mantle ï¬‚ow, melting, and dehydration of the iceland mantle plume

ELSEVIER Earth and Planetary Science Letters 165 (1999) 81–96

Mantle flow, melting, and dehydration of the Iceland mantle plume

Garrett Ito a,Ł, Yang Shen b, Greg Hirth c, Cecily J. Wolfe c

a Department of Geology and Geophysics, School of Ocean and Earth Science and Technology, University of Hawaii,Honolulu, HI 96822, USA

b Graduate School of Oceanography, University of Rhode Island, Narragansett, RI 02882, USAc Department of Geology and Geophysics, Woods Hole Oceanographic Institution, Woods Hole, MA, USA

Received 9 February 1998; revised version received 1 October 1998; accepted 2 October 1998

Abstract

Recent studies have shown that the extraction of water from the mantle due to partial melting beneath mid-ocean ridgesmay increase the viscosity of the residuum by 2–3 orders of magnitude. We examine this rheological effect on mantleflow and melting of a ridge-centered mantle plume using three-dimensional numerical models. Results indicate that theviscosity increase associated with dehydration prevents buoyancy forces from contributing significantly to plume upwellingabove the dry solidus. Consequently, upwelling in the primary melting zone is driven passively by plate spreading and meltproduction rates are substantially lower than predicted by models that do not include the rheological effect of dehydration.Predictions of along-axis crustal thickness, bathymetric, and gravity variations are shown to be consistent with observationsat Iceland and along the Mid-Atlantic Ridge. Furthermore, these predictions result from a model of a plume with relativelyhigh excess temperature (180ºC) and narrow radius (100 km) — properties that are consistent with estimates previouslyinferred from geochemical and seismological observations. Calculations of incompatible trace-element concentrationssuggest that observed along-axis geochemical anomalies primarily reflect incompatible element heterogeneity of the plumesource. 1999 Elsevier Science B.V. All rights reserved.

Keywords: Iceland; dehydration; mantle plumes; mid-ocean ridges; melting; hot spots

1. Introduction

Several geophysical and geochemical observa-tions support the mantle plume hypothesis [1] forthe origin of the Iceland hot spot. For example,the broad bathymetric swell along the Mid-AtlanticRidge (MAR) axis (Fig. 1) has been proposed toreflect transport of low density plume material awayfrom an Iceland plume source [2]. This scenario issupported by along-axis gradients in trace-element

Ł Corresponding author. Tel.: C1 808 956 4777; Fax: C1 808956 5512; E-mail: [email protected]

and isotope compositions that suggests mixing be-tween the plume and normal mid-ocean ridge basalt(MORB) sources (e.g. [3,4]). The plume hypothe-sis is also supported by the elevated mantle poten-tial temperature (¾200ºC) required by one-dimen-sional (1D) melting models to explain the crustalthickness at Iceland [5,6], and the major- [7,8]and trace-element [9] concentrations at Iceland andalong the Reykjanes Ridge. Compelling evidencefor an Icelandic mantle plume is revealed in com-pressional-wave (P-wave) and shear-wave (S-wave)tomographic models that show a cylindrical shapedvelocity low extending from a depth of ¾100 km to

0012-821X/99/$ – see front matter c 1999 Elsevier Science B.V. All rights reserved.PII: S 0 0 1 2 - 8 2 1 X ( 9 8 ) 0 0 2 1 6 - 7

82 G. Ito et al. / Earth and Planetary Science Letters 165 (1999) 81–96

Fig. 1. Bathymetry map (illuminated from the northwest) of the North Atlantic showing the Iceland hot spot along the Mid-AtlanticRidge. Data are combined shipboard and Etopo5 bathymetry [13]. Contour interval is 0.5 km.

at least 400 km beneath Iceland [10]. Furthermore,P-to-S phase conversions at the 410-km and 660-kmseismic discontinuities [11] indicate this anomalyoriginates in the lower mantle. Both of these seismo-logical studies suggest that the Iceland plume has anexcess temperature greater than ¾150ºC and a radiusless than ¾200 km.

While the plume hypothesis for Iceland is widelyaccepted, fluid dynamic calculations have failed tosimultaneously explain observational constraints onboth crustal and mantle structure. Ribe et al. [12] andIto et al. [13] incorporated melting in geodynamicmantle flow models and proposed two end-member

models of the Iceland plume. The first model hada relatively broad (radius ¾300 km) plume sourcewith a moderate temperature anomaly (∆T ¾ 75ºC)[12,13]. This model successfully predicted observedcrustal thickness, bathymetric, and gravity varia-tions along the MAR [12,13], but required a plumesource with temperature anomaly too low and radiustoo broad to be consistent with geochemical [7–9]and mantle seismological observations [10,11]. Thesecond end-member model had a relatively narrowplume source (radius <100 km) and a greater tem-perature anomaly (>150ºC) — properties consistentwith the geochemical [7–9] and seismological ob-

G. Ito et al. / Earth and Planetary Science Letters 165 (1999) 81–96 83

servations [10,11]. This second model, however, pre-dicted unreasonably high crustal thicknesses (>160km) at Iceland, and therefore over-predicted bathy-metric and gravity anomalies along the MAR. Anarrow, hot plume model would only be feasible iflarge volumes of melt migrate several hundreds ofkilometers along the MAR [13]. However, we areunaware of any process that could promote suchstrong along-axis melt migration. Along-axis crustalflow has been proposed [14] but requires low crustalviscosities that may be at odds with experimentalconstraints [15] as well as seismic data that sug-gest relatively low temperatures in the lower crust atIceland [16,17].

In this study, we introduce a third model that, byincorporating the effects of water content on man-tle rheology, does not require substantial along-axismelt transport. Laboratory experiments indicate thatthe viscosity of the mantle is extremely sensitiveto water content and may increase by 2–3 ordersof magnitude due to the extraction of water fromolivine during melting beneath mid-ocean ridges[18]. We investigate the effects of a high viscos-ity, ‘dehydrated’ layer on mantle flow and meltingof a ridge-centered mantle plume, and then examinethe consequences on geophysical and geochemicalanomalies. We show that when this rheological ef-fect is incorporated, models of a high-temperature,narrow plume source can successfully predict theobserved crustal structure at Iceland and along theMAR.

2. Estimated viscosity increase due to mantledehydration

Analyses of laboratory experiments indicate thatthe water content of the MORB source is sufficient toreduce the effective viscosity (� D −=Pž, see Table 1for definition of variables) of peridotite deformed inthe dislocation creep regime by 2–3 orders of magni-tude relative to anhydrous peridotite [18]; dislocationcreep is likely the dominant deformation mechanismof the upper mantle [19]. The rheological effects ofthe extraction of water during partial melting areillustrated in Fig. 2a using the analysis of Hirth andKohlstedt [18]. Assuming a water content compara-ble to the MORB source (125 š 75 wt ppm, e.g.,

Table 1Notation

Variable Meaning Value Units

cp specific heat 103 J kg�1ºC�1

C0 trace-element sourceconcentration

CL trace-element meltconcentration

D fluid depth 400 kmE activation energy 1.9 ð 105 J mol�1

F degree of depletionNF average melt fraction

g acceleration of gravity 9.8 m s�2

I identity matrixKD bulk partition coefficientp pressure PaQ plume volume flux km3 My�1

R gas constant 8.314 J K�1 mol�1

∆S entropy change onmelting

400 J kg�1ºC

T potential temperature ºCT0 reference potential

temperature1350 ºC

TR real temperature KTR0 real temperature at

mid-depth of box1743 K

∆T plume temperatureanomaly

180 ºC

u mantle flow rate vector km My�1

U ridge full spreading rate 19 km My�1

V activation volume 4 ð 10�6 m3 mol�1

W along-axis plume width kmÞ coefficient of thermal

expansion3.4 ð 10�5 K�1

þ coefficient of depletiondensity reduction

0.024

Pž strain rate My�1

� melting rate My�1

� thermal diffusivity 31 km2 My�1

� viscosity Pa s�0 reference viscosity 3.5 ð 1019 Pa s² mantle density kg m�3

²0 mantle reference density 3300 kg m�3

− stress Pa

[18,20]) and potential temperature of 1530ºC, we es-timate that hydrous melting initiates at a pressure of¾5.8 GPa, or depth of ¾180 km. From this depth tojust below the dry solidus, fractional melting calcu-lations predict ¾1% melting to occur, during which¾75% of the original water content is extracted.This loss in water is predicted to result in a 4–5fold increase in mantle viscosity (Fig. 2a). As the


Fig. 2. (a) Variations in viscosity as a function of pressure, temperature, and water content (solid profile) due to adiabatic decompressionand melting of mantle with a potential temperature of 1530ºC. The dotted profiles are for a constant potential temperature without theeffects of dehydration. (b) Viscosity profiles through the center of the plumes in numerical models. The dashed profile shows temperatureand pressure dependence of Case 1, without dehydration; the solid profile shows added effects of dehydration of Case 2. Viscosityincreases gradually above the dry solidus due to latent cooling and increases rapidly in the thermal boundary layer near the surface.These effects are not included in (a).

upwelling mantle crosses the dry solidus, melt pro-ductivity increases rapidly and the remaining wateris extracted, leading to an abrupt increase in viscos-ity by a factor of fifty. The retention of melt in themantle reduces mantle viscosity; however, this effectis not considered since the reduction in viscosity islikely to be small (within a factor of two) for retainedmelt contents less than ¾3% [21]. Thus, above thedry solidus, where most melting occurs, plume vis-cosity may be fifty times greater than below the drysolidus.

The Iceland plume may have twice the watercontent of the ambient upper mantle [22–24] as wemodel. Using a water content comparable to theMORB source simplifies numerical computationsand allows us to examine what is likely a lower-bound viscosity increase at the dry solidus. A factorof two greater water content would approximatelyhalve plume viscosity [18] below the melting zoneand increase the depth at which melting begins by25–35 km; it would not affect viscosity in the pri-mary melting zone above the dry solidus. A highersource water content would therefore only affect theflow of the plume beneath the dry solidus, and asdiscussed below, this has little impact on our re-sults.

3. Governing equations and numerical method

We simulate the effects of dehydration on mantlerheology by incorporating an abrupt viscosity in-crease at the dry solidus (Fig. 2b). This viscosityjump is controlled numerically by a pre-exponentialfactor A in the Arrhenius relationship,

� D A�0 exp²

E C pV

RTR� E C ²0g.0:5D/V

RTR0

¦(1)

[13], where A is 1.0 and 50.0 below and above thedry solidus, respectively. The ambient and referenceviscosity �0 and real temperature TR0 are definedat a depth of 200 km .0:5D/ (see Table 1). Thetemperature and pressure dependence of viscosity iscontrolled by the activation energy E and activationvolume V . To simulate the behavior of non-Newto-nian rheology for these steady-state calculations, Eand V are reduced relative to experimentally deter-mined values [25]. For the values chosen, a plumetemperature anomaly of 200ºC reduces the effectiveviscosity by a factor of five. A cut-off viscosity of500 �0 ensures numerical stability (maximum lateralviscosity variation is 103) and is adequate to simulaterigid lithospheric plates.


The equilibrium equations include conservationof mass

r Ð u D 0 (2)

momentum

r Ð − D ∆²g (3)

and energy

@T

@tD �r2T � u Ð rT � T ∆S

cp� (4)

In Eq. 3, the 3D stress tensor − depends on the strainrate tensor Pž according to − D 2� Pž � pI, and mantledensity variation ∆² depends on thermal expansionÞ and degree of melt depletion F such that

∆² D �²0.Þ∆T C þF/ (5)

[13]. Eq. 4 describes the balance in energy trans-fer due to thermal diffusion, advection, and latentheat loss associated with melting. We account forhydrothermal cooling at the ridge axis by enhancingthermal diffusion by a factor of eight at depths withinthe crust [26]. This effect results in a relatively coolcrust (mean temperature <600ºC) beneath Iceland,consistent with observations of deep earthquakes(12–14 km [17]) and low mid-crustal S-wave attenu-ation [16].

The rate at which depletion F changes at fixedcoordinates in the mantle is governed by the relation-ship

@F

@tD �u Ð rF C � (6)

where � is the melting rate experienced by individ-ual pieces of mantle. � is proportional to upwellingrate and is governed by the local potential temper-ature T and the relation between melt fraction Fand homologous temperature described by McKen-zie and Bickle [6]. We only calculated melting rel-ative to the dry solidus, thus the small amount ofmelt produced between the wet and dry solidi (¾1%[18]) is not considered. We also assume that meltingstops when clinopyroxene is consumed (‘cpx-out’ atmaximum F of 25%) because a large increase intemperature may be required for significantly moremelting to occur [27]. In our models, melting stops ata depth of ¾40 km beneath Iceland due to the effectsof hydrothermal cooling and the cpx-out criterion.

This depth is roughly consistent with preliminarysurface wave analyses over central Iceland, whichshow an abrupt decrease in S-wave velocity at adepth of ¾50 km — a velocity boundary which maymark the upper extent of the partially molten mantle(I. Bjarnason, personal comm., 1998). A depth of¾40 km is also consistent with a final melting depthof ¾45 km inferred from basalt chemistry [8].

The melt production rate per unit length ofridge axis is calculated by integrating melting ratesin cross-sections perpendicular to the ridge axis.Crustal thickness is calculated by dividing melt pro-duction rate by the full-spreading rate (U D 19km=My [28]) and therefore represents the amount ofcrust that would be created if all melt generated inthe mantle migrates perpendicular to and accretes atthe ridge axis. The dependence of calculated crustalthickness on input plume temperatures and viscosi-ties may be uncertain by as much as 50% owingto uncertainties in the amount of melt produced perkilobar of decompression; the McKenzie and Bickle[6] melting model predicts an average of 1% ofdepletion per kilobar of decompression, but meltproductivity may vary by a factor of two through themelting column (e.g. [29,30]).

We use the numerical technique of Ito et al. [13] tosolve Eqs. 2–6 in Cartesian geometry as illustrated inFig. 3. The top surface of the box moves at a constanthorizontal rate of 0:5U to define the half spreadingrate of the ridge axis (located at x D z D 0). Thetop is also maintained at T D 0ºC, which generates athermal boundary layer that thickens with increasingx . The top corresponds to the isostatic surface ofa 7-km-thick oceanic crust, therefore, variations inpredicted crustal thickness do not affect lithostaticpressure in the melting zone.

A plume source is simulated by imposing a tem-perature anomaly ∆T in a columnar region in thelower portion of the box (i.e. z > 240 km) atx D y D 0. Temperature is maximum at the centerof the plume source .T D T0 C ∆T / and decreasesas a Gaussian function of radial distance to T0 atthe full plume source radius. The lower portion ofthe box (z > 240 km) is maintained at a potentialtemperature T0 D 1350ºC except inside the plumesource; thus the energy equation (Eq. 4) is solvedonly in the upper portion of the box (240 ½ z ½ 0km) where the plume interacts with the ridge axis


Fig. 3. Perspective view of 3D numerical model geometry. Shading denotes temperatures and vectors show flow (length proportional toflow rate) of the dehydration model (Case 2). Black contours are intervals of 50ºC and white contours are at intervals of 200ºC. Verticalplane on the right is a cross-section along the ridge axis .x D 0/, while the vertical plane to the left is a cross-section perpendicular tothe ridge axis .y D 0/. Both top .z D 0/ and bottom boundaries .z D D/ are isothermal planes with the bottom, shear stress free, and thetop, fixed at a horizontal velocity of 0:5U . All boundaries are closed to flow both in and out of the box.

and melts. All boundaries are closed to flow; thebottom and side boundaries are free slip and theside boundaries are insulating. By symmetry, thereflecting sides allow this quarter of a plume-ridgesystem to represent a circular plume and two-platespreading ridge. Calculations were run until the sys-tem achieved steady-state as determined by the pointat which along-axis plume width, maximum crustalthickness, and Nusselt number were within 2% oftheir extrapolated asymptotic values.

4. Effects of dehydration on mantle flow andmelting rate

4.1. Case 1: without dehydration viscosity increase

In the first model, the viscosity increase due to de-hydration is not incorporated (Fig. 2b). We considera plume radius of 100 km and temperature anomaly,∆T D 180ºC (Fig. 4a,b). The details of the modelare similar to that described by Ito et al. [13], and are

therefore not discussed here. The relevant attributesare as follows: (1) shallower than ¾100 km, theplume upwelling decreases and the plume spreadslaterally beneath the thermally controlled rheologicalboundary layer; (2) at the plume center, the averageupwelling rate in the melting zone (depths 40–115km) is high, 130 km=My (Fig. 5a), which results inhigh melting rates (Fig. 4b) and unreasonably largecrustal thicknesses (270 km) at Iceland (Fig. 5b);and (3) adjacent to the plume (100 < y < 200 km),predicted upwelling and melt production are mini-mum because in this region upwelling rate is smalland plume flow is predominantly lateral (Fig. 4a).Far from the plume, where mantle temperature isnormal, this model predicts a crustal thickness of6.5–7.0 km.

4.2. Case 2: with dehydration viscosity increase

The model parameters for Case 2 are the same asin Case 1, except that we include the influence of de-hydration on mantle viscosity (Fig. 2b and Fig. 4c,d).

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Fig. 4. Perspective views of cross sections through the center of the plume perpendicular to the ridge axis and along the ridge axis. Diagrams on the left show viscosity (shaded),temperature (contours at 50ºC intervals for T ½ 1300ºC and 300ºC intervals for T < 1300ºC), and flow vectors (size proportional to magnitude) for (a) the model without theviscosity increase due to dehydration (Case 1) and (c) the model that includes a fifty-fold increase in viscosity at the dry solidus (Case 2). Diagrams on the right show extent ofdepletion (shaded) and melting rate contours for (b) Case 1 and (d) Case 2. Contour interval is 0.1 My�1 in (b) and 0.02 My�1 in (d).


Fig. 5. (a) The average vertical velocity beneath the ridge axis, above the dry solidus is shown along the ridge axis. The dashed profile isfor Case 1, without dehydration (maximum is 130 km=My at a distance of 0 km), and the solid profile is for Case 2, with dehydration.(b) Predicted melting rate per length of ridge axis and crustal thickness due to Case 1 (dashed, maximum is 270 km at a distanceof 0 km) and Case 2 (solid) are compared with thicknesses estimated from seismic refraction data. Seismic measurements along theReykjanes Ridge (dots) and at older seafloor near the continental margins (triangles) are from [33]. The vertical gray bar shows the rangeof thicknesses near Krafla volcano [32], ¾120 km north of Vatnajokull volcano, which marks the center of the mantle plume [10]. Thehorizontal gray bar is the average crustal thickness in an ¾100 km-long profile along the Kolbeinsey Ridge [50]. We also note that acrustal thickness of central Iceland of 38–40 km is reported by [31].

The primary difference in predicted mantle flow isthat upwelling rates in the melting zone in Case 2are reduced substantially relative to that in Case 1and therefore lateral plume spreading occurs beneaththe dry solidus, or ¾100 km deeper than in Case1. At the plume center, the mean upwelling rate inthe melting zone is ¾11 km=My (Fig. 5a), an orderof magnitude less than that calculated in Case 1.Likewise, melting rates are lower and the crust isproportionally thinner (Fig. 4d, Fig. 5b). The thick-est ridge axis crust (20–33 km) is predicted to belocalized within ¾100 km of the plume center. Thisstructure results from the high temperatures overthe plume center, which thicken the melting regionand enhance upwelling near the base of the meltingzone. At along-axis distances of 150–500 km, crustalthicknesses of 10–20 km are produced by hot plumematerial that has spread along-axis away from theplume source. At distances 500–800 km, the crust

tapers from a thickness of 10 km to 6 km, which re-flects the limit of hot material transported along-axisfrom the outer edges of the plume source. Beyond¾800 km the model ridge axis is unaffected by theplume and calculated crustal thickness remains near6 km.

4.3. Discussion of model results

When dehydration is not considered (Case 1), theviscosity in the primary melting zone remains low(<5 ð 1019 Pa s, Fig. 4a) and density variations arepredicted to drive large variations in upwelling andmelting rate along the ridge axis (Fig. 4b, Fig. 5a).In contrast, when dehydration is considered (Case2), the predicted viscosity in the melting zone ishigh enough (>3 ð 1020 Pa s, Fig. 4c) to preventplume buoyancy from contributing significantly toupwelling as indicated by the small variation in av-


erage upwelling rate along the ridge axis (Fig. 5a).Upwelling in the melting zone is largely a passiveresponse to plate spreading. Consequently, plumetemperature has little influence on mantle flow in themelting zone and acts primarily to thicken and widenthe region of partial melting. Melting predicted bythis model is analogous to 1D passive upwellingmodels proposed by [7–9] that suggest a mantletemperature anomaly of ¾200ºC. Similar to the pas-sive upwelling models, Case 2 predicts a maximumcrustal thickness of 33 km, which is consistent withthe 30–40-km thickness range measured seismically[31–33] (Fig. 5b).

As noted earlier, the Iceland plume source mayhave twice the water content as simulated in ourmodel. While this would not affect viscosity andmantle flow above the dry solidus, the higher watercontent would reduce the viscosity by a factor of twoand enhance flow of the plume below dry solidus.Previous numerical studies have demonstrated thatthe dominant parameters controlling the steady-statewidth W to which a plume spreads along a ridge axisare spreading rate U of the ridge and volume flux Qof upwelling plume material [12,13,34]. These stud-ies showed that W D C.Q=U/1=2, where the scalingcoefficient C is 2.5–3.0. Case 2 yields a volume fluxof 6.4 ð 106 km3=My, a full plume width of ¾1620km, and C D 2:8, thereby indicating that dehydra-tion has little effect on the above relationship. Wesuggest that a lower plume viscosity below the drysolidus would affect only the relationship betweenplume radius r , excess temperature ∆T , and flux Q.Assuming laminar (Poiseuille) flow, Q ¾ ∆Tr 4=�.Therefore, to yield the same plume flux and alongaxis width with the same ∆T , a factor of two greaterwater content would require a plume radius ¾20%smaller than that modeled in Case 2.

5. Comparisons of dehydration model withgeophysical observations

5.1. Along-axis variations in topography and gravity

Topographic and gravity anomalies reflect sub-surface density variations associated with crustalthickness as well as mantle density variations. Thegravity data in Fig. 6 are a compilation of shipboard

Fig. 6. Comparisons between predicted (solid) and observed(gray) (a) topography and (b) Bouguer gravity anomalies alongthe MAR. Dashed curves are contributions due to mantle densityvariations alone, which contribute 35% of the total predictedtopographic anomaly (3.7 km) and 30% of the total predictedBouguer gravity anomaly (�318 mGal). The remaining 65% and70% of the topographic and gravity anomalies, respectively, arepredicted to result from the thickened crust.

and on-land measurements [35] as well as satellite-derived gravity data [36]. We removed the effectsof seafloor topography [37] using a spectral method[38] assuming a seafloor–water density contrast of1900 kg=m3. We then combined the marine datawith the on-land Bouguer gravity data to producea continuous profile along the MAR. We generatedtheoretical topographic and Bouguer gravity profilesfrom our models using the procedure of Ito et al.[13], which accounts for lateral variations in mantledensity (Eq. 5) and lower crustal density associatedwith the high Mg content of the Icelandic crust[9,13]. Crustal thickness topography is computed byassuming Airy isostasy, while mantle topography iscalculated by assuming Pratt type isostasy with acompensation depth of 200 km.

As noted by Ito et al. [13], large variations incrustal thickness as calculated in Case 1 predict un-realistically large bathymetric and gravity anomalies;therefore, we here focus on predictions of our dehy-dration model. Fig. 6a illustrates that the predicted


along-axis topography of our dehydration model issimilar in amplitude and wavelength to the observedtopography along the MAR. Predicted topographyis most consistent with observations along the Kol-beinsey Ridge to the north of Iceland but under-pre-dicts topography at distances >¾500 km south ofIceland along the Reykjanes Ridge. The predictedBouguer gravity profile is also generally consistentin amplitude and wavelength to the observed pro-file. The largest discrepancies occur directly overIceland where the model over-predicts the amplitudeof the observed anomaly by ¾20%, and along theReykjanes Ridge where it predicts a more positiveanomaly than observed.

5.2. Mantle tomography

The results from the recent ICEMELT broad bandseismic experiment provide constraints on the widthand temperature anomaly of the Iceland mantleplume [10,11]. We performed tomographic inver-sions of synthetic P-wave delay times generatedfrom our dehydration model to compare this modelwith the inversions of the ICEMELT seismic exper-iment. P-wave velocity perturbations due to varia-tions in temperature (decrease in velocity of 6.25ð 10�3% per 1ºC increase in temperature [39])and due to melt retention (decrease of 1.25% per1% pore volume of retained melt [39]) were con-sidered. Melt retention was calculated by assumingvertical porous melt migration with a permeabilitythat yielded maximum retained melt percentages of4.7% in the plume at depths <50 km and 2.9% be-neath the ridge far from the plume (see Ito et al.[13] for details). Additional tomographic inversionsdemonstrated that the effects of mantle composi-tional variations due to melt depletion (an increase invelocity by 0.1% per 1% increase in depletion [39])are not resolvable by the ICEMELT ray set becausethe associated velocity variations are predicted to besmall (¾1%), vary over a broad length scale, andoccur only in the shallowest 100 km of the mantlewhere ray paths are nearly vertical and do not cross[10].

A cross section of the input velocity anomalymodel is shown in Fig. 7a. Because inversions re-cover only lateral velocity perturbations rather thanabsolute velocities, this input model is referenced to

Fig. 7. Cross-sections of velocity variations taken along the lineshown in inset map. (a) Input velocity model generated frommantle temperature and porosity variations of our dehydrationmodel. Inverted P-wave velocity variations from synthetic traveltimes as generated from predicted variations in mantle (b) tem-perature alone and (c) temperature and melt retention. Contourintervals of velocity perturbations are 0.2%.

a vertical velocity profile taken far from the plumeand ridge. Velocity variations deeper than ¾180 kmreflect the temperature structure of the plume source.Shallower than ¾180 km, the velocity variations re-flect the ponding and lateral spreading of the hotplume in conjunction with the effects of melt reten-tion in the upper 100 km.


From this input model, we calculated syntheticdelay times and inverted for seismic structure, earth-quake relocations, and station terms using the sameray set and methods of the ICEMELT experiment[10]. Only linear inversions were used for seismicvelocity structure. The effect of temperature aloneon inverted structure is shown in Fig. 7b. In thedepth interval 0–150 km, the inverted velocity vari-ation over the plume is ¾0.1%. This small velocityvariation reflects the limited resolution of the to-mographic method in the shallowest 100 km of themantle as well as the small lateral temperature vari-ations in the melting zone caused by latent heat loss(Fig. 4c, Fig. 7a). In the depth interval 150–400km, the inversion recovers ¾50% of the maximumvelocity variation in the input model and resolvesthe narrow, cylindrical low-velocity zone associatedwith the plume source. The combined effects of tem-perature and melt retention on inverted structure areillustrated in Fig. 7c. Although much of the veloc-ity variation due to melt retention is absorbed inthe station terms (which are designed to account forshallow structure such as mantle structure at depths< ¾100 km and differences in crustal thickness andelevation), some of the effects of melt ‘smear’ downto depths as great as 300 km. This smearing in-creases velocity variations by 0.1–0.2% relative tothe inversions that include only temperature effects.

The inverted structure from our model is gen-erally consistent with the ICEMELT tomographicresults. Inversions of our model fail to recover thelow-velocity ‘plume head’ ponding in upper 150km due to the resolution limitations at depths <100km and the low-magnitude, broad-wavelength lateralvelocity variations predicted at depths of 100–150km. Indeed, a shallow plume head anomaly is notrevealed in the ICEMELT tomographic model as apossible consequence of these factors. The narrow‘plume stem’ below 150 km is resolved by our in-versions and is consistent in dimension with the lowvelocity anomaly recovered by the ICEMELT inver-sion [10]. The recovered amplitude for our syntheticplume anomaly of ¾0.8% (Fig. 7c) is less than the¾2% P-wave anomaly resolved by ICEMELT. Suchdifferences in amplitude, however, may in part reflectuncertainties in the relationships between the seismicwave velocities and temperature, such as the possibleeffects of anelastic dispersion [40].

6. Along-axis variations in incompatible elementconcentration

Variations in isotopic ratios [4,24] along the MARindicate a compositionally heterogeneous mantlesource near Iceland. Correlated variations in incom-patible element concentrations [3,24] suggest en-richments in these elements as well; however, sinceelemental concentrations are influenced by partialmelting, heterogeneity in source composition is dif-ficult to distinguish and has been treated in only 1Dpassive upwelling models [8]. Here we examine howmelting alone affects trace-element concentrations ofridge basalts in order to distinguish between our twomodels and to assess the degree of heterogeneity ofthe mantle source.

The effects of melting on along-axis variationsin trace-element concentration are calculated fromour numerical models by assuming modal fractionalmelting [41]. The concentration of an element in themelt, CL , relative to that of the source, C0 at eachmodel cell is,

CL

C0D 1

KD.1� F/.1=KD�1/ (7)

where F is the depletion of each cell and KD is thebulk partition coefficient [42]. We calculated CL=C0

of accumulated fractional melts along the ridge axisby weighting values in each model cell by meltingrate and averaging over ridge-perpendicular planes.For comparison, we also computed the average ex-tent of melting NF by weighting the depletion of eachcell by its melting rate and averaging over ridge-per-pendicular planes. Again we do not consider meltingbetween the wet and dry solidi which only affectscalculations of melting rate for low degree (<¾1%)melts.

Fig. 8 shows predicted variations in CL=C0, of ac-cumulated melts along the model ridge axis for bulkpartition coefficients between 0.01–0.1. Without thedehydration viscosity boundary (Case 1), strong vari-ations are predicted with a maximum in CL=C0 oc-curring over the plume source (e.g. CL=C0 > 6:0, forKD D 0:01) and a minimum occurring immediatelyadjacent to the plume at a distance of ¾200 km(e.g., CL=C0 ¾ 1 ð 10�5, for KD D 0:01) (Fig. 8a).The high enrichments over the plume source reflectlarge contributions of low-degree melts predicted


Fig. 8. Effects of melting on along-axis variation in the relativemelt concentration .CL=C0/ of incompatible trace-elements withdifferent bulk partition coefficients KD (labeled) for (a) Case 1,without the dehydration viscosity boundary and (b) Case 2, withthe dehydration viscosity boundary. Short wavelength (¾100–200 km) variations in concentrations are due to numerical errorsin flow and depletion calculations at the base of the meltingzone, which are small relative to mean values, but are amplifiedby Eq. 7 at low KD values. (c) Accumulated average meltfraction (see text for calculation) along the ridge axis for Case 1(dashed) and Case 2 (solid).

by high melting rates near the base of the meltingzone (Fig. 4b). These factors are reflected by theminimum in average melt fraction (<0.1) over theplume source (Fig. 8c). The CL=C0 minimum at adistance of ¾170 km reflects a maximum in NF , aresult predicted from mantle that initially melted atthe center of the plume but subsequently flowed tothe sides of the plume where it melted further. Thegradual increase in CL=C0 at distances >200 kmreflects decreasing along-axis transport of previouslydepleted material and decreasing mantle temperaturewhich reduces the total degree of melting. Thus,for Case 1, CL=C0 reflects shallow deflection and

lateral spreading of the plume that generates largealong-axis variations in upwelling, melting rate, andaverage melt fractions.

By incorporating the rheological effects of dehy-dration, melting in Case 2 is predicted to generateonly modest variations in incompatible element con-centrations along the ridge axis (Fig. 8b). This resultis primarily a consequence of deflection of plumematerial below the melting zone, more uniform up-welling rates in the melting zone, and thus smallvariations in mean extent of melting (Fig. 8c). En-richment is predicted to decrease toward the plumesource due to the increase in NF and then increaseslightly over the plume source due to enhanced melt-ing rates at the base of the melting zone (Fig. 8b).This enhanced low-degree melting is also evident ina slight decrease in NF directly over the plume source(Fig. 8c). The average melt fraction is still elevatedover the plume source relative to values far fromthe plume, consistent with findings of previous 1Dpassive upwelling models [7–9].

Along the MAR, the concentration of incompat-ible elements such as K2O and La tapers graduallyfrom peaks at Iceland to MORB-like values over adistance of ¾500 km on both sides of Iceland [3,24].Fig. 9a shows K2O composition along the ridge axisand a Gaussian fit to the data. There is little evidencein the data for the short wavelength, high ampli-tude variations in CL=C0 predicted by Case 1. Afactor, other than melting, that may account for theobserved variations in CL=C0 is large variations insource composition C0. In Case 2, however, a largefluctuation in C0 (0.01–100%) would be requiredto match the Gaussian curve in Fig. 9b, assumingKD D 0:01 for K2O [43]. Such a source variabilityis impossible. In contrast, the smaller variations inCL=C0 predicted by Case 2 require much smallervariations in the mantle source. This model can ex-plain the observed K2O concentrations with a sourceconcentration C0 of ¾3 ð 10�2% at the plume cen-ter that gradually decreases away from the plumeto ¾5 ð 10�3%. This result for Case 2 supports thehypothesis that the Iceland plume source is enrichedin incompatible trace-elements [3,24]. Like our pre-vious plume models, however, Case 2 predicts verylittle mixing between the plume and ambient mantletherefore can not explain the along-axis gradient inC0. Our model thus requires the lateral heterogeneity


Fig. 9. (a) Observed variations in K2O along the MAR near Iceland [24] are shown with a Gaussian fit to isolate the long wavelengthvariation. (b) Source concentration of K2O is calculated by dividing the Gaussian curve in (a) with the computed along-axis variations inCL=C0 in Fig. 8a for KD D 0:01. The dashed curve is computed from the model without dehydration (maximum value off the scale is100% and cannot explain a CL=C0 D 1ð 10�7 predicted 100–200 km away from the plume center); the solid curve is from the modelwith dehydration.

in incompatible element content shown in Fig. 9b tobe present in the plume stem below a depth of atleast 200 km.

The above analysis further indicates that Case 1is a poor description of melting and=or crustal accre-tion near Iceland unless along-axis melt migrationcan smooth out the large variations in the predictedconcentrations of incompatible elements. Case 2 is amore likely description of melting if along-axis melttransport is insignificant.

7. Upper mantle viscosity

The essence of the dehydration model is thatplume viscosities in the melting zone are suffi-ciently high to inhibit buoyant upwelling. Post-glacial rebound [44] and post-seismic deformation[45] studies, however, suggest relatively low upper-mantle viscosities of 1 ð 1018–5 ð 1019 Pa s and3 ð 1018–3 ð 1019 Pa s, respectively. To compare

model and geologically constrained viscosities effec-tively we must consider the effects of non-Newtonianrheology as well as a layered viscosity structure.

Deformation in the upper-mantle most likely oc-curs in the dislocation creep regime [19] in whichPž / − n, where n ¾ 3:5 (e.g. [19,18]). Consequently,the effective viscosity, � D −=Pž, depends strongly onthe strain rate according to

� / Pž.1�n/=n (8)

The dehydration model predicts a viscosity in themelting zone of ¾5 ð 1020 Pa s at strain rates of0.04–0.06 My�1 Sigmundsson and Einarsson [44]reported a strain rate due to post-glacial rebound atVatnajokull glacier of ¾0.5 My�1, and Pollitz andSacks [45] modeled a strain rate of ¾1 My�1. UsingEq. 8 to normalize model viscosities to the observedstrain rates reduces our model viscosity to 9.6 ð1019 Pa s for Pž D 0:5 My�1 and 5.9 ð 1019 Pa s forPž D 1:0 My�1. The differences between these nor-malized viscosities and the upper-bound estimates


of the two studies are within the uncertainty of ourmelting rate calculations; numerical tests showedthat halving the model upper-mantle viscosity in-creases the predicted melting rate by ¾25%, a factorwithin the ¾50% uncertainty in our melting calcula-tions. Still, normalized model viscosities are higherthan the preferred viscosity of 3 ð 1018 Pa s ofPollitz and Sacks [45].

An additional factor to consider is the possibil-ity that upper-mantle viscosity changes significantlywith depth. The sensitivity of surface deformation toviscosity at a given depth depends on the wavelengthof the deformation; greater wavelengths ‘feel’ vis-cosity at greater depths. Scaling analyses (after [46])indicate that the deformation wavelengths of 50–100km measured by [44,45] are most sensitive to vis-cosities within ¾50 km of the surface. In contrast,model melting calculations are least sensitive to theviscosity at the top of the model and most sensitiveto the average viscosity throughout the melting zoneand below. For example, a shallow (depths <50 km)mantle layer with high melt retention could yieldlow viscosities that would strongly affect surface de-formations but only minimally affect the larger-scalemantle flow and melting rate. Further geologic dataon deformation at different strain rates and wave-lengths at Iceland are needed to more rigorouslyconstrain the non-Newtonian and layered rheologicalbehavior of the Iceland plume.

The viscosity structure simulated by our dehy-dration model may have general implications forthe dynamics of plume–ridge interaction. Dehydra-tion generates a compositionally controlled rheo-logical boundary layer that is relatively uniformin thickness in the across-axis direction (Fig. 4c).In contrast, a thermally controlled boundary layerthickens significantly with distance away from theridge axis (Fig. 4a). The implication is that com-munication between a plume and nearby ridge axismay occur due to gravitational spreading of theplume beneath a relatively flat rheological boundary,and a ridge-ward sloping boundary caused by litho-spheric cooling may not be as important to plume-ridge interaction as suggested in previous studies[47,48].

8. Conclusions

Our 3D numerical models predict that a fifty-foldincrease in viscosity due to the extraction of waterduring partial melting prevents buoyancy forces fromcontributing substantially to plume upwelling abovethe dry solidus. As a result, predicted melting ratesare sufficiently low to allow a plume with a relativelyhigh temperature anomaly to yield crustal thick-nesses comparable to those measured seismicallyon Iceland. The resulting predictions of along-axiscrustal thickness, bathymetry, and Bouguer-gravityanomalies are also consistent with the correspond-ing observations along the Kolbeinsey and Reyk-janes ridge axes. Furthermore, tomographic inver-sions of P-wave travel times synthesized from pre-dicted mantle temperatures and melt retentions areconsistent with inversions from the ICEMELT exper-iment. Thus, this geodynamic model of the Icelandplume and MAR system is the first to simultane-ously explain observational constraints on along-axiscrustal structure and mantle seismic structure. Cal-culations from the dehydration model suggest thatgeochemical variations along the MAR largely re-flect variations in source concentration of incompati-ble elements such as K2O and La below the meltingzone. Along-axis variations in average degree ofmelting are predicted to be small and thus contributeonly moderately to the incompatible element varia-tions. A more general implication for plume–ridgesystems is that because the rheological boundary dueto dehydration is predicted to be relatively flat, theslope of a thermally controlled rheological bound-ary may have minimal influence on plume–ridgeinteraction.

Acknowledgements

The SOEST Young Investigator Fellowship, Uni-versity of Hawaii, funded G. Ito for this research. Y.Shen was supported by NSF grant OCE-953017, G.Hirth was supported by NSF grant EAR-9405845,and C. Wolfe was supported by OCE-9618125. Wethank R. Batiza and B. West for their valuable dis-cussions and suggestions. We also extend much ap-preciation to R. Buck and an anonymous reviewerfor their insightful and thorough reviews of this


manuscript. All of the figures were generated us-ing GMT software [49]. SOEST contribution #4688.[RO]

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mantle ï¬‚ow, melting, and dehydration of the iceland mantle plume

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