flow and melting of a heterogeneous mantle: 1. method and ...€¦ · and isotopic compositions of...

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Earth and Planetary Science L

Flow and melting of a heterogeneous mantle:

1. Method and importance to the geochemistry of ocean

island and mid-ocean ridge basalts

Garrett Ito*, John J. Mahoney

School of Ocean and Earth Science and Technology, POST 810, University of Hawaii, Honolulu, HI 96822, USA

Received 5 May 2004; received in revised form 1 September 2004; accepted 26 October 2004

Available online 24 December 2004

Editor: B. Wood

Abstract

Understanding the partial melting process is key to our ability to relate geochemical characteristics of hotspot and mid-

ocean ridge lavas to the dynamics and chemical structure of the mantle. We present a method of computing the trace-element

and isotopic compositions of magmas generated by melting a heterogeneous source in mantle plumes and beneath mid-ocean

ridges. The method simulates fractional melting with thermodynamically consistent melting functions of three mantle

lithologies, each with a distinct trace-element and isotopic composition. A key assumption is that enriched mantle peridotite

(EM) and pyroxenite (PX) both begin melting deeper than depleted mantle peridotite (DM). Model calculations can explain

many features observed in a compilation of ocean island basalt (OIB) and mid-ocean ridge basalt (MORB) data. In particular,

La/Sm and Sr, Nd, and Pb isotope ratios are most variable and extend to compositions most distinct from average MORB

compositions in islands formed on relatively old seafloor (N~16 m.y.). The compositions of hotspot islands erupting on

younger seafloor are less variable and overlap more appreciably with common MORB compositions. Models predict these

observations to result from the effect of lithospheric thickness in limiting the extent of partial melting. Beneath old seafloor

where the lithosphere is thick, models predict the overall extent of partial melting and the extent of DM melting to be small;

therefore, magma compositions are most sensitive to changes in the relative proportions of EM and PX, as well as to mantle

temperature. Beneath young seafloor where the lithosphere is thin, models predict more extensive melting of all lithologies.

Progressive extraction of the different components during melting can also explain the general topology of isotopic arrays

defined by OIBs globally. Our models not only predict testable variations in trace-element and isotopic ratios with mean extent

of partial melting, but also show that pyroxenite can complicate such correlations because it can melt to very high extents, in

many cases, completely. If the thickness of the mantle plume layer beneath the lithosphere exceeds that of the DM melting

zone, an increase in the mantle flow rate with depth, which is predicted for mantle plumes, can enhance the flux of

incompatible elements and isotopes derived from PX and EM, relative to the case of the more uniform flow profile expected

beneath mid-ocean ridges. Thus, differences in both mantle flow and lithospheric thickness between mid-ocean ridges and

hotspots can lead to important distinctions in the isotopic and trace-element characteristics of MORBs and OIBs, independent

0012-821X/$ - s

doi:10.1016/j.ep

* Correspon

E-mail addr

etters 230 (2005) 29–46

ee front matter D 2004 Elsevier B.V. All rights reserved.

sl.2004.10.035

ding author. Tel.: +1 808 956 9717; fax: +1 808 956 5154.

esses: [email protected] (G. Ito)8 [email protected] (J.J. Mahoney).

G. Ito, J.J. Mahoney / Earth and Planetary Science Letters 230 (2005) 29–4630

of any compositional differences between their respective mantle sources. In addition, variations in mantle flow alone can

contribute to geographic variations in hotspot geochemistry observed both in intraplate settings and where hotspots interact

with mid-ocean ridges.

D 2004 Elsevier B.V. All rights reserved.

Keywords: ocean island basalt (OIB); mid-ocean ridge basalt (MORB); mantle heterogeneity; partial melting; mantle plume; mantle convection

1. Introduction

The geochemistry of ocean island basalt (OIB) and

mid-ocean ridge basalt (MORB) reflects physical and

chemical processes in the mantle ranging from the

global [1–3] to the local scale [4–8]. One key linkage

between the geochemical properties that we can

measure in volcanic rocks and those of the mantle

source materials is the process of melting. A great

deal has been learned about mantle melting through

laboratory experiments, geochemical observations,

and theory [9–16]. To date, studies of mantle melting

have focused largely on mid-ocean ridge melting,

owing in part to the relative simplicity of the

structure and composition of most oceanic crust.

Correspondingly, most theoretical treatments have

focused on melting of peridotite having relatively

limited heterogeneity. The greater diversity of hot-

spot-related magmatism in terms of both tectonic

settings and geochemical compositions offers an

opportunity to extend our understanding of the

mantle but requires consideration of the upper-mantle

dynamics beneath hotspots, as well as the process of

melt generation and accumulation from a heteroge-

neous mantle.

The concept that compositional heterogeneity is

present in the mantle as veins, streaks, or blobs

smaller than typical volumes of upper mantle

melting zones is widely discussed in the geochem-

ical literature [17–22]. Compelling evidence for such

heterogeneity is recognized at hotspots [4,23–29]

and at mid-ocean ridges [19,30–37]. Both the

differences in source composition and associated

melting behavior can strongly influence magma

composition, possibly contributing to large and often

correlated changes in incompatible element and

isotope ratios [32,33,38]. For example, mafic materi-

als may be important melting components [2,24–

26,39–42] and the low melting temperature of

pyroxenite [43,44] relative to peridotite can cause

variations in the fraction of each component sampled

by melting and give rise to chemical mixing trends

in erupted magmas [38,42,44]. Furthermore, the

sensitivity of the solidus of peridotite to incompat-

ible element and volatile content [15,33,46,47] can

allow for variable extraction of heterogeneous

peridotite [32,48]. Although its importance is well

recognized, the melting of a veined mantle has

received relatively little quantitative, theoretically

based treatment.

The purpose of this manuscript is to quantitatively

explore the consequences of melting a heterogeneous

mantle on the incompatible-element and isotopic

composition of OIBs and MORBs. We begin by

describing a simple method for calculating the

composition of melts as they form and mix. Melting

and melt mixing are both coupled to mantle flow.

We assume that narrow, buoyant upwellings cause

OIB volcanism and show that the difference between

such bmantle plumeQ flow and the flow beneath mid-

ocean ridges is one factor that can contribute to

differences between OIB and MORB geochemistry.

A second important factor is lithospheric thickness,

which limits the extent to which different lithologies

melt. Comparisons between model predictions and

existing data sets are used to examine possible

causes for global OIB and MORB systematics, and

for local variability within individual ocean island

groups.

2. Method: Melting model

2.1. Governing equations

Partial melting beneath hotspots and mid-ocean

ridges predominantly occurs as the asthenosphere

ascends and decompresses. Melting ceases as the

G. Ito, J.J. Mahoney / Earth and Planetary Science Letters 230 (2005) 29–46 31

asthenosphere is diverted sideways beneath the litho-

sphere (Fig. 1). A simple way to compute the com-

position and volume of melts integrated over the

whole melting zone is to relate them to the properties

of the residue flowing out of the melting zone [10–

13]. This material forms a bresidual mantle columnQ(RMC) [11] beneath mid-ocean ridges and, as we

describe below, forms a bresidual mantle cylinderQ(also RMC) beneath intraplate hotspots. The trace-

element concentration Ci of pooled magmas derived

from mantle source i can be calculated by assuming

Fig. 1. (a) Solidi for enriched mantle (EM, dashed), pyroxenite (PX, gray)

(dotted) and predicted temperature T profile (black curve) for a starting pot

each lithology as labeled with their respective mass fraction in the mantle,

(variables are defined by [15]), are 0.25, 0.02, 10 kJ/mol, and 1336 8C, resp(defined in [15]) and minor, incompatible component I are 0.598 and 0.012

productivity for each lithology. (d) Isoviscous, axisymmetric flow (arrow

cylinder of buoyant fluid beneath a rigid top boundary. The thickness of the

Predicted radial flow along the black curve in Panel (d), where upwelling a

theory (dashed curve, see text), and horizontal flow driven passively by

represent the horizontal flow of the residue exiting the melting zone U( P

(RMC). (f) Predicted melting functions F( P) for the mantle lithologies, a

perfect mixing of melts derived from each depth, or

pressure P of the RMC,

Ci ¼C0i

Z P2i

P1i

EiðFiÞFi Pð ÞU Pð ÞdPZ P2i

P1i

Fi Pð ÞU Pð ÞdP: ð1Þ

Here, C0i is the concentration of a trace element in

source i, Ei(Fi) is the factor by which the melt is

enriched relative to the source after melting to a mass

, and depleted mantle (DM, black line); also shown are the adiabat

ential temperature of 1450 8C. (b) Predicted isobaric productivity for

/i. For EM and DM, values assumed for KD, DC*sol/liq, DHA

fus, TAfus

ectively [15]. For EM, assumed proportions for major component A

, respectively; for DM, they are 0.606 and 0.004. (c) Predicted melt

with size proportional to flow rate; streamlines in bold) due to a

plume layer exiting the melting zone H is shown schematically. (e)

nd melting have stopped (solid); radial flow predicted by lubrication

plate spreading at a mid-ocean ridge (vertical line). These curves

) and are proportional to the width of the residual mantle cylinder

s labeled in Panel (c).


fraction Fi, and U is the speed at which the residue is

exiting the melting zone. Both Fi and U are functions

of pressure P. The pressure range of the RMC for

source i is defined by the beginning P1i and ending

melting pressures P2i. Eq. (1) simply describes an

average concentration, C0iEi(Fi), of accumulated

incremental melts that were extracted from each

portion of the RMC, weighted by the amount of melt

extracted, Fi(P)U(P)dP. To solve Eq. (1) we must

define functions of Ei(Fi), Fi(P), and U(P).

2.2. Enrichment function E(F)

The enrichment function Ei(Fi) describes an

idealization of elemental extraction from the solid

resulting from melting and melt–solid interaction.

Here, we consider accumulated, fractional melting

[49], which assumes that infinitesimal melt incre-

ments form in chemical equilibrium with the solid

but are immediately taken out of equilibrium with

the solid prior to mixing with other melt increments.

The composition of an infinitesimal melt increment

is governed by the modal mineralogy of each solid

lithology ([13,40,44]; assuming that they do not

chemically equilibrate, as discussed below), liquid–

mineral partition coefficients [13,50], and pressure-

dependent phase transitions ([47,51]; see Table 1 of

Background Dataset in Appendix A). The accumu-

lated enrichment functions Ei(Fi) are analytical

solutions of fractional melt compositions normalized

by C0i and integrated (i.e., accumulated) over F

through the different solid-phase intervals ([13,52];

i.e., Eq. 11 of [13]).

2.3. Melting function F(P)

A key quantity in describing the melting function

F(P) is melt productivity BF/BP, the fraction of

melt generated per increment of decompression.

Following [45], we assume that the system remains

in thermal equilibrium (implying characteristic

dimensions of heterogeneities b102 m) but in

chemical disequilibrium. Although the likelihood

of chemical disequilibrium in a partially molten

mantle has been questioned [53], an analysis of

compaction and chemical diffusion time scales

demonstrates that disequilibrium can exist, given

reasonable properties of many upper mantle systems

[54]. With the above assumptions, the melt produc-

tivity of lithology i depends on thermal coupling

with the other j lithologies, each comprising a mass

fraction /j of the mantle assemblage approximately

according to:

� BF

BPi

¼

BT

BPi

��F

� aTiqcp

þ T

cp

Xjp i

�/jDSj

�BT=BPijF � BT=BPjjF

BT=BFjjp

��

BT

BFi

��p

þ /TDSi

cpþ T

cp

Xjp i

�/jDSj

BT=BFijPBT=BFjjP

� :

ð2Þ

See Table 1 for the definition of variables and

[15,45,55] for further explanation.

We consider a mantle composed of three lithol-

ogies: benrichedQ mantle (EM) peridotite, bdepletedQmantle (DM) peridotite, and pyroxenite (PX). For

peridotite melting, we use basic thermodynamic and

mass-balance principles to describe the dependence

of BT/BFi|p (=BF/BTi�1|p) on F [15]. This simple

method treats peridotite as an assemblage of three

compositional components: two major components

forming a solid solution and a small quantity of a

third, incompatible component I. This ternary system

captures many of the essential aspects of more

complex calculations that consider nine oxide com-

ponents in peridotite [14,15,55–57], notably, minimal

BF/BP at the onset of melting and an increase in BF/

BP with F up to the point of clinopyroxene

exhaustion, where BF/BP suddenly drops ([55];

Fig. 1). We assume that DM behaves as nominally

dry peridotite and thus calibrate its melting behavior

(see Fig. 1 caption) to qualitatively match that

predicted by [14]. The DM solidus-depth function

is derived empirically [58]. We simulate enriched

mantle (EM) with a higher concentration of the

incompatible component I compared with DM,

which represents an elevated water content. Con-

sequently, EM begins melting at a greater pressure

than DM and has a greater depth zone over which

melt productivity is low (Fig. 1). The increase in I is

such that the change in solidus and BF/BP functions

relative to DM is comparable with adding 0.05 wt.%

water according to the parameterization of [51]. For

pyroxenite melting, we use the experimentally con-

strained solidus pressure and BF/BT|p functions of

Table 1

Definition of variables

Variable Meaning Value Unit

cp Specific heat at constant pres-

sure

1200 J kg�1 8C�1

C Concentration of a trace

element in the eruptible

magma

C0i Concentration of a trace

element in starting source i

Ci Concentration in the melt

arising from source i

Cpm Concentration in estimated

primitive mantle [62]

Ei Concentration of accumulated,

incremental melt normalized

by C0i

F Weight fraction of partial

melting

g Acceleration of gravity 9.8 m s�2

H Characteristic thickness of

plume layer exiting melting

zone

km

HDM Thickness of DM melting

zone beneath lithosphere

km

P Pressure GPa

P0 Pressure at the base of the

lithosphere

GPa

R Isotope ratio

DS Change in entropy in

converting solid to melt

200 J8C�1 kg�1

T Potential temperature 8CU Normalized horizontal flow

rate out of the melting zone

z Depth below the lithosphere km

a Coefficient of thermal

expansion

3�10�5

/l Mass fraction of lithology

i in mantle

q Mantle density 3300 kg m�3


[43] (experiments were done at 2–3 GPa, therefore,

applying these functions for higher pressures is an

extrapolation). From the known functions of BF/

BTi|p, we use Eq. (2) to calculate BF/BPi for each

lithology present (i.e., /jN0). We then numerically

integrate over pressure to yield Fi(P) (Fig. 1f) for

application in Eq. (1).

2.4. Mantle flow function U(P)

We assume that hotspot or OIB volcanism is

caused by decompression melting of a cylindrical

upwelling (mantle plume) of low-density material

interacting with the base of a stationary lithospheric

plate. To derive the appropriate function, U(P), we

examine the two-dimensional (2D) axisymmetric

flow of an isoviscous (asthenospheric) fluid con-

tained in a half-space with a rigid top boundary

(i.e., the base of the lithosphere; Fig. 1d). Buoyant

fluid is contained in a (plume) cylinder of radius R,

extending from a depth z=H below the lithosphere

to a sublithospheric depth of z=11H (hence, the

base of the plume stem is sufficiently deep to

minimize its effects on shallow flow), where H is

the characteristic thickness of the plume layer that

forms beneath the lithosphere and exits the melting

zone. Following [59], we solve for mantle flow by

filling the cylinder with buoyant particles and

numerically integrating analytical solutions of the

momentum equation for incompressible flow from

each particle [60]. Material is predicted to rise in the

cylinder and turn horizontal as it interacts with the

lithosphere. The most rapid flow is predicted to be

deep below the lithosphere, decreasing to zero at the

base of the lithosphere to satisfy the boundary

condition. Decompression melting rate will be zero

where the vertical component of flow is zero. Along

a contour of zero-upwelling, the rate of (radial) flow

out of the melting zone decreases toward the

lithosphere (Fig. 1e). This radial flow profile is

one form of U(P).

Another way to evaluate U(P) is to approximate

the portion of material flowing radially beneath the

lithosphere as a thin layer, using lubrication theory.

Buoyancy drives radial flow subject to the boundary

conditions of zero-flow at the base of the lithosphere

and zero-shear stress at the base of the plume layer.

These conditions are appropriate for an isoviscous

fluid [61] and yield a flow rate that increases as

quadratic function of depth (Fig. 1e). Normalized by

the flow rate at the base of the layer, the horizontal

flow as a function of depth z is:

U zð Þ ¼ 2 z=Hð Þ � z=Hð Þ2: ð3Þ

Eq. (3) is converted to a function of pressure with

the relation P=P0+qgz, where P0 is the pressure at

the base of the lithosphere, q=3300 kg/m3, and g is

the acceleration of gravity. This function is very

similar to the profile computed above for 2D


axisymmetric flow (cf. curves in Fig. 1e); for

simplicity, we will use Eq. (3) for U(P).

The thickness of the plume layer exiting the

melting zone is H (Fig. 1d). This variable controls

the maximum pressure P1i in the integral of Eq. (1);

P1i is either the solidus pressure of lithology i or the

pressure at the base of the plume layer (P1i=

P0+qgH), whichever is less. This means that the

RMC could extend as deep as the solidus but could be

shorter if buoyancy pushes material to shallower

depths prior to exiting the melting zone. The mini-

mum pressure corresponds to the base of the litho-

sphere P2i=P0. In the following calculations, we

assume H=100 km, saving a discussion of the effects

of varying H for Section 5.3.

This form of mantle flow contrasts with that

commonly assumed for mid-ocean ridge melting

[11,12,62]. Instead of decreasing toward the base

of the lithosphere, horizontal mantle flow that is

driven kinematically by two diverging plates is

nearly uniform with depth (Fig. 1e) and approx-

imately equal to the half spreading rate of the plates.

The normalized flow function U(P) is therefore

equal to one and does not appear in the equivalent

equations presented previously [11,12]. Buoyancy

associated with melting can drive a type of active

flow [62], but in contrast to deep mantle plume

buoyancy, this relatively shallow, melt-related buoy-

ancy tends to push the mantle more rapidly through

the upper portion of the melting zone. This would

effectively widen the RMC near its top, producing a

nearly opposite effect to that of the deeper plume

buoyancy simulated here.

2.5. Melt mixing and composition of eruptible

magmas

Using Eq. (1), we solve for the concentrations of

trace elements in melts derived from each mantle

lithology. The final concentration in the eruptible

magma is then calculated by weighting the concentra-

tions by the amount of melt derived from each source

C ¼

X3i¼1

Ci/i

Z P2i

P1i

Fi Pð ÞU Pð ÞdP

X3i¼1

/i

Z P2i

P1i


If Ci is the concentration of an element with a

radiogenic isotope, then the isotope ratio in the

eruptible magma R is:

R ¼

X3i¼1

RiCi/i

Z P2i

P1i

Fi Pð ÞU Pð ÞdP

X3i¼1

Ci/i

Z P2i

P1i

Fi Pð ÞU Pð ÞdP; ð5Þ

where Ri is the ratio in source i.

Eqs. (4) and (5) are simply mixing equations.

Oftentimes, simpler mixing equations are used to infer

the proportions that each component contributes to a

given magma composition, and these proportions are

assumed to be the same as those in the source material

(i.e., /i ). However, Eqs. (1), (4), and (5) reveal how

melting and mantle flow can contribute to mixing

proportions. Eq. (5) is conceptually the same as the

isotope mixing equation in [38], but the integrals in

Eq. (5) describe a specific mechanism that controls

mixing proportion, namely, melt flux, which is

controlled by mantle flow.

3. Model predictions

3.1. Mantle source compositions

The composition of magmas clearly depends on

the starting composition of the lithologies melting,

C0i. We define a single composition for each of the

three lithologies considered in this paper (see

Background Datasets, Table 2, in Appendix A).

Not varying C0i minimizes the number of free

variables and allows us to focus on the effects of

melting. Compared to estimated primitive mantle [63],

EM is assumed to be enriched in the most incompat-

ible trace elements, and DM is assumed to be depleted

in the most incompatible trace elements, with relative

concentration increasing with increasing compatibil-

ity. PX is assumed to have the median incompatible-

element composition of the MORB data set that we

have used (see Section 4). We also assume that each

lithology has a different radiogenic isotope composi-

tion. We assume EM to have isotope ratios similar to

the postulated bEM1Q or bEM2Q end-members, PX to


be isotopically similar to the proposed bHIMUQ [2],and DM to be similar to bDMMQ [5].

3.2. Changes in composition with extent of partial

melting

We now show some predictions of Eqs. (1)–(5).

Our purpose is to build an intuitive understanding of

the process of melting in the presence of hetero-

geneities and mantle flow. In these calculations, we

assume an anomalously hot plume mantle with a

potential temperature of 1450 8C, or a temperature

excess of DT=100 8C. In reality, temperature is likely

to vary significantly in a mantle plume, but the

simplicity of our models limits our calculations to

simulating only the average mantle temperature. We

consider DT=100 8C to represent a moderate, average

excess temperature.

For a given mantle lithology, Eqs. (1)–(5) predict

the well-understood behavior of maximum incompat-

ible-element concentrations Ci being produced at the

onset of melting, when the (maximum) extent of

Fig. 2. (a–c) Predicted melt compositions from mantle made of only EM an

from mantle made of EM, DM, and pyroxenite with fraction /DM=0.9 and

those in left column. Source compositions are shown as circles (EM, i.e.,

FEMmax=0.2 correspond to the sudden drop in EM and DM melt productivity,

phase (see Fig. 1c and f). A decrease in BF/BP means that a greater vertic

DP=(BP/BF)DF), and this translates to a larger volume of high-degree D

melting Fimax (Fi

max=Fi(P2i)) is near zero. Continued

melting leads to decreasing Ci roughly in proportion

to 1/Fimax (see Background Dataset in Appendix A for

the evolution of Ci with Fimax). Enrichment Ei=Ci/C0

is greater for more incompatible elements than for less

incompatible elements; therefore, ratios like La/Sm

also decrease with increasing Fimax.

For a case in which only EM is present (/EM=1,

/DM=0), La/Sm is maximized for all FEMmax (Fig. 2a).

Cases that also include DM (/DMN0) predict concen-

tration curves that diverge from and fall below the

curve for /EM=1, once DM begins to melt (FEMmax

c0.065). With regard to isotope ratios, when only

EM is melting, isotope ratios remain constant and

equal to those of EM (Fig. 2b and c). As DM melts,

isotope ratios become more DM-like with increasing

extent of melting. The greater /DM is, the closer the

isotope ratios are to DM for a given value of FEMmax.

The converse is also true.

Fig. 2d–f shows predictions with PX added. Here,

DM is always assumed to be 90% of the source mantle,

and EM and PXmake up the remaining portion. Again,

d DM, with various fractions of EM as labeled. (d–f) Predicted ratios

labeled fractions of EM. Gray curves in right column are the same as

EM2), triangles (PX), and squares (DM). Kinks in the curves near

BF/BP, associated with the exhaustion of clinopyroxene as a melting

al length of mantle experiences a given change in melt fraction (i.e.,

M melts added to the mixture over a given change in FEMmax.

Fig. 3. Excesses in La/Sm, 87Sr / 86Sr, and 206Pb / 204Pb caused by

mantle plume flow compared with mid-ocean ridge mantle flow

Numbers indicate the fraction of EM (/EM) composing the

mantle mixture; /DM=0.9 and PX make up the remaining

fraction.


at the onset of melting, only EM controls the com-

positions. Once PX begins to melt (FEMmax=~ 0.01),

La/Sm and 87Sr /86Sr decrease, while 206Pb/ 204Pb

increases toward the PX source value. As melting

continues, DM begins to melt at FEMmax=~ 0.07. From

this point, La/Sm, 87Sr/86Sr, and 206Pb/204Pb decrease

gradually toward values of the DM source.

The large and rapid change in all compositions at

the onset of PX melting reflects a large influx of

elements from PX caused by two factors. First, PX

is assumed to be enriched in incompatible elements

relative to peridotite. Second, PX melts very

quickly, in this case, melting 100% over a pressure

interval of b2 GPa (Fig. 1). This behavior results

because peridotite is more abundant than PX, EM

melts at a much lower rate (i.e., BF/BTj| p) than PX

does, and DM is largely subsolidus; therefore,

peridotite melting consumes very little latent heat

and more is available for PX melting (Eq. (2)). By

comparison, if PX were the only material present, then

complete melting would require ~4 GPa of decom-

pression. These results show how a small amount of

PX in the mantle can have a large influence on the

trace-element and isotopic composition of eruptible

magmas.

3.3. Mantle plume flow versus mid-ocean ridge flow

The above calculations include the increasing

rate of mantle flow with depth given by Eq. (3). To

illustrate the importance of such plume flow, we

compare solutions using the same starting sources, but

with the uniform flow appropriate for mid-ocean

ridges (U(P)=1). Predicted compositions with mid-

ocean ridge flow are subtracted from those with plume

flow to quantify the relative benrichmentQ caused by

mantle plume flow alone (indicated by D in Fig. 3).

Over most of the interval that DM is melting,

calculations with mantle plume flow predict higher

values of La/Sm, as well as more EM- and/or

PX-like isotope signatures compared with the calcu-

lations with mid-ocean ridge flow. This result is

caused by the relatively high mantle plume flow

U(P) near the base of the melting zone, where

melting is limited to low degrees and where incom-

patible elements are extracted most efficiently from

EM and PX. Shallower in the melting zone, the

decreasing rate of mantle exiting the melting zone

.

U(P) decreases the flux of incompatible-element-

depleted melts (generated at higher FEMmax), as well as

the DM isotope signatures. The enrichment caused by

mantle plume flow tends to be largest nearest the

onset of DM melting (FEMmax = 0.07– 0.12) and gen-

erally decreases with continued melting. Because of

the assumed composition of the EM end-member,

plume flow elevates La /Sm and 87Sr /86Sr most

substantially, relative to mid-ocean ridge flow, when

EM is most abundant in the starting mantle. Similarly,

the degree to which Pb isotope ratios are elevated

by mantle plume flow increases with the amount

of PX originally present. Thus, mantle plume flow

could be one cause for the heavier sampling of

PX and EM components at hotspots than at mid-

ocean ridges, independent of any mantle source

differences.


4. Importance to OIB and MORB genesis

4.1. Chemical variations with seafloor age

The above calculations predict systematic changes

in magma geochemistry as a function of the

maximum fraction of partial melting F max. One

factor that limits F max is lithospheric thickness

(proportional to P2 in Eqs. (1), (4), and (5)). We

thus anticipate a dependence of magma geochemistry

on seafloor age at the time of volcanism. We compiled

geochemical data for various hotspot island groups,

primarily from the GEOROC database (http://georoc.

mpch-mainz.gwdg.de). Seafloor age at the time of

volcanism was determined by subtracting known or

Fig. 4. Observed ratios of tholeiitic basalts from various ocean island groups

Data for some hotspots are gray and some are colored: Iceland (black), G

(light blue), Hawaii and Hawaiian-Emperors (purple), Society (white), Can

from bnormalQ sections of mid-ocean ridges (see text). Red curves encomp

similar to EM 2 [5]) fraction /EM=0.1 and pyroxenite fraction /PX=0

/PX=0.08. Solid curves show predictions for mantle plume flow (U( P) g

mantle potential temperature, assumed to be 1350 8C, is the lower limit for

The mantle fraction of DM is /DM=0.9. Dashed curves are solutions for

estimated sample ages from the magnetically deter-

mined ages of the surrounding abyssal seafloor [64].

We also compiled geochemical data for the Mid-

Atlantic Ridge (MAR), East Pacific Rise, and Indian

Ocean ridges, principally from the PETDB database

(http://petdb.ldeo.columbia.edu/petdb/). To isolate

bnormalQ from anomalous MORBs, we only used

data for samples collected within the depth range of

2500–3500 m. This depth range is meant to eliminate

potential regions in which the mantle is anomalously

hot or cool. We also eliminate regions identified as

hotspot-influenced by [65] and [66].

Fig. 4 shows several key, frequently measured

geochemical ratios versus the square-root of seafloor

age at the time of volcanism. The MORB data are

(circles) vs. the square-root of seafloor age at the time of volcanism.

alapagos (dark blue), Easter (red), Pitcairn (yellow), Cook-Austral

ary (brown), and Samoa (orange). Green histograms summarize data

assed by light orange shading are calculations with EM (isotopically

; blue curves and light green shaded area are for /EM=0.02 and

iven in Eq. (3)), with excess temperatures DT of 0–200 8C (Normal

mantle plumes. Temperature increases to the right between curves.)

DT =0 8C and mid-ocean ridge flow (U( P)=1).

http://www.georoc.mpch-mainz.gwdg.de

http://www.petdb.ldeo.columbia.edu/petdb/






represented as histograms along the vertical axis at

zero seafloor age. A simple change in compositions

with seafloor age, as would be predicted by a given

model calculation, is not evident. Indeed, variability

within island chains can be as large as or larger than

the variability between different chains. However,

what is evident is that both the greatest composi-

tional ranges and the compositions most distinct

from those of average MORB tend to be among

islands on older seafloor (N~16 m.y.). In contrast,

islands erupting on relatively young seafloor (b~16

m.y.) or thin lithosphere exhibit comparatively li-

Fig. 5. Isotope ratios of basalts from mid-ocean ridges (green) and the sam

using the same source compositions as in Fig. 4. Solid (gray) curves show

indicate fraction of EM in the mantle (/EM) with / DM= 0.9; note that /PX

each mantle component. The dashed curves are broadly consistent with th

(black) hotspot trends. Solid curves would better predict the Cook-Austral (

many ocean islands, the trends of the Society (white), Samoa (orange), Ha

by mixing of EM with a material having less radiogenic Pb (not shown) tha

PX, a fifth end-member, such as bCQ [67] or bFOZOQ [5], or a mixture of

mited variability in the ratios shown, overlapping

appreciably with the MORB values.

We compare predictions of a few models (curves in

Fig. 4) with these data. Here, we assume that litho-

spheric thickness is 7 km for zero-age seafloor and

thickens in proportion to the square root of age (e.g.,

thickness is ~90 km beneath the recent Hawaiian

islands).We consider mean excess mantle temperatures

of DT=0, 100, and 200 8C and two starting composi-

tions: a mixture of EM (isotopically similar to EM2)

and DM (/EM|/DM=0.1|0.9), and a mixture of all three

lithologies (/EM|/PX|/DM=0.02|0.08|0.9).

e ocean island groups as in Fig. 4. Dashed curves show calculations

results for a different EM end-member, similar to EM1. Numbers

=1�/ DM�/EM. Large open circles show assumed isotope ratios of

e Easter (red), Canary (brown), Galapagos (dark blue), and Iceland

light blue) trend if PX began melting deeper than EM1. Like those of

waiian (purple), and Pitcairn (yellow) data could be better explained

n the pyroxenite composition shown. This source could be a different

the two.


Models predict magma composition to be most

sensitive to both mantle temperature and starting

composition for older plate ages, where F max is

relatively low, and least sensitive to these variables

for younger plates, where F max is relatively high. In

addition, predicted compositions are always most

MORB-like on younger seafloor. It is notable that

the model magma compositions encompass a large

fraction of the total Nd–Sr–Pb isotopic and La/Sm

range observed in OIBs globally with changes in only

two model variables (lithospheric thickness and

temperature) and with only two starting mantle

compositions.

The observed Pb isotope ratios in detail show a

maximum total range of composition near seafloor

ages of 20–40 m.y., with lower variability at both

younger and older seafloor ages. Models successfully

explain this general behavior and do so because PX is

predicted to largely control the Pb isotope signature at

the intermediate seafloor ages, with DM and EM

becoming increasingly important at the younger and

older ages, respectively. We also note that the low208Pb / 206Pb ratios of Hawaii could be predicted with

an EM source with lower 208Pb / 206Pb, more similar

to EM1 (see also Fig. 5).

Finally, we illustrate the importance of mantle

flow. Most of the curves shown in Fig. 4 assume

mantle plume flow Eq. (3); however, the dashed

curves assume mid-ocean ridge flow (U(P)=1 and

DT=0). At zero seafloor age, these curves fall within

the range of observed mid-ocean ridge compositions.

They illustrate the natural tendency for mid-ocean

ridge flow to produce melts with higher mean extents

of melting and to more heavily sample DM.

4.2. OIB and MORB isotopic arrays

Melting of a heterogeneous mantle also may

contribute to the formation of elongate barraysQ in

isotope space observed in OIB and MORB data

[2,5,67]. Such arrays suggest important mixing

processes between distinct isotopic end-members,

but the mixing processes are not well understood.

One possibility is that mixing occurs primarily in the

solid state as a consequence of mantle convection

[5,67,68]. Alternatively, mixing trends can arise by

the progressive melting of a heterogeneous mantle

[32,38,48]. Both processes may be occurring, but

here we show that melting of a heterogeneous mantle

alone can account for a large fraction of the observed

isotopic variability in such arrays.

Predicted and observed isotope arrays are dis-

played in Fig. 5. For starting mantle mixtures of only

EM and DM, isotope ratios are predicted to begin

near those of EM and then trend toward DM values

with increasing extent of partial melting. Likewise,

starting mixtures of only PX and DM yield mixing

arrays between PX and DM values. For mixtures of

all three lithologies, magma compositions start near

EM, trend toward PX, and then turn toward DM

values.

Although details of the curves depend on the

precise nature of the model mantle source, source

end-members representing only four isotopic starting

compositions yield predictions that largely encom-

pass the OIB and MORB data; moreover, the

predicted trends are broadly consistent with many

of the observed trends [e.g., Samoa (orange dots),

Pitcairn (yellow), Easter (red), Canary (brown),

Iceland (black), Galapagos (blue), and Cook-Austral

(light blue)]. An observation that appears to be

diagnostic of the melting process that we are

simulating is the apparent bend in the Hawaiian

hotspot (purple) array, from moderate 206Pb/204Pb

(18.5–19) towards low 206Pb/204Pb (V18) at moder-

ate values of 87Sr/86Sr (0.7035–0.7040) and143Nd/144Nd (0.5129–0.5130). Nevertheless, many

of the observed arrays would be matched better by

including a source similar to our PX end-member,

but with lower 206Pb/204Pb and 208Pb/204Pb, resem-

bling the proposed bcommonQ (C or FOZO) isotopic

end-member [5,67]. We do not explicitly model this

end-member, but we anticipate that the process that

we are simulating could explain the isotopic trends

toward this composition found in many data arrays,

including MORB data [67], if this end-member

usually begins melting shallower than EM and PX,

but deeper than DM. In any case, it is clear that a

large portion of the mixing implied in OIB isotopic

arrays could be accomplished by the partial melting

process. Moreover, magma compositions in Fig. 4

can be seen to extend well into the MORB range for

cases with high Fmax; thus, as noted in the previous

section, the melting process alone can contribute

significantly to the isotopic and incompatible-ele-

ment differences between OIBs and MORBs.

Fig. 6. Predicted variations with mean extent of melting as defined

in text. DM is 90% of the mantle (/DM=0.9). Numbers indicate the

fraction of EM in the mantle, and PX composes the remaining

portion. Here, the isotopic composition of EM is EM2.


5. Discussion

5.1. Incomplete magma mixing

An important limitation to our method is that we

only model complete mixing of melts generated

between the base of the melting zone and a

specified minimum pressure (P2). What we are

therefore effectively assuming when comparing

predictions with observations (Figs. 4 and 5) is that

individual lavas or magma batches (commonly

represented by data for a single sample) from a

hotspot represent mixtures of melts aggregated from

the base of the melting zone to different heights.

Only in this way does our model address the

possibility of incomplete mixing of melts derived

from different parts of the melting zone. In addition,

if incomplete mixing of melts contributes to the

compositional variability within a group of lavas

from a hotspot erupting on seafloor of a given age,

the predicted composition for the corresponding

seafloor age (Fig. 4) is most relevant to the average

or median composition. We therefore expect lava

compositions to scatter about the individual predicted

compositions at a given seafloor age.

5.2. Mean degree of melting and importance of

pyroxenite

The above restrictions noted, our calculations re-

veal some potential complexities in relationships

between isotopes, incompatible elements, and extent

of melting that may not have been recognized without

this or a similar quantitative treatment. Incompatible

element concentrations are known to be related, in

part, to the mean degree of melting F. We define F as

a weighted average,

FF ¼Xi

fi/i

Z P2

P1

Fi Pð Þ2U Pð ÞdPZ P2

P1


Most relations between magma composition and F in

the current literature pertain to peridotite melting;

however, pyroxenite is likely to melt much more

extensively than peridotite. To define a quantity F that

can be related to peridotite melting, we incorporate a

factor fi. This factor is 1 for peridotite (EM and DM)

but b1 for PX. Setting fPX=0.15, for example, implies

that 100% melting of PX yields magma compositions

equivalent to melting peridotite by 15%.


Intuitively, the mean extent of melting is always

less than the total extent of melting Fimax. For

reference, if mantle flow U and productivity BF/BP

were uniform and only one lithology were present, F

would equal Fmax/2. Mixtures of only the two

peridotite lithologies (EM and DM) yield FbFEMmax/2

because BF/BP increases with melting and because

FDMmaxbFEM

max (Fig. 6). With our assumption of com-

plete mixing, calculations predict the most extreme

EM-type isotopic signatures (e.g., 87Sr/86SrN0.7050)

to be present only at low extents of melting (Fb ~ 0.03

and FEMmaxb0.1 for /EMj/DMj/PX=0.1j0.9j0; see Fig.

6). It may be possible to test these predictions using

major element compositions of lavas possessing

strongly EM1- or EM2-type isotopic compositions,

although careful consideration should be taken if EM-

type peridotite contains material derived from sub-

ducted marine sediments.

The presence of pyroxenite adds some complexity.

First, pyroxenite drastically increases F for the same

FEMmax (Fig. 6a), yielding strongly HIMU-type isotopic

compositions (e.g., 206Pb/204PbN20) at appreciable

values of F (0.04–0.06). Second, our calculations

predict more complex correlations between isotope

ratios, La/Sm, and F when pyroxenite is present. For

example, Sr and Pb isotopic compositions are

predicted to change minimally over a wide range of

F (0.02–0.08), whereas La/Sm decreases gradually by

30–55%. Also, radiogenic Pb content both increases

(for Fb ~ 0.02) and decreases (for F N ~ 0.06) with

increasing F and decreasing La/Sm. These outcomes

are simple to understand in the context of melting of a

heterogeneous mantle, but they highlight the potential

complexities that should be considered in future

efforts to relate isotope ratios, incompatible element

concentrations, and extent of partial melting.

5.3. Mantle plume flow and thickness, and implica-

tions for spatial variations at hotspots

As we have illustrated, mantle flow can strongly

influence magma compositions. This prediction

allows for the possibility that spatial variations in

mantle flow can contribute to geographic variations in

the geochemistry of hotspot volcanoes [69–71] in the

absence of spatial variations in mantle composition.

For example, in the case in which a mantle plume is

rising beneath a mid-ocean ridge, lavas erupted

directly over the mantle plume will be most influ-

enced by mantle plume flow, which can enhance the

melting of EM and PX relative to DM. On the other

hand, lavas erupting along the ridge axis, well away

from the plume, will be most influenced by mid-ocean

ridge flow and will tend to possess compositions more

like normal MORB, all else being equal. Could this

type of difference in mantle flow contribute signifi-

cantly to along-axis geochemical gradients, such as

those documented for the Iceland–MAR system

[72,73]? If so, the effects of mantle plume flow in

enhancing magmatic concentrations of incompatible

elements and EM and PX isotopic signals would have

to overcome the opposing effect of elevated mantle

plume temperatures to increase the extent of partial

melting.

The ability of plume flowUas we have treated

itUto enhance EM and PX melting depends on the

characteristic thickness H of plume material flowing

out of the melting zone (Fig. 2d) relative to the

thickness of the melting zone. So far, we have

considered a single value of H and compared

solutions with and without plume flow for the same

mantle temperatures and lithospheric thicknesses

(Figs. 3 and 4). To address plume–ridge interaction,

we modify these parameters. We consider an average

potential temperature of Tp=1450 8C, a lithospheric

thickness of 30 km (i.e., the thickness of the Icelandic

crust is 30–46 km [74,75]), and we vary H. To

simulate mid-ocean ridge melting, we assume

Tp=1350 8C, a lithospheric thickness of 7 km, and

uniform mantle flow. We then calculate La/Sm,87Sr/87Sr, and 206Pb/204Pb for each case and then take

the difference between the two cases, DLa/Sm,

D87Sr/87Sr, and D206Pb/204Pb. These results are

compared with the difference in median values of

the above ratios for Iceland and for sections of the

MAR not influenced by hotspots.

Fig. 7 illustrates how increasing H relative to the

thickness of the DM melting zone HDM (DM

solidus depth for Tp=1450 8C minus the lithospheric

thickness of 30 km gives HDM=63 km) increases

DLa/Sm, D87Sr/87Sr, and D206Pb/204Pb. Plume flow

leads to lower values of these ratios than does mid-

ocean ridge flow when H/HDMb1.3 for the Sr and

Pb isotopes and when H/HDMb1 for La/Sm. Plume

flow produces greater ratios than does mid-ocean

ridge flow when H/HDMN1–1.3. For these relatively

Fig. 7. Differences in La/Sm, 87Sr/86Sr, and 206Pb/204Pb between a

plume model (Tp=1450 8C, lithospheric thickness of 30 km, plume-

driven mantle flow) and a mid-ocean ridge model (Tp=1350 8C,lithospheric thickness of 7 km, uniform mantle flow) increase with

plume layer thickness, H. In both models, /DM=0.9, the amount of

EM is labeled, and PX makes up the remaining portion. Left axes

show the differences normalized by the difference between median

Iceland values (La/Sm=1.96; 87Sr/86Sr=0.7032; 206Pb/204Pb=18.49)

and median MAR values (La/Sm=1.0; 87Sr/86Sr=0.7027;206Pb/204Pb=18.33).


thick plume layers, predicted differences in the

above ratios can be appreciable fractions of the

observed differences between the Iceland and MAR

median values.

A recent seismological study suggests that the

layer of plume material beneath Iceland is ~200 km

[76], whereas a mean excess plume temperature of

100–200 8C [76] implies that the DM melting zone

extends 60–100 km beneath the lithosphere. It is thus

possible that the plume flow of a heterogeneous

mantle can contribute substantially to the apparent

enhancement of EM and PX [36,69,72] in the

Icelandic hotspot magmas compared with the normal

MAR magmas. Indeed, the trace-element inversions

of [77] have already suggested that rapid plume flow

deep in the melting zone is important beneath Iceland.

Studies that incorporate 3D mantle flow and melting

are needed to test more completely the importance of

each on spatial geochemical variations. In addition,

although the current models do not address the

elevated 3He/4He ratios of Iceland basalts, future

efforts to do so will have to consider a high 3He/4He

component and at what depth it is likely to begin

melting relative to the other lithologies. Finally, we

hope that the above illustration of the importance of

plume thickness H will help motivate future geo-

physical studies to place improved bounds on H at

Iceland and other hotspots.

5.4. Implications for large-scale mantle structure

It is important to note that the model calcu-

lations that we have used for comparison with

MORB and OIB data assume only small variations

in the starting source compositions. The amount of

DM was fixed at 90%, and we varied only the

proportions of EM and PX. Yet, in many cases,

melts derived from this restricted range of source

mixtures span almost the full range of hotspot La/

Sm and Nd–Pb–Sr isotopic compositions and often

extend well into the MORB range. The general

implication is that mantle plumes may not be as

compositionally different from MORB source man-

tle as commonly believed. In turn, this leads to the

question of whether there is a need for composi-

tional layering in the mantle to account for the

geochemical differences between OIBs and MORBs

[22], and if so, how significant is the distinction

between mantle layers, at least in the portion of

the mantle that feeds OIB and MORB volcanism.

We leave these questions to our companion study

[78].

6. Conclusions

We have taken a rudimentary approach to

simulating flow and melting of a heterogeneous

mantle. We assume that the mantle is composed of


three source materials (EM, PX, and DM) with distinct

trace-element and isotopic compositions and with

different melting functions. Magma composition is

assumed to be governed by the perfect mixing of

fractional melts. Magma composition is also controlled

by the rate at which the residue flows through the

melting zone as a function of depth. For an isoviscous

mantle plume, this rate is predicted to be a maximum at

the base of the plume layer and to decrease upward

toward the lithosphere, in contrast to a uniform flow

profile expected beneath mid-ocean ridges.

A compilation of OIB data shows that incompat-

ible-element ratios (e.g., La/Sm) and Sr, Nd, and Pb

isotope ratios are most variable and extend to

compositions most distinct from those of average

MORB in OIBs erupted on lithosphere older than

~16 m.y. Ocean island volcanoes erupting on

younger seafloor exhibit much more limited varia-

bility, and their compositional range overlaps more

with that of MORBs. These general systematics are

explained well by our calculations, in which thick

lithosphere limits the maximum extent of melting

and the amount of DM melting to low values, and

therefore magma composition is very sensitive to (a)

differences in mantle temperature and (b) the relative

proportions of EM and PX. Decompression beneath

thinner lithosphere or younger seafloor more exten-

sively melts all three source materials and therefore

minimizes differences in magma composition. Our

models can also explain many aspects of OIB

isotopic arrays if individual OIB lavas (or more

realistically, magma batches) represent melts ex-

tracted at different depths in the melting column.

In addition to predicting a wide range of OIB

compositions, the models predict compositions that

extend well into the MORB range, all with the same

starting mantle source composition.

Relative to mid-ocean ridge flow, mantle plume

flow can enhance the incompatible element concen-

tration and isotopic expression of EM and PX if the

plume thickness exceeds the thickness of the DM

melting zone by ~30%. Thus, differences in mantle

flow, in addition to lithospheric thickness, can lead to

geochemical differences between intraplate OIBs and

MORBs. Differences in mantle flow may also

contribute to geographic variations in magma compo-

sition at hotspots, including hotspots near or at mid-

ocean ridges. All of these results suggest that mantle

plume material may be more similar in composition to

MORB source mantle than previously thought. Our

calculations, however, are limited to simulating the

mean compositions of whole melting zones. More

sophisticated 3D models are needed to evaluate more

completely the importance of variable flow and

melting of a heterogeneous mantle on correlations

among incompatible elements, isotope ratios, and

mean extent of melting on intra-hotspot geochemical

variations and on the differences between hotspots

and mid-ocean ridges.

Acknowledgements

We appreciate the thorough reviews provided by

Marc Hirschmann, Yaoling Niu, and Paula Smith. We

thank R. Batiza, C. Lesher, and J. Sinton for

discussions during the earlier stages of this work. This

project was funded by NSF grants OCE02-21889 and

OCE00-04498. SOEST contribution number 6500.

Appendix A. Supplementary data

Supplementary data associated with this article can

be found, in the online version, at doi:10.1016/

j.epsl.2004.10.035.

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