Download Flow and melting of a heterogeneous mantle

Earth and Planetary Science Letters 230 (2005) 29 – 46
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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 midocean 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
* Corresponding author. Tel.: +1 808 956 9717; fax: +1 808 956 5154.
E-mail addresses: [email protected] (G. Ito)8 [email protected] (J.J. Mahoney).
0012-821X/$ - see front matter D 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.epsl.2004.10.035
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G. Ito, J.J. Mahoney / Earth and Planetary Science Letters 230 (2005) 29–46
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 hotspot-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 heterogeneous 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 geochemical 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 materials 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 incompatible 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 midocean 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
asthenosphere is diverted sideways beneath the lithosphere (Fig. 1). A simple way to compute the composition 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 traceelement concentration C i of pooled magmas derived
from mantle source i can be calculated by assuming
31
perfect mixing of melts derived from each depth, or
pressure P of the RMC,
Z P2i
C0i
Ei ðFi ÞFi ð PÞU ð PÞdP
P1i
:
ð1Þ
Ci ¼
Z P2i
Fi ð PÞU ð PÞdP
P1i
Here, C 0i is the concentration of a trace element in
source i, E i ( F i ) is the factor by which the melt is
enriched relative to the source after melting to a mass
Fig. 1. (a) Solidi for enriched mantle (EM, dashed), pyroxenite (PX, gray), and depleted mantle (DM, black line); also shown are the adiabat
(dotted) and predicted temperature T profile (black curve) for a starting potential temperature of 1450 8C. (b) Predicted isobaric productivity for
each lithology as labeled with their respective mass fraction in the mantle, / i. For EM and DM, values assumed for K D , D C*sol/liq, DH Afus, TAfus
(variables are defined by [15]), are 0.25, 0.02, 10 kJ/mol, and 1336 8C, respectively [15]. For EM, assumed proportions for major component A
(defined in [15]) and minor, incompatible component I are 0.598 and 0.012, respectively; for DM, they are 0.606 and 0.004. (c) Predicted melt
productivity for each lithology. (d) Isoviscous, axisymmetric flow (arrow with size proportional to flow rate; streamlines in bold) due to a
cylinder of buoyant fluid beneath a rigid top boundary. The thickness of the plume layer exiting the melting zone H is shown schematically. (e)
Predicted radial flow along the black curve in Panel (d), where upwelling and melting have stopped (solid); radial flow predicted by lubrication
theory (dashed curve, see text), and horizontal flow driven passively by plate spreading at a mid-ocean ridge (vertical line). These curves
represent the horizontal flow of the residue exiting the melting zone U( P) and are proportional to the width of the residual mantle cylinder
(RMC). (f) Predicted melting functions F( P) for the mantle lithologies, as labeled in Panel (c).
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G. Ito, J.J. Mahoney / Earth and Planetary Science Letters 230 (2005) 29–46
fraction F i , and U is the speed at which the residue is
exiting the melting zone. Both F i and U are functions
of pressure P. The pressure range of the RMC for
source i is defined by the beginning P 1i and ending
melting pressures P 2i . Eq. (1) simply describes an
average concentration, C 0i E i ( F i ), of accumulated
incremental melts that were extracted from each
portion of the RMC, weighted by the amount of melt
extracted, F i ( P)U( P)dP. To solve Eq. (1) we must
define functions of E i ( F i ), F i ( P), and U( P).
2.2. Enrichment function E( F)
[54]. With the above assumptions, the melt productivity 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
BT aTi
T X
BT =BPi jF BT =BPj jF
þ
DS
/
j
j
BPi F qc p
cp jpi
BT =BFj jp
:
¼
X
BT T DSi
T
BT =BFi jP
þ
/
þ
DS
/
j
j
BF c
c
BT =BF j
i p
p
p
jpi
j P
ð2Þ
The enrichment function E i ( F i ) 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 increments 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 pressuredependent phase transitions ([47,51]; see Table 1 of
Background Dataset in Appendix A). The accumulated enrichment functions E i ( F i ) are analytical
solutions of fractional melt compositions normalized
by C 0i 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
See Table 1 for the definition of variables and
[15,45,55] for further explanation.
We consider a mantle composed of three lithologies: benrichedQ mantle (EM) peridotite, bdepletedQ
mantle (DM) peridotite, and pyroxenite (PX). For
peridotite melting, we use basic thermodynamic and
mass-balance principles to describe the dependence
of BT/BF i |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 components 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. Consequently, 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 constrained solidus pressure and BF/BT|p functions of
G. Ito, J.J. Mahoney / Earth and Planetary Science Letters 230 (2005) 29–46
Table 1
Definition of variables
Variable Meaning
Value
Unit
cp
1200
J kg1 8C1
9.8
m s2
km
C
C 0i
Ci
C pm
Ei
F
g
H
H DM
P
P0
R
DS
T
U
z
a
/l
q
Specific heat at constant pressure
Concentration of a trace
element in the eruptible
magma
Concentration of a trace
element in starting source i
Concentration in the melt
arising from source i
Concentration in estimated
primitive mantle [62]
Concentration of accumulated,
incremental melt normalized
by C 0i
Weight fraction of partial
melting
Acceleration of gravity
Characteristic thickness of
plume layer exiting melting
zone
Thickness of DM melting
zone beneath lithosphere
Pressure
Pressure at the base of the
lithosphere
Isotope ratio
Change in entropy in
converting solid to melt
Potential temperature
Normalized horizontal flow
rate out of the melting zone
Depth below the lithosphere
Coefficient of thermal
expansion
Mass fraction of lithology
i in mantle
Mantle density
km
GPa
GPa
200
J8C1 kg1
8C
km
3105
3300
kg m3
[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/BP i for each
lithology present (i.e., / j N0). We then numerically
integrate over pressure to yield F i ( 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
33
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 contained 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 ð zÞ ¼ 2ð z=H Þ ð z=H Þ2 :
ð3Þ
Eq. (3) is converted to a function of pressure with
the relation P =P 0+qgz, where P 0 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
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G. Ito, J.J. Mahoney / Earth and Planetary Science Letters 230 (2005) 29–46
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 P 1i in the integral of Eq. (1);
P 1i is either the solidus pressure of lithology i or the
pressure at the base of the plume layer ( P 1i =
P 0+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 minimum pressure corresponds to the base of the lithosphere P 2i =P 0. 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 approximately 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 buoyancy 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 concentrations by the amount of melt derived from each source
Z P2i
3
X
Ci /i
Fi ð PÞU ð PÞdP
C¼
i¼1
3
X
i¼1
Z
P1i
:
P2i
/i
P1i
Fi ð PÞU ð PÞdP
ð4Þ
If C i is the concentration of an element with a
radiogenic isotope, then the isotope ratio in the
eruptible magma R is:
3
X
R¼
Z
i¼1
3
X
i¼1
P2i
Fi ð PÞU ð PÞdP
Ri Ci /i
Z
P1i
;
P2i
ð5Þ
Fi ð PÞU ð PÞdP
Ci /i
P1i
where R i 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,
C 0i . 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 C 0i 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 incompatible trace elements, and DM is assumed to be depleted
in the most incompatible trace elements, with relative
concentration increasing with increasing compatibility. PX is assumed to have the median incompatibleelement composition of the MORB data set that we
have used (see Section 4). We also assume that each
lithology has a different radiogenic isotope composition. We assume EM to have isotope ratios similar to
the postulated bEM1Q or bEM2Q end-members, PX to
G. Ito, J.J. Mahoney / Earth and Planetary Science Letters 230 (2005) 29–46
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 heterogeneities 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 incompatible-element concentrations C i being produced at the
onset of melting, when the (maximum) extent of
35
melting F imax ( F imax=F i ( P 2i )) is near zero. Continued
melting leads to decreasing C i roughly in proportion
to 1/F imax (see Background Dataset in Appendix A for
the evolution of C i with F imax). Enrichment E i =C i /C 0
is greater for more incompatible elements than for less
incompatible elements; therefore, ratios like La/Sm
also decrease with increasing F imax.
For a case in which only EM is present (/ EM=1,
max
/ DM = 0), La/Sm is maximized for all F EM
(Fig. 2a).
Cases that also include DM (/ DMN0) predict concentration curves that diverge from and fall below the
max
curve for / EM =1, once DM begins to melt ( F EM
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
max
isotope ratios are to DM for a given value of F EM
.
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 PX make up the remaining portion. Again,
Fig. 2. (a–c) Predicted melt compositions from mantle made of only EM and DM, with various fractions of EM as labeled. (d–f) Predicted ratios
from mantle made of EM, DM, and pyroxenite with fraction / DM=0.9 and labeled fractions of EM. Gray curves in right column are the same as
those in left column. Source compositions are shown as circles (EM, i.e., EM2), triangles (PX), and squares (DM). Kinks in the curves near
max
F EM
=0.2 correspond to the sudden drop in EM and DM melt productivity, BF/BP, associated with the exhaustion of clinopyroxene as a melting
phase (see Fig. 1c and f). A decrease in BF/BP means that a greater vertical length of mantle experiences a given change in melt fraction (i.e.,
max
DP=(BP/BF)DF), and this translates to a larger volume of high-degree DM melts added to the mixture over a given change in F EM
.
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G. Ito, J.J. Mahoney / Earth and Planetary Science Letters 230 (2005) 29–46
at the onset of melting, only EM controls the commax
positions. Once PX begins to melt ( F EM
= ~ 0.01),
87
86
La/Sm and Sr / Sr decrease, while 206Pb / 204Pb
increases toward the PX source value. As melting
max
continues, DM begins to melt at F EM
=~ 0.07. From
87
86
206
this point, La/Sm, Sr/ Sr, and Pb/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/BT j | 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 decompression. 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 midocean 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 calculations 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 incompatible elements are extracted most efficiently from
EM and PX. Shallower in the melting zone, the
decreasing rate of mantle exiting the melting zone
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.
U( P) decreases the flux of incompatible-elementmax
depleted melts (generated at higher F EM
), as well as
the DM isotope signatures. The enrichment caused by
mantle plume flow tends to be largest nearest the
max
onset of DM melting ( F EM
= 0.07– 0.12) and generally 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 midocean ridges, independent of any mantle source
differences.
G. Ito, J.J. Mahoney / Earth and Planetary Science Letters 230 (2005) 29–46
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 P 2 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
37
estimated sample ages from the magnetically determined ages of the surrounding abyssal seafloor [64].
We also compiled geochemical data for the MidAtlantic 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
Fig. 4. Observed ratios of tholeiitic basalts from various ocean island groups (circles) vs. the square-root of seafloor age at the time of volcanism.
Data for some hotspots are gray and some are colored: Iceland (black), Galápagos (dark blue), Easter (red), Pitcairn (yellow), Cook-Austral
(light blue), Hawaii and Hawaiian-Emperors (purple), Society (white), Canary (brown), and Samoa (orange). Green histograms summarize data
from bnormalQ sections of mid-ocean ridges (see text). Red curves encompassed by light orange shading are calculations with EM (isotopically
similar to EM 2 [5]) fraction / EM = 0.1 and pyroxenite fraction / PX = 0; blue curves and light green shaded area are for / EM = 0.02 and
/ PX = 0.08. Solid curves show predictions for mantle plume flow (U( P) given in Eq. (3)), with excess temperatures DT of 0–200 8C (Normal
mantle potential temperature, assumed to be 1350 8C, is the lower limit for mantle plumes. Temperature increases to the right between curves.)
The mantle fraction of DM is / DM = 0.9. Dashed curves are solutions for DT = 0 8C and mid-ocean ridge flow (U( P) = 1).
38
G. Ito, J.J. Mahoney / Earth and Planetary Science Letters 230 (2005) 29–46
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 compositional 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-
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 lithospheric 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 compositions: 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).
Fig. 5. Isotope ratios of basalts from mid-ocean ridges (green) and the same ocean island groups as in Fig. 4. Dashed curves show calculations
using the same source compositions as in Fig. 4. Solid (gray) curves show results for a different EM end-member, similar to EM1. Numbers
indicate fraction of EM in the mantle (/ EM) with / DM = 0.9; note that / PX = 1/ DM/ EM. Large open circles show assumed isotope ratios of
each mantle component. The dashed curves are broadly consistent with the Easter (red), Canary (brown), Galápagos (dark blue), and Iceland
(black) hotspot trends. Solid curves would better predict the Cook-Austral (light blue) trend if PX began melting deeper than EM1. Like those of
many ocean islands, the trends of the Society (white), Samoa (orange), Hawaiian (purple), and Pitcairn (yellow) data could be better explained
by mixing of EM with a material having less radiogenic Pb (not shown) than the pyroxenite composition shown. This source could be a different
PX, a fifth end-member, such as bCQ [67] or bFOZOQ [5], or a mixture of the two.
G. Ito, J.J. Mahoney / Earth and Planetary Science Letters 230 (2005) 29–46
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 low
208
Pb / 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
39
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 displayed 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 encompass 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), Galápagos (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 moderate values of 87 Sr/ 86 Sr (0.7035–0.7040) and
143
Nd/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, resembling 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 F max; thus, as noted in the previous
section, the melting process alone can contribute
significantly to the isotopic and incompatible-element differences between OIBs and MORBs.
40
G. Ito, J.J. Mahoney / Earth and Planetary Science Letters 230 (2005) 29–46
5. Discussion
5.1. Incomplete magma mixing
factor f i . This factor is 1 for peridotite (EM and DM)
but b1 for PX. Setting f PX=0.15, for example, implies
that 100% melting of PX yields magma compositions
equivalent to melting peridotite by 15%.
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 ( P 2). 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 reveal 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 F̄. We define F̄ as
a weighted average,
Z P2
Fi ð PÞ2 U ð PÞdP
X
P1
F¼
F̄
fi /i Z P2
:
ð6Þ
i
Fi ð PÞU ð PÞdP
P1
Most relations between magma composition and F̄ in
the current literature pertain to peridotite melting;
however, pyroxenite is likely to melt much more
extensively than peridotite. To define a quantity F̄ that
can be related to peridotite melting, we incorporate a
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.
G. Ito, J.J. Mahoney / Earth and Planetary Science Letters 230 (2005) 29–46
Intuitively, the mean extent of melting is always
less than the total extent of melting F imax. For
reference, if mantle flow U and productivity BF/BP
were uniform and only one lithology were present, F̄
would equal F max/2. Mixtures of only the two
max
peridotite lithologies (EM and DM) yield F̄bF EM
/2
because BF/BP increases with melting and because
max
max
F DM
bF EM
(Fig. 6). With our assumption of complete mixing, calculations predict the most extreme
EM-type isotopic signatures (e.g., 87Sr/86SrN0.7050)
to be present only at low extents of melting (F̄b ~ 0.03
max
and F EM
b0.1 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 EMtype peridotite contains material derived from subducted marine sediments.
The presence of pyroxenite adds some complexity.
First, pyroxenite drastically increases F̄ for the same
max
F EM
(Fig. 6a), yielding strongly HIMU-type isotopic
compositions (e.g., 206Pb/204PbN20) at appreciable
values of F̄ (0.04–0.06). Second, our calculations
predict more complex correlations between isotope
ratios, La/Sm, and F̄ when pyroxenite is present. For
example, Sr and Pb isotopic compositions are
predicted to change minimally over a wide range of
F̄ (0.02–0.08), whereas La/Sm decreases gradually by
30–55%. Also, radiogenic Pb content both increases
(for F̄b ~ 0.02) and decreases (for F̄ N ~ 0.06) with
increasing F̄ 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 implications 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
41
directly over the mantle plume will be most influenced 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 significantly 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 T p=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
T p=1350 8C, a lithospheric thickness of 7 km, and
uniform mantle flow. We then calculate La/Sm,
87
Sr/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 H DM (DM
solidus depth for T p=1450 8C minus the lithospheric
thickness of 30 km gives H DM=63 km) increases
DLa/Sm, D87Sr/87Sr, and D206Pb/204Pb. Plume flow
leads to lower values of these ratios than does midocean ridge flow when H/H DMb1.3 for the Sr and
Pb isotopes and when H/H DMb1 for La/Sm. Plume
flow produces greater ratios than does mid-ocean
ridge flow when H/H DMN1–1.3. For these relatively
42
G. Ito, J.J. Mahoney / Earth and Planetary Science Letters 230 (2005) 29–46
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 geophysical studies to place improved bounds on H at
Iceland and other hotspots.
5.4. Implications for large-scale mantle structure
Fig. 7. Differences in La/Sm, 87Sr/86Sr, and 206Pb/204Pb between a
plume model (T p=1450 8C, lithospheric thickness of 30 km, plumedriven mantle flow) and a mid-ocean ridge model (T p=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; 87 Sr/ 86 Sr=0.7027;
206
Pb/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
It is important to note that the model calculations 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 mantle as commonly believed. In turn, this leads to the
question of whether there is a need for compositional 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
G. Ito, J.J. Mahoney / Earth and Planetary Science Letters 230 (2005) 29–46
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 incompatible-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 variability, 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 extensively 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 extracted 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 concentration 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 composition at hotspots, including hotspots near or at midocean ridges. All of these results suggest that mantle
43
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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