Braun and Kelemen [2002] (who alsoprovide data on the size/frequency relationships of dunitechannels in the mantle section of the Oman ophiolite).

Of course, in porous media, hydrodynamic dispersionoutweighs molecular diffusion at sufficiently large veloci-ties. We can estimate these effects as well. Bear [1988]gives relationships for the ratio of the total longitudinal dis-persion to molecular diffusion Dl/Dm as a function of thegrain-scale Peclet number

Pea =w0a

Dm(3)

where a is the grain radius. For Pea ∼< 1, Dl ≈ Dm butfor Pea > 1 then Dl ≈ PeaDm which is actually inde-pendent of molecular diffusivity. Assuming a grain size of

21/DaD is identical to what we called a Peclet number in Spiegelman

and Kenyon [1992].

Spiegelman et al.: Channel induced chemical variation 11

1 mm and the parameters used above, Pea ∼ 5. In thisregime, the Damkohler number is also independent of meltvelocity and we can estimate the minimum channel width asd =

√10al ≈ 17 m which is similar to the previous esti-

mate. This may be an overestimate of the dispersion, andtherefore of the required channel width as the longitudinaldispersivity tends to be larger than the transverse diffusivitywhich controls chemical spreading across the channels.

Moreover, these estimates may also be conservative be-cause they neglect the lateral advection of depleted meltsinto the channels, which counteracts diffusive spreading.Again, we can estimate this effect using another Peclet num-ber

Peh =u0d

Deff(4)

which measures the importance of horizontal advection atmelt velocity u0 to horizontal diffusion/dispersion. ForPeh ∼> 10, advection dominates over diffusion. Using theparameters for a 10m wide channel from the previous fewparagraphs suggests that a horizontal component of velocityu0 ∼> 2 mm yr−1, is sufficient to support horizontal con-centration gradients. This velocity is significantly smallerthan the solid upwelling velocity, while the horizontal com-ponent of velocity near the channel edges in Fig. 7b is ap-proximately 5 times faster than the solid upwelling velocity.This suggests that lateral advection should be able to sus-tain channel variability despite the homogenizing effects ofdiffusion/dispersion.

Future work will check these simple scaling argumentsby explicitly including dispersion. If the scaling argumentsare reasonable, however, they suggest that dispersion mayhomogenize channels < 5–10 m wide while allowing sig-nificant variability to be preserved in larger channels. Animportant test of these ideas is to look for across channelvariation in field exposures such as the Oman ophiolite.

3.2. Comparison to Observations

While there is considerable work to do to explore the be-havior and chemical consequences of the channeling mecha-nism presented here, we can begin to discuss how well thesemodels account for available observations. Comparison ofthe models to data, however, requires considering the parti-tioning behavior of specific elements. For the rare earth el-ements, this requires at least two bulk partition coefficientsfor each element. The first corresponds to melting in thegarnet lherzolite stability field and the second in the spinellherzolite stability field (see Table 1). This introduces an-other input variable, the depth of the garnet-spinel transition

relative to the depth of channel initiation.3

Figure 8 shows trace element patterns calculated from thechannel structure in Fig. 7b with the partition coefficientsin Table 1. As before, each of these distributions is calcu-lated by sampling the melt compositions at the top of thecolumn weighted by the melt flux. These distributions aresimilar to those observed in melt inclusions and lavas (Figs.1–2). Highly incompatible elements show about two ordersof magnitude variation, while there is about a factor of twovariation for moderately incompatible elements such as Yb.Moreover the most enriched melts are only about a factor oftwo more enriched than the mean and there is a pronounced“tail” of ultra-depleted melts.

The principal difference between Figs. 8a and 8b is howthe channels sample the garnet-spinel transition. In Fig. 8a,channels are initiated below the garnet-spinel transition, sothat the centers of the channels transport mixtures of deepmelts with clear garnet signatures. In Figure 8b, channelsare initiated at a depth shallower than the garnet/spinel tran-sition, so the garnet signature is subdued. In both cases,however, the edges of the channels are strongly fractionatedin the heavy rare earths leading to a factor of 2 variability inYb. The large and obvious garnet signatures in Fig. 8a arenot seen in mid-ocean ridge basalt. All else being equal, thissuggests that channels of focused melt flow do not extendto the garnet-spinel transition. More generally, these calcu-lations demonstrate, again, that the distribution of chemicalvariability, rather than the mean compositions, are a sensi-tive indicator of the geometry of melt transport networks.

In addition to calculating the distribution of melt com-positions, we can also calculate the expected distribution of“abyssal peridotite” compositions (i.e. solid residues) pro-duced by these models. Unlike the melts, which are sampledfrom the distribution of compositions weighted by melt flux,the residues should be sampled from compositions weightedby area at the top of the model domain. Since most of thearea is composed of inter-channel regions, the majority ofresidues are highly depleted. Figure 9 illustrates clinopyrox-ene compositions that are in equilibrium with melts at thetop of the column, weighted by area, and compares themto the range of clinopyroxene compositions in abyssal peri-dotites [e.g. Johnson et al., 1990; Johnson and Dick, 1992]and Oman harzburgites [Kelemen et al., 1997] Again, thecorrespondence between model and observation is surpris-ingly good.

3In fact, there is also continuous variation of distribution coefficientsthroughout a realistic melting column, due to changing proportions ofolivine, orthopyroxene, and clinopyroxene, as well as spinel and garnet, inthe residue. However, we have not yet attempted to incorporate this effectin the modeling described in this paper.

Spiegelman et al.: Channel induced chemical variation 12

a Ba Th U La Ce Nd Sm Eu Gd Tb Dy Ho Er Tm Yb10

−2

10−1

100

101

102

cf /cs 0

Mean concentration13.61% Batch melt

Center melts

Depleted edges

b Ba Th U La Ce Nd Sm Eu Gd Tb Dy Ho Er Tm Yb10

−2

10−1

100

101

102

cf /cs 0

Mean concentration13.61% Batch melt

Center melts

Depleted edges

Figure 8. Melt composition distributions from initial mod-els with a two-level partition coefficient structure to modelU-Series and REE’s. The background melt and solid flowfield is the same as in Fig. 7b with the channels beginningabout half-way up the box. Compositions are calculated forhighly incompatible elements (Ba,Th,U) and REE’s using atwo level partition coefficient field with D1 up to a heightzd and D2 from zd to the top. Specific bulk partition coeffi-cients are given in Table 1 corresponding to garnet and spinelperidotite. Each figure shows synthetic data sets sampledout of the distribution given by the melt flux. The black lineshows the mean of the distribution, the red line is the analyticsolution for a batch melt with the mean degree of melting.While both models have the same mean, the distributions aredifferent. (a) Garnet-spinel transition at zd = 0.6. Channelstap into the garnet region giving enriched center melts withclear garnet signature. (b) zd = 0.4 channels occur abovethe gt-sp transition leaving a muted garnet signature. In bothcases, the large fractionations in Yb come from includingshallow, near-fractional melts from the channel edges.

a

Cho

ndrit

e no

rmal

ized

con

cent

ratio

n

OMB-43 OMB-31 OMB-30 OMB-27 OMB-23 OMB-22 OMB-16 OMB-14B OMB-14A

Cpx in Oman

harzburgite

b

abyssal perid

0.01

0.1

1

10

La Ce Nd Sm Dy Er Yb

b La Ce Nd Sm Eu Gd Tb Dy Ho Er Tm Yb10

−2

10−1

100

101

cs /cs 0

Spidergrams/Area weighted z=1 and t=92.0016, all x

Figure 9. Comparison of observed distribution of clinopy-roxene compositions in abyssal peridotites to model calcula-tions. (a) Clinopyroxene compositions in harzburgites fromthe mantle section of the Oman ophiolite [Kelemen et al.,1995a] superimposed on the range of compositions fromabyssal peridotites [Johnson et al., 1990; Johnson and Dick,1992], showing the predominance of highly depleted sam-ples. (b) Distributions of clinopyroxenes in equilibrium withmelts at the top of the melting column corresponding to Figs.7b and 8b. This distribution is sampled uniformly by area (asif we were sampling residues from the top of the column)and is dominated by depleted inter-channel samples.

Table 1. Bulk partition coefficients used for Figures 8–9field Ba Th U La CeGarnet 0.0001 0.0027 0.0054 0.0057 0.0105Spinel 0.0001 0.0008 0.0010 0.0039 0.0064

Nd Sm Eu Gd TbGarnet 0.0285 0.0515 0.0705 0.0962 0.1340Spinel 0.0134 0.0170 0.0206 0.0210 0.0224

Dy Ho Er Tm YbGarnet 0.1811 0.2487 0.3170 0.4634 0.6140Spinel 0.0244 0.0246 0.0253 0.0279 0.0302

Spiegelman et al.: Channel induced chemical variation 13

3.3. Further tests/further work

Figures 8–9 are encouraging and suggest that, possiblyfor the first time, there are physically consistent geochemicaltransport models that produce distributions of melt and solidresidues similar to what is actually observed. The physicalbasis for these distributions is easily understood and quanti-fies many of the qualitative ideas inherent in “dynamic melt-ing models”. However, to produce these distributions re-quires including the fluid-mechanics of melt transport thatcontrol the amount of mixing between melts formed at dif-ferent depths. Nevertheless, even these transport models arehighly simplified with respect to possible melting regimesand it is worth reviewing, briefly, some additional tests ofthese models.

In addition to calculating distributions of stable trace el-ements in melts and residues, these models can also beused to calculate the effects of melt transport on uraniumseries (U-series) disequilibrium. Some important observa-tions that have not been explained by traditional meltingmodels include the correlation between Thorium excessesand elemental U/Th ratios, in which samples with highU/Th have smaller excesses [e.g. Lundstrom et al., 1999].This is particularly clear for Alvin collected samples from9◦N EPR that show correlations between (230Th/232Th) and(238U/232Th) as well as an intriguing anti-correlation be-tween (226Ra/230Th) and (230Th/238U) for samples withidentical Sr and Nd isotopes [Sims et al., 2001]. These obser-vations are not well explained by models of dynamic meltingand ingrowth [e.g. Williams and Gill, 1989; McKenzie, 1985]which produce positive correlations in Ra vs. Th. Theyare also not explained by open-system models of U-seriesexcesses [Spiegelman and Elliott, 1993; Lundstrom et al.,1995b, a] that can produce Ra and Th excesses in differentparts of the melting regime but, in their simplest form, do notfractionate U/Th ratios from source. Recently, Lundstrom[2000] and Jull et al. [2000, 2002] have developed simpli-fied “two-porosity” models to allow for multiple paths forthorium and radium [see also Iwamori, 1994, 1993]. Thesemodels can explain the U-series observations, but requirespecification of many parameters. Our models should pro-duce similar geochemical results, but with fewer input pa-rameters combined with richer interaction between channeland inter-channel regions. Initial results [Spiegelman andKelemen, 2002] of U-series calculations seem promising.

In addition to explaining U-series observations, anotherobvious test of these models is to look for spatial variabil-ity of composition in dunites of different sizes in the mantlesection of ophiolites. Such work could put constraints on theimportance of dispersion in mantle melt transport, as wellas determine whether variability resides at the sub-channelscale, or whether different melts are transported by different

types of channels in a drainage network. However, this willbe difficult, as most chemical variability in melt composi-tion and models is in highly incompatible elements whoseconcentration is difficult to measure in dunites. Conversely,moderately incompatible to compatible element abundancesthat are easy to measure in dunites (e.g., Ca, Ti, Al, Cr, Fe,Mg, Ni), are subject to subsolidus redistribution in mantlesamples, and show little variation in melts and models. Thus,a serious test of model predictions for dunites awaits trace el-ement data on a large number (of very rare) clinopyroxenesas a function of dunite width, or measurement of slowly dif-fusing, highly incompatible elements (e.g. REE) in olivine.

Finally there is the issue of source heterogeneity. Themodels shown so far demonstrate that melt transport cancause significant variability, even in melts arising from ahomogeneous source. Nevertheless, it is clear from isotopedata that the mantle source of mid-ocean ridge basalts is het-erogeneous. Future work will investigate how a channel net-work samples a heterogeneous source, and how this affectscorrelations between trace element and isotopic variability.At this point, one can imagine several scenarios. For ex-ample, if channels nucleate on melting heterogeneities (e.g.veins/pyroxenites) it is possible that they would preservecorrelations present in the source. Alternatively, if channelnetworks cross heterogeneities, this could destroy correla-tions between trace element and isotope variability.

Developing models to test these ideas is possible. How-ever, it will also be useful to develop a better understand-ing of correlations between trace element variability and iso-topic variability in mid-ocean ridge basalt. For the few datasets where both isotope and trace element data are availableon the same samples [Niu et al., 1999, e.g.], there is often aweak correlation between isotopic enrichment and trace ele-ment enrichment, but this tends to be weaker than the inter-correlations between trace elements and isotopes separately.

The results in this paper suggest that well characterizeddata sets with a statistically meaningful number of analysesof trace elements and isotopes, could provide dramatic newinsight into the structure of melt transport networks beneathmid-ocean ridges.

4. Conclusions

1. Field and chemical evidence both suggest that melttransport in the mantle occurs in a channelized net-work.

2. Physically consistent models, in which channels ariseas a result of reactive melt transport, can produce or-ders of magnitude variability in trace element compo-sitions of melts on short length scales from homoge-neous sources.

Spiegelman et al.: Channel induced chemical variation 14

3. The distributions of melt compositions are similarto those produced by models of “dynamic melting”.However, the physical transport models transpose thevertical variability produced by polybaric, dynamicmelting into horizontal variability across individualchannels. Moreover, for models that produce similarmelt compositions, estimates of “retained melt frac-tion” from dynamic melting models are larger thanmelt porosities in channelized models.

4. The centers of porous melt channels in our modelstransport mixtures of melts produced across the melt-ing column, including trace element enriched, small-degree melts from depth. The edges of the channels,however, transport highly depleted, shallow melts pro-duced in the compacting, inter-channel region.

5. Slow laminar flow with negligible dispersion can pre-serve this lateral structure in channels ∼> 10 m wide.

6. Preliminary comparison to data from melt inclusions,lavas and abyssal peridotites shows that these modelsproduce variability similar to that observed.

7. These models suggest that important information onthe structure of partially molten regions is containedin the distributions of variability.

Acknowledgments. Peter Reiners and an anonymous re-viewer provided very helpful reviews. This work was supportedby NSF grants OCE-9530307 to Spiegelman, OCE99-070079 andOCE01-37327 to Spiegelman and Kelemen, and OCE94-16616,OCE98-19666, and OCE01-18572 to Kelemen et al. This is LDEOcontribution xxxx.

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This preprint was prepared with AGU’s LATEX macros v5.01, with theextension package ‘AGU++’ by P. W. Daly, version 1.6b from 1999/08/19.