Mantle melting as a function of water content beneath back&hyphen;arc basins

Mantle melting as a function of water content beneath back-arc basins

Katherine A. Kelley,

1,2,3

Terry Plank,

Timothy L. Grove,

Edward M. Stolper,

Sally Newman,

and Erik Hauri

Received 15 March 2005; revised 25 January 2006; accepted 29 March 2006; published 28 September 2006.

[

]

Subduction zone magmas are characterized by high concentrations of H

presumably derived from the subducted plate and ultimately responsible for melting at

this tectonic setting. Previous studies of the role of water during mantle melting

beneath back-arc basins found positive correlations between the H

O concentration of the

mantle (

) and the extent of melting (

), in contrast to the negative correlations

observed at mid-ocean ridges. Here we examine data compiled from six back-arc basins

and three mid-ocean ridge regions. We use TiO

as a proxy for

, then use

calculate

from measured H

O concentrations of submarine basalts. Back-arc basins

record up to 0.5 wt % H

O or more in their mantle sources and define positive,

approximately linear correlations between

and

that vary regionally in slope and

intercept. Ridge-like mantle potential temperatures at back-arc basins, constrained

from Na-Fe systematics (1350

–1500

C), correlate with variations in axial depth and wet

melt productivity (

30–80%

/wt %

). Water concentrations in back-arc mantle

sources increase toward the trench, and back-arc spreading segments with the highest

mean

are at anomalously shallow water depths, consistent with increases in crustal

thickness and total melt production resulting from high H

O. These results contrast

with those from ridges, which record low

(<0.05 wt %) and broadly negative

correlations between

and

that result from purely passive melting and efficient melt

focusing, where water and melt distribution are governed by the solid flow field. Back-arc

basin spreading combines ridge-like adiabatic melting with nonadiabatic mantle

melting paths that may be independent of the solid flow field and derive from the H

supply from the subducting plate. These factors combine significant quantitative

and qualitative differences in the integrated influence of water on melting phenomena in

back-arc basin and mid-ocean ridge settings.

Citation:

Kelley, K. A., T. Plank, T. L. Grove, E. M. Stolper, S. Newman, and E. Hauri (2006), Mantle melting as a function of water

content beneath back-arc basins,

J. Geophys. Res.

111

, B09208, doi:10.1029/2005JB003732.

1. Introduction

[

] Water has long been understood to play a major role

in the generation of subduction zone magmas. In essence,

water lowers the mantle solidus [e.g.,

Kushiro et al.

, 1968],

which ultimately drives melting of the mantle wedge

beneath arcs and back-arc basins due to a flux of water

originating from the dehydrating, subducting slab. This has

been the working paradigm for subduction zone magma

genesis for more than 20 years, supported by the widespread

observations that subduction zone lavas are vesicular and

explosive, contain hydrous phenocrysts [e.g.,

Gill

, 1981],

follow hydrous liquid lines of descent [

Sisson and Grove

1993a], are enriched in fluid-mobile trace elements

[e.g.,

Morris et al.

, 1990], and carry trace element and

isotopic signatures characteristic of subducting sediment

and oceanic crust [e.g.,

Tera et al.

, 1986;

Plank and

Langmuir

, 1993;

Miller et al.

, 1994]. High H

O concen-

trations in arc magmas have been inferred or estimated

using innovative analytical and experimental techniques,

[e.g.,

Anderson

, 1979, 1982;

Sisson and Grove

, 1993a,

1993b;

Gaetani et al.

, 1994], and direct measurements of

O in submarine glasses and melt inclusions have sup-

ported these earlier estimates of dissolved H

O in arc and

back-arc lavas [e.g.,

Muenow et al.

, 1980;

Aggrey et al.

1988;

Muenow et al.

, 1991;

Danyushevsky et al.

, 1993;

Sisson and Layne

, 1993;

Stolper and Newman

, 1994]

(hereinafter referred to as S&N94). Notably, a significant

increase in the number of direct measurements of volatile

contents in arc and back-arc magmas in recent years [e.g.,

Kamenetsky et al.

, 1997;

Roggensack et al.

, 1997;

Sisson

and Bronto

, 1998;

Newman et al.

, 2000;

Fretzdorff et al.

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 111, B09208, doi:10.1029/2005JB003732, 2006

Department of Earth Sciences, Boston University, Boston,

Massachusetts, USA.

Department of Terrestrial Magnetism, Carnegie Institution of Wa-

shington, Washington, D. C., USA.

Now at Graduate School of Oceanography, University of Rhode

Island, Narragansett, Rhode Island, USA.

Department of Earth, Atmospheric and Planetary Sciences,

Massachusetts Institute of Technology, Cambridge, Massachusetts, USA.

Division of Geological and Planetary Sciences, California Institute of

Technology, Pasadena, California, USA.

0148-0227/06/2005JB003732$09.00

B09208

1of27

2002;

Kent et al.

, 2002;

Cervantes and Wallace

, 2003;

Sinton et al.

, 2003;

Walker et al.

, 2003] has set the stage

for a quantitative investigation of water in natural subduc-

tion zone settings.

[

] Back-arc basins are natural places to begin such a

study because they can be treated, in many ways, like mid-

ocean ridges. The driest back-arc basin melts are composi-

tionally equivalent to mid-ocean ridge melts and thus, like

mid-ocean ridge magmas, can be interpreted as melts

generated by varying extents of adiabatic decompression

melting of ascending mantle. For example, the driest back-

arc basin basalts overlap with MORBs on Na

8.0

-axial depth

plots (Figure 1 [see also

Klein and Langmuir

, 1987]) and

plots of Na

O versus FeO (Figure 2 [see also

Langmuir et

al.

, 1992;

Taylor and Martinez

, 2003]). Both inter- and

intrabasin systematics of back arcs were recently explored

Taylor and Martinez

[2003], who compared major and

trace element variations (e.g., Na

8.0

,Fe

8.0

,Ti

8.0

(8.0)

Ba/La) of four back-arc basins to global MORB; their work

emphasizes the hybrid nature of the back-arc basin melting

process, identifying MORB-like geochemical systematics in

relatively dry back-arc melts and showing how these

systematics are perturbed in wetter samples by the addition

of H

O-rich material from the subducted slab. The melting

process in back arcs is also not complicated, as it may be in

arcs, by the effects of overlying crust, since crustal assim-

ilation is a small concern and crustal thickness will not

impact the melting column because it is a passive conse-

quence of melting just as at ridges. Additionally, back arcs

are less subject to the thermal influence of the cold

subducting slab, and may reflect ambient upper mantle

temperature variations as ridges do. Back-arc basins are

therefore potentially ideal sites for studying the effects of

variations in mantle temperature and water contents on

mantle melting with fewer complicating factors than arcs.

[

] The quantitative relationship between water and man-

tle melting over the range of tectonic settings has been

investigated in only a few localities, with contrasting results.

S&N94 evaluated the importance of water in the formation

of magmas at the Mariana trough back-arc spreading center

Figure 1.

8.0

versus axial depth in global MORB and

back-arc basins. (a) MORB and back-arc basin regional

averages from

Klein and Langmuir

[1987]. The black

circles are MORB, and the barred shaded symbols are back

arcs. Abbreviations are as follows: MT, Mariana trough;

ESR, East Scotia ridge; LB, Lau basin.

Klein and Langmuir

[1987] reported two values for the Mariana trough at

17.39

N (4000 m depth) and at 18.01

N (4400 m depth).

(b) Back-arc basin basalts from the compilation in this study

superimposed on the data and trends of

Klein and Langmuir

[1987]. The white symbols are average back arcs (unfiltered

for H

O content (this study, Table 3)), the black symbols are

average, dry back-arc basin basalts (H

O < 0.5 wt % (this

study, Table 3)), the barred shaded symbols are back arcs

from

Klein and Langmuir

[1987] as in Figure 1a, and the

shaded field is the MORB array from Figure 1a. Abbrevia-

tions are as follows: WB, Woodlark basin; NFB, North Fiji

basin; NLB, northern Lau basin; SLB, southern Lau basin;

MB, Manus basin; other abbreviations as in Figure 1a.

Figure 2.

Regionally averaged Na

(Fo90)

versus Fe

(Fo90)

MORB and back-arc basin basalts (Na

OandFeO

concentrations corrected to equilibrium with Fo

; see

section 2). The shaded points are MORB from

Langmuir et

al.

[1992]. The black line connected by open circles shows

the MORB model curve with potential temperatures from

Langmuir et al.

[1992]. Symbols are averages of the driest

back-arc basin basalts from each region (<0.5 wt % H

same as solid symbols in Figure 1b and Table 3); the open

diamond is the Mariana trough (MT); the open star is the

East Scotia ridge (ESR); the open square is the Woodlark

basin (WB); the shaded inverted triangle is the North Fiji

basin (NFB); the open triangle is the Sumisu rift (SR); the

solid circle is the northern Lau basin (NLB); the open circle

is the southern Lau basin (SLB); and the shaded square is

the Manus basin (MB). The Sumisu rift and southern Lau

basin contain no dry basalts, but average data for these

regions are shown for reference.

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KELLEY ET AL.: MANTLE MELTING BENEATH BACK-ARC BASINS

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B09208

using concentrations of volatile, major, and trace elements

from submarine glasses. This work was the first to recog-

nize correlations between trace elements and water contents

of subduction-related lavas and suggested a positive,

roughly linear relationship between the extent of mantle

melting (i.e., melt fraction;

) and the H

O concentration of

the mantle (Figure 3a). The basis for pure ‘‘flux melting’’

models originates from this study. Correlations between

O and trace elements in volcanic arc melts [e.g.,

Grove

et al.

, 2002;

Cervantes and Wallace

, 2003;

Walker et al.

2003] provide supporting evidence for the importance of the

flux melting mechanism beneath arcs, although nominally

dry arc melts from Japan [

Tatsumietal.

, 1983], the

Cascades [

Bartels et al.

, 1991], and Java [

Sisson and

Bronto

, 1998] implicate mantle decompression as another

means of melt generation beneath arcs. In contrast to the

positive correlation between H

Oand

described or

inferred for back-arc basin and arc lavas, recent models of

hot spot-influenced, ‘‘damp’’ mid-ocean ridges [

Detrick et

al.

, 2002;

Asimow et al.

, 2004;

Cushman et al.

, 2004]

suggest a negative correlation between H

O and

(e.g.,

Figure 3b, hLKP curve). The differences in the relationships

between water content and extent of melting in two such

similar tectonic settings as back-arc basins and mid-ocean

ridges present a dilemma that we address in this study.

[

] Theoretical, empirical, and experimental investiga-

tions of the role of water in mantle melting underscore

the differences observed in natural settings. For example,

experimental work [

Gaetani and Grove

, 1998] (hereinafter

referred to as G&G98), thermodynamic modeling

[

Hirschmann et al.

, 1999], and empirical parameterizations

of experimental and thermodynamic data [

Katz et al.

, 2003]

have shown that the positive melting trend observed in the

Mariana trough is readily reproduced through isothermal,

isobaric equilibration of fertile mantle with increasing H

content (Figure 3b, MELTS, G&G98, and KSL

curves),

although such conditions do not translate easily into a

physical melting process in the earth [S&N94;

Hirschmann

et al.

, 1999;

Asimow and Langmuir

, 2003]. Parameters such

as temperature and pressure certainly vary in natural sys-

tems, and the apparent similarities between these studies

and the Mariana trough trend may indeed be only coinci-

dental. On the other hand,

Asimow and Langmuir

[2003]

used simple thermodynamic models to propose that adding

water to decompression melting regimes at mid-ocean

ridges will, seemingly paradoxically, increase total melt

production but simultaneously decrease the mean extent

of melting. This situation arises when pooling melts from a

two-dimensional (2-D) triangular melting regime because

low-

, wet melts originate from the large source volume at

the triangle’s base. Such a geometry can thus lead to a

decrease in mean

with increasing H

O in the mantle

(Figure 3b, hLKP curve). Although this effect has been

documented at hot spot-influenced mid-ocean ridges

[

Detrick et al.

, 2002;

Asimow et al.

, 2004;

Cushman et

al.

, 2004], it has not been seen in the high-H

O lavas from

back-arc basins.

Katz et al.

[2003] also developed an

empirical parameterization of hydrous, adiabatic melting.

The relationship between H

O content and extent of melting

in their hydrous, adiabatic melting model, however, con-

trasts with both the observed trend in the Mariana trough

and with other efforts to model hydrous, adiabatic melting

(Figure 3b, KSL

curve). Their model produces positive

correlations between H

O in the source and

, but the

steepness of the trend suggests that H

O addition does not

lead to a significant increase in extent of melting, and thus

that H

O-fluxed melting contributes volumetrically very

little to the final melt produced by adiabatic decompression

in this model. For back-arc basins, therefore, we must

presently choose between, on the one hand, an unlikely

melting process (i.e., flux-induced, isothermal, isobaric

melting) that produces trends similar to those observed in

nature or, on the other hand, an apparently more realistic

melting process (i.e., polybaric, hydrous, adiabatic melting)

for which current models do not reproduce observed trends.

[

] In the work reported in this paper, we studied aspects

of the differences between ridge and back-arc melting

Figure 3.

versus

from the literature. (a) Original

figure from S&N94 showing their Mariana trough data and

the linear best fit. (b) Models compiled from the literature

for wet melting of peridotite. The thin, solid black line

(S&N94) is the S&N94 Mariana trough best fit line from

Figure 3a; the thick, short-dashed, shaded line (MELTS)

is the isobaric, isothermal MELTS calculation from

Hirschmann et al.

[1999] at 1350

C and 1 GPa; the thin,

long-dashed, black line (G&G98) is the fit to the isobaric,

isothermal experimental results from G&G98 at 1350

C and

1.5 GPa; the triple-dotted black line (KSL

) is an adiabatic

model result of

Katz et al.

[2003] for

= 1250

C; the solid

shaded line (KSL

) is an isobaric, isothermal model result

from

Katz et al.

[2003] at 1250

C and 1 GPa; the bold black

line (hLKP) is an adiabatic model result from

Asimow and

Langmuir

[2003] for

= 1350

C, pooled from a 2-D

melting triangle.

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KELLEY ET AL.: MANTLE MELTING BENEATH BACK-ARC BASINS

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B09208

systematics, focusing in particular on discriminating be-

tween the competing effects of H

O, decompression, and

mantle temperature on melt production. Using available

measurements of the water contents of glasses from several

back-arc basins, we first show that the positive H

O-

trend

of the Mariana trough found by S&N94 is a general

phenomenon in back-arc basin settings. In detail, however,

these trends differ in important ways from one back-arc

region to another. We then use these differences and their

correlations with other geochemical and geophysical param-

eters and the contrasts with comparable data from mid-

ocean ridge basalts to demonstrate the unique way in which

water drives melting beneath back-arc spreading centers.

2. Methods and Data Treatment

[

] In order to test the competing models of wet melting,

we must be able to determine and compare the extent of

mantle melting (

) and the concentration of H

O in the

mantle (

) over a broad range of mid-ocean ridge and

back-arc basin basalt compositions. Here, we present the

methods we used to filter and correct the data, to calculate

and

, and to estimate other relevant factors such as

mantle potential temperature (

), axial depth, and crustal

thickness in a self-consistent manner. Readers more inter-

ested in an outline of the methodology than in the details

may skip to the methods summary presented in section 2.8.

2.1. Back-Arc Basin Basalt Data

[

] We compiled a global data set of major element

and volatile measurements for 408 glasses and olivine-

hosted melt inclusions from six back-arc basin localities

(Mariana trough [

Volpe et al.

, 1987;

Hawkins et al.

, 1990;

S&N94;

Gribble et al.

, 1996, 1998;

Newman et al.

, 2000],

Sumisu rift [

Hochstaedter et al.

, 1990a], Manus basin

[

Danyushevsky et al.

, 1993;

Kamenetsky et al.

, 2001;

Sinton

et al.

, 2003;

Shaw et al.

, 2004], North Fiji basin [

Aggrey et

al.

, 1988;

Danyushevsky et al.

, 1993], Lau basin [

Aggrey et

al.

, 1988;

Danyushevsky et al.

, 1993;

Sinton et al.

, 1993;

Pearce et al.

, 1995;

Kamenetsky et al.

, 1997;

Peate et al.

2001;

Kent et al.

, 2002; A. J. Kent, unpublished data, 2002;

S. Newman, unpublished data, 1994] and East Scotia ridge

[

Muenow et al.

, 1980;

Leat et al.

, 2000;

Fretzdorff et al.

2002;

Newman and Stolper

, 1995; S. Newman, unpublished

data, 2002]) and three mid-ocean ridge and ridge-like

regions (Gala

́pagos spreading center [

Cushman et al.

2004], Mid-Atlantic Ridge and Azores platform [

Dixon et

al.

, 2002], and Woodlark basin [

Muenow et al.

, 1991;

Danyushevsky et al.

, 1993]).

[

] Before using these data to model

and

, we first

considered how the composition of each glass may have

changed through degassing and crystal fractionation. To

assess how degassing may have affected H

O, we examined

another volatile species, CO

, which has much lower

solubility than H

O in silicate melt and degasses nearly to

completion before H

O degassing initiates during open

system degassing [

Dixon et al.

, 1995]. The presence of

measurable CO

is thus an indicator that H

O has likely not

been significantly affected by degassing, but CO

data are

not published for many of the samples used in this study.

The combined concentrations of H

O and CO

in a melt,

however, are pressure sensitive and, in submarine lavas,

usually reflect vapor saturation or supersaturation at or near

the hydrostatic pressure of eruption [

Dixon and Stolper

1995]. We thus calculated the saturation pressure of each

sample with respect to pure H

O (i.e., CO

= 0 ppm).

Glasses with pure H

O saturation pressures equal to or

greater than their collection depths probably reached satu-

ration with H

O vapor and experienced some H

O degass-

ing. To account for uncertainties in eruption/collection

depth and the chance that lava flowed downhill from the

eruption site, we included only those samples with pure

O saturation pressures at least 30 bars less than the

pressure at the collection depth. Exceptions to these criteria

were made in the case of basaltic melt inclusions, which are

often trapped at high pressure within the magma chamber

and, if H

O concentrations are high (e.g., at the Valu Fa

ridge), may record H

O saturation pressures much higher

than those at the sample collection depth. In these cases,

only melts with measured CO

concentrations >30 ppm

were considered undegassed.

[

] To compensate for the effects of crystal fractionation,

all samples that were determined to have escaped significant

O degassing were back corrected to primary mantle melts

using several steps. The regional data sets were first filtered

to exclude all glasses with MgO < 7 wt %, in order to

eliminate highly fractionated compositions. One exception

to this criterion was made in the case of the Manus basin,

where basalt compositions with MgO

6.25 wt % were

included in order to allow a greater number of samples to

represent this region. Of the remaining samples, those with

MgO < 8 wt % were corrected to 8 wt % MgO using the

8.0

and Na

8.0

expressions from

Klein and Langmuir

[1987] and the TiO

2(8.0)

and H

(8.0)

expressions from

Taylor and Martinez

[2003]:

FeO

MgO

ðÞ

;

373

MgO

ðÞ

;

TiO

ðÞ

TiO

MgO

;

ðÞ

MgO

We then employed an additional fractionation correction to

8.5 wt % MgO because most melts are still on olivine +

plagioclase cotectics at 8 wt % MgO and adding olivine

only (see below) at this point leads to false high Fe. The

fractionation slopes for this step are shallower than those

above, but consistent with olivine + plag cotectic slopes

predicted by the liquid line of descent algorithm of

Weaver

and Langmuir

[1990]:

ðÞ

;

135

ðÞ

;

TiO

ðÞ

TiO

ðÞ

;

ðÞ

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Glasses with initial MgO between 8.0 and 8.5 wt % were

corrected to 8.5 wt % MgO only along these linear ol + plag

cotectics by substituting the measured glass concentrations

of FeO, Na

O, TiO

and H

O for Fe

8.0

,Na

8.0

,TiO

2(8.0)

and

(8.0)

and substituting the measured concentration of

MgO for the 8.0 term inside the parentheses in equations (5),

(6), (7), and (8). We then back corrected these 8.5% MgO-

equivalent compositions, as well as all glasses with initial

MgO

8.5 wt % (to which no correction had yet been

applied), to primary mantle melts by adding equilibrium

olivine (using K

ol-liq

[Mg

Fe] = 0.3) to each glass

composition in 1% increments until in equilibrium with Fo

(as in the work of S&N94). These corrected liquid composi-

tions provide Fe

(Fo90)

and Na

(Fo90)

, which are discussed

throughout and are used to calculate mantle potential

temperature (see section 2.7), and

and

(i.e., TiO

2(Fo90)

and H

(Fo90)

), which are input to equations (9) and (10)

below. Most samples required

15% olivine addition to reach

equilibrium, but to avoid artifacts from overcorrection,

the few samples requiring >30% olivine addition were

excluded. These three criteria (degassing, MgO content, and

fractionation) are the only constraints used to filter the data;

50% of the original data compilation (

=224)passedthe

filter and were used for the modeling.

2.2. Modeling Mantle Melt Fractions and Water

Contents of Mantle Sources

[

] S&N94 performed a multielement inversion on a

suite of Mariana trough glasses to constrain melt fraction

and source composition. This inversion was based on the

simplifying assumption that variations in Mariana trough

basalt chemistry reflect variable extents of melting corre-

lated with mixing of two source components: one similar to

the mantle source of normal mid-ocean ridge basalt

(NMORB) and the other a water-rich component derived

from the subducted slab. They chose the most MORB-like

basalt composition and assumed it reflected 5% batch

melting of unmodified NMORB source to obtain the com-

position of this source component. They then used an

iterative procedure based on the H

O, TiO

O, Na

and P

contents of each glass to solve simultaneously for

the composition of the H

O-rich component, the fraction of

this component in the source of each sample, and the extent

of melting of the source by which each sample was

produced. Although this method succeeds for the Mariana

trough, the assumptions (1) of a two-component system

(requiring that enough data exist to define clear mixing

relationships and that additional components are not in-

volved), (2) of a H

O-poor NMORB mantle source and a

O-rich component that are constant in composition, and

(3) of 5% melting to produce the NMORB end-member

Figure 4.

TiO

versus H

O in back-arc basin basalts,

calculated to equilibrium with Fo

(see text): (a) Mariana

trough (after S&N94); (b) mid-ocean ridges (Mid-Atlantic

Ridge (FAZAR), Gala

́pagos spreading center (GSC)) and

back-arc basin segments (North Fiji basin, East Scotia ridge

E5–E8) showing positive correlations; (c) mid-ocean ridge

(Woodlark basin) and back-arc basin segments (East Scotia

ridge E2–E4 and E9) showing both negative and positive

correlations; and (d) back-arc basin segments showing

negative correlations (northern and southern Lau basin,

Manus basin, Sumisu rift).

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KELLEY ET AL.: MANTLE MELTING BENEATH BACK-ARC BASINS

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B09208

may not apply to other regions. An alternative approach is

therefore necessary because, in many regions, data sets are

limited, the compositions of the mantle source and/or slab-

derived component may vary regionally, and the extent of

melting of the MORB-like end-member is unlikely to be

constant for all back arcs.

[

] Rather than performing a best fit based on several

relatively incompatible elements (including some likely

present in significant concentrations in the slab-derived

components) to constrain

for each sample, we used

TiO

in glasses as a single-element proxy for melt fraction

(

). Like any other element that is incompatible during

mantle melting, TiO

decreases monotonically in the melt

with increasing

of a single source. While it is difficult to

identify a truly ‘‘conservative’’ element in subduction zones

(i.e., an element not added from the subducted slab [

Pearce

and Parkinson

, 1993]), TiO

holds promise in this regard

because of its low overall abundance in arc lavas and the

possibility that it, like other high field strength elements,

mayberetainedinresidualrutileintheslabduring

dehydration [e.g.,

Ryerson and Watson

, 1987]. We thus

adopted the approximation that, except for dilution, the

TiO

content of sources in a given mantle wedge are

independent of the amount of slab-derived component they

contain. Moreover, systematics of Mariana trough basalts

are consistent with low TiO

in the H

O-rich component

(S&N94), as the data show that increasing H

O concen-

trations correlate with decreasing TiO

and, by proxy,

increasing

(Figure 4a (see also S&N94). This correlation

is the starting point of the linear wet melting function and

was indeed the observation that led S&N94 to first suspect a

positive correlation between the water content and melt

fraction of the source of Mariana trough lavas.

[

] On the basis of this observation for the Mariana

trough (Figure 4a), we used TiO

to calculate

for all the

filtered and corrected back-arc basin basalt and MORB data.

To model

, the fraction of melting, we solved the batch

melting equation to yield

ðÞ

;

where

is the concentration of TiO

in the mantle source

(Table 1; see sections 2.4–2.5),

is the concentration of

TiO

in the melt in equilibrium with Fo

(from basalt data,

see section 2.1), and

is the bulk distribution coefficient

for Ti during mantle melting (Table 2; see section 2.3). To

obtain the concentration of H

O in the source, we re-solved

this equation in terms of H

O to yield

ðÞþ

;

where

is the concentration of H

O in the mantle

source (hereinafter referred to as

is the

concentration of H

O in the melt in equilibrium with Fo

(from basalt data, see section 2.1),

is the output of

equation (9), and

is the bulk distribution coefficient

Table 1.

Mantle Source Constraints for Back-Arc Basins and Ridges

Basin

Region/Segment

Source Model

Removed, %

Mariana trough

DMM

0.133

0.000

0.012

Sumisu rift

DMM

0.10

0.130

0.003

Lau basin

CLSC

DMM

1.00

0.107

0.014

0.002

ELSC-VFR

DMM

2.50

0.083

0.024

0.006

ILSC

DMM

0.133

0.000

0.003

MTJ

DMM

0.133

0.000

0.003

Manus basin

MSC

DMM

0.80

0.112

0.015

0.005

ETZ

DMM

0.80

0.112

0.015

0.005

DMM

0.15

0.128

0.005

0.004

DMM

0.80

0.112

0.015

0.005

East Scotia ridge

E2–E4

DMM

0.133

0.000

0.006

E5–E6

DMM

0.15

0.128

0.005

0.004

E7–E8

DMM

0.40

0.121

0.006

0.005

Ti/Y

0.192

0.007

North Fiji basin

Ti/Y

0.151

0.012

N160

Ti/Y

0.198

0.024

Woodlark basin

west/D’Entrecasteaux

Ti/Y

0.172

0.013

center

DMM

0.50

0.119

0.014

0.003

east

DMM

0.40

0.121

0.012

0.005

northeast

DMM

0.10

0.130

0.003

GSC

Cushman et al.

[2004]

0.143

Cushman et al.

[2004]

0.108

Cushman et al.

[2004]

0.105

Azores

Ti/Y

0.189

0.014

Ti/Y

0.143

0.002

Ti/Y

0.139

0.003

Ti/Y

0.137

0.003

DMM source model denotes the use of prior melt extraction to constrain source variation. Ti/Y source model denotes cases where the mantle source is

enriched, and the TiO

/Y model is used to constrain source characteristics.

Columns denote errors on the value of

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for H

O during mantle melting (from S&N94; see Table 2

and section 2.3).

[

] While end-member batch melting is probably not a

realistic melting process, it is a useful approximation for

determining the bulk

of basaltic partial melts of the

mantle. For example, equation (9) provides a fair approx-

imation of the bulk melt fraction (as reflected in incompat-

ible element concentrations) at mid-ocean ridges despite the

likely complexity of the melting regime and melting process

in this environment [

Plank and Langmuir

, 1992;

Plank et

al.

, 1995]. As a relevant example, the Na

8.0

and Ti

8.0

variations in mid-ocean ridge basalts are well described

by pooling of melts produced by polybaric, adiabatic,

fractional melting with

s that vary as a function of

pressure, temperature, composition, and mode (Figure 5

[see also

Langmuir et al.

, 1992]). The Na

8.0

-Ti

8.0

trend,

however, is also adequately reproduced with the simplest

model (batch melting with constant

and

s (Figure 5)).

Since back arcs tap mantle similar to MORB, and because

we know less about the melting process in these settings, we

adopted this simple model as our starting point.

2.3. Partition Coefficients

[

] The partition coefficients used in the batch melting

model impact the results of these calculations. The

used

here derives from the simplified MORB model above

(Figure 5) and describes partitioning between melt and

lherzolitic mantle. Published mantle/melt

s for Ti range

up to 0.11 [

Kelemen et al.

, 1993], but a value this high is not

permitted in the batch melting model, as it produces

negative values for

in high-Ti samples. The value used

here (0.04) reflects an average

within the range pre-

dicted for appropriate variations in pressure, temperature,

and melt composition along a polybaric path (e.g., 0.01–

0.06 [

Langmuir et al.

, 1992]; <0.01–0.08 [

Baker et al.

1995]), and we assess the effect of this uncertainty on the

calculations below. In rare cases, extents of melting pre-

dicted by the batch melting model exceed 20%. At such

high melt fractions, one might expect clinopyroxene (cpx)

to become exhausted from the mantle, and the liquid to

instead reflect equilibrium partitioning between melt and a

two-phase harzburgitic mantle. For the few back-arc sam-

ples where cpx may have been exhausted from the mantle

(e.g., the Manus basin, based on CaO/Al

), we selected a

harzburgite/melt

of 0.05 (average of

s reported by

Grove et al.

[2002],

Pearce and Parkinson

[1993], and

Kelemen et al.

[1993]). Because this

is similar to the

lherzolite

, the change has a small effect on the calculated

and

. The

used here (0.012) is adopted from

S&N94 in order to be consistent with that study. The value

is similar to that for the LREE, consistent with variations

observed in MORB [

Michael

, 1988;

Dixon et al.

, 2002]. We

evaluate the effect of lowering

in section 2.6 below.

2.4. Modeling Depleted Mantle Source Compositions

[

] The composition of the depleted mantle end-member

in the sources of back-arc basin magmas is crucial to the

model results, and so we carefully consider here the likely

variation of

in global back-arc basin and ridge regions.

Two variables primarily control the TiO

concentration of a

partial melt of mantle peridotite: the initial concentration of

TiO

in the peridotite and the melt fraction. So while

Taylor

and Martinez

[2003] attribute TiO

variations in back-arc

basins largely to variations in source composition, varia-

tions in

would also lead to TiO

variations for a constant

source composition, and the challenge is to distinguish

whether a melt with low TiO

reflects high

, or a highly

depleted mantle, or both. The key to doing so is to use not

just TiO

, but several elements with different

s during

mantle melting; i.e., although the concentration of a single

element in a melt can be modeled by an infinite number of

combinations of source concentration and

, the relative

abundances of elements with differing mantle/melt

s can

Table 2.

Mantle/Melt Partition Coefficients and Starting

Composition

Element

D (Mantle/Melt)

DMM

Th, ppm

0.0015

0.0137

Nb, ppm

0.003

0.21

Ta, ppm

0.005

0.0138

La, ppm

0.0075

0.234

Ce, ppm

0.011

0.772

O, ppm

0.012

116

Pr, ppm

0.015

0.131

Nd, ppm

0.02

0.713

Sm, ppm

0.03

0.27

Zr, ppm

0.03

7.94

Eu, ppm

0.035

0.107

Gd, ppm

0.04

0.395

TiO

, wt %

0.04

0.133

Tb, ppm

0.048

0.075

Dy, ppm

0.06

0.531

Ho, ppm

0.07

0.122

Er, ppm

0.08

0.371

Yb, ppm

0.095

0.401

Y, ppm

0.095

4.07

Lu, ppm

0.105

0.063

Depleted MORB mantle composition from

Salters and Stracke

[2004].

Figure 5.

8.0

versus Na

8.0

in North Atlantic MORB

(shaded circles [

Langmuir et al.

, 1992]) with model fits to

the data trend. The thin black line with open squares (LKP)

is a polybaric, adiabatic, fractional, pooled melting model,

with

s varying as a function of pressure, temperature,

composition, and mode (taken from

Langmuir et al.

[1992, Figure 55]). The bold line with solid circles

(const.

, this study) is batch melting with constant

(

= 0.02,

= 0.04) and constant mantle source

(

= 0.29 wt %,

= 0.133 wt %).

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distinguish variations in source composition from variations

due to differing extents of melting. For example, source

depletion affects highly incompatible elements (e.g., Nb)

more than moderately incompatible elements (e.g., Ti

(Figure 6a)), while high degrees of melting will affect both

elements almost equally provided

(Figure 6b). Here,

we attempt to account for TiO

variations in mantle sources

using a model based on the systematic variations of a suite

of elements in lavas from each basin.

[

] A complicating factor in separating variations in the

MORB-like mantle composition from variations in extent of

melting at subduction zones is that there are probably no

elements in the mantle wedge that are completely unaffected

by the mass flux from the subducting slab. Nevertheless, for

back-arc basin lavas, we will assume most trace element

enrichments (e.g., LREE) are additions from the slab-

derived, H

O-rich component, whereas incompatible ele-

ment depletion is a feature of the MORB-like mantle. We

therefore chose several relatively conservative elements,

spanning a range of mantle/melt

s (Y, Ti, Zr, Nb, and

Ta) to set constraints on mantle source variations. These

high field strength elements vary systematically during

mantle melting at mid-ocean ridges and, unlike the light

rare earth elements and Th, are expected to be retained in

the slab by residual rutile [

Pearce and Parkinson

, 1993].

These are thus among the elements in the mantle least

affected by addition of slab-derived components.

[

] Figure 7 illustrates how we determined the compo-

sition of the end-member mantle sources for the back-arc

spreading centers, to ultimately derive

. We did this by

fitting the conservative element pattern (rather than the full

trace element pattern, most of which is sensitive to slab

additions (e.g., Figure 7)) of natural lava samples with a

melt removal model to determine the source composition of

the ‘‘slab-free’’ mantle end-member for each basin or

subregion within a basin. Mantle source variation is

expressed as a function of prior melt removal from an

average mantle composition. We chose as the starting point

the depleted MORB mantle (DMM) composition of

Salters

and Stracke

[2004], which represents an average composi-

tion of the mantle that provides the source of MORB. The

melt removal model controls the trace element character-

istics of the mantle source by removing a specified fraction

of melt (

) from DMM using batch melting and the bulk

mantle/melt

s in Table 2. That is,

represents a melt

fraction that has been removed from the mantle prior to the

melting that takes place within the ridge or back-arc magma

source. The removal of

creates depletion of the mantle

before it enters into the ridge and back-arc sources. Subse-

quent melting of these depleted sources, which is the

melting step that generates mid-ocean ridge and back-arc

basin magmas (

, as defined in section 2.2), employs these

same

s. Source depletion (the removal of

from DMM)

has a large effect on the shape of the trace element pattern of

a melt (Figure 6a), whereas

controls the absolute abun-

dances of all elements, shifting the whole pattern up or

down with a minimal effect on shape (Figure 6b), because

is usually a small value (<3%) and

is a large value

(typically 10–20%) with respect to the

s modeled. Prior

melt removal (

) has the largest effect on the most incom-

Figure 7.

Trace element models constraining mantle source characteristics for basins and segments with depleted mantle

sources (equal to or more depleted than DMM), normalized to DMM of

Salters and Stracke

[2004]. Figures for each region

are split between two panels. Top panels show complete trace element patterns for two melt compositions encompassing the

geochemical range of the region, with Th and the REE in filled symbols and the conservative elements (CEs; see text) in

open symbols. Bottom panels isolate the CEs, with bold and dashed lines showing model curves for the CE patterns,

varying

and

as illustrated in Figure 6. The shaded fields around these model curves illustrate the errors on the model

(see Table 1), constrained by determining the range of model pattern shapes permissible by any pair of CEs (including 10%

errors in the concentration of each element; see text). Within a given basin, segments with similar mantle characteristics are

grouped together. (a, b) Mariana trough. (c, d) Manus basin, ER segment. (e, f) Manus basin, MSC, ETZ, and SR segments.

(g, h) Lau basin, MTJ and ILSC segments. (i, j) Lau basin, CLSC segment. (k, l) Lau basin, ELSC and VFR segments, with

additional curve (solid shaded line) illustrating the misfit of a variable

-constant

model. (m, n) Sumisu rift. (o, p)

Woodlark basin, NE segment. (q, r) Woodlark basin, east segment. (s, t) East Scotia ridge, E2–E4 segments. (u, v) East

Scotia ridge, E5–E6 segments. (w, x) East Scotia ridge, E7–E8 segments. See text for data sources.

Figure 6.

Model melt trace element compositions normal-

ized to DMM of

Salters and Stracke

[2004]. (a) Illustrating

the effect of mantle source variation on the shape and

position of the trace element pattern, keeping

constant at

10%. The curves show the effects of 0, 1, and 3% prior

batch melt removal from source on the shape of the pattern.

(b) Illustrating the effect of variable melt fraction on the

shape and position of the trace element pattern, keeping

source concentrations constant (at DMM (Table 2)). Curves

show 5, 10, and 20% batch melts of unmodified DMM,

using

s as in Table 2.

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Figure 7

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B09208

Figure 7.

(continued)

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B09208

patible elements (e.g., Nb and Ta), which may change in

source concentration by a factor of 10 with as little as 2.5%

melt removed, whereas TiO

would vary by only a factor of

1.5, using the batch melting model. Removing melt using a

fractional melting model would lead to even smaller

changes in TiO

relative to the more incompatible elements,

and we thus used the batch removal model because it allows

for greater variation of TiO

in the mantle source. The

concentration of Nb or Ta, relative to TiO

(and other

elements), therefore provides a constraint on the amount

of depletion necessary in the mantle source of each region.

This constraint is a minimum in the sense that Nb and Ta

could theoretically be added from the slab, causing the

mantle to appear less depleted than it actually is. These

constraints are then used to estimate the mantle source

composition and

for most back-arc spreading segments

(Table 1, Figure 7), and we apply a constant source

composition to each segment. We unfortunately cannot, in

many cases, perform this analysis with the exact samples

used to model

and

because most of these glasses do

not have the necessary trace element data. In such cases,

trace element data from whole rock samples in the same

local area were used to establish regional source character-

istics beneath each spreading segment [

Hochstaedter et al.

1990b;

Nohara et al.

, 1994;

Pearce et al.

, 1995;

Dril et al.

1997;

Fretzdorff et al.

, 2002;

Sinton et al.

, 2003].

[

] Figure 7 illustrates back-arc regions where the man-

tle sources were successfully modeled relative to DMM.

The conservative elements (CEs) Nb, Ta, Zr, Ti, and Y

reflect mantle source characteristics, whereas rare earth

elements and Th indicate the extent of geochemical enrich-

ment from the slab. As a general rule, lavas with lower

absolute concentrations of CEs (i.e., higher

) show greater

absolute abundances in slab-derived elements than low-

lavas from the same regions, suggesting a link between

and the extent of slab-derived input at back-arc basins (such

that larger extents of melting are associated with greater slab

input of the non-CEs). The mantle depletion model devel-

oped here makes a fair approximation of the CE patterns

and thus the mantle source characteristics of basins and

intrabasin segments tapping variably depleted mantle. In

fact, most regions require little to no prior melt removal (

0.2%) to explain the CE patterns (e.g., Mariana trough,

Sumisu rift, MTJ, ILSC, Manus ER, ESR E2–E6, Wood-

lark basin NE (Table 1)). The CE patterns are also generally

parallel within a given basin spreading segment (

varia-

tion) rather than of variable shape (source variation), which

supports the assertion that

is the dominant variable

controlling CE variation on local scales. A few regions

require more depleted mantle (

1–2.5%

; e.g., CLSC,

ELSC-VFR, Manus MSC-ETZ (Table 1)), which relates to

low Nb concentrations (<1 ppm).

[

] We acknowledge that the model curves are not

perfect fits to the CE patterns in Figure 7, likely due to

variable data quality (particularly for Nb and Ta) and

possible additions from the slab in some cases. Conserva-

tive trace element variations could, alternatively, arise

dominantly or exclusively from variations in mantle source

composition. We evaluated this possibility by holding

constant and attempting to fit the CE patterns of lavas only

through changing mantle depletion. This model falls short

in two ways. First, the extent of prior melt removal

necessary to explain variations in the less incompatible

elements Zr and Y removes too much Nb and Ta to match

the shape of the full CE pattern in multiple samples from a

given region (e.g., Figure 7l). Niobium and tantalum could,

however, be added from the slab, which would elevate their

concentrations above the ambient mantle and explain why

the full CE pattern is poorly modeled. Second, the extents of

prior melt removal (

) necessary to broadly reproduce the

Figure 8.

TiO

/Y versus Na

O, demonstrating the model

used to constrain mantle source characteristics for segments

with enriched mantle sources (more trace element enriched

than the DMM of

Salters and Stracke

[2004]). TiO

and Y

have similar mantle/melt

s for N-MORB, whereas

absolute concentrations of incompatible elements like

O, which are relatively invariant in the mantle source,

vary systematically as a function of

. (a) TiO

/Y versus

O in MORB, with a batch melting model curve (bold

line) approximating the MORB trend, showing the relative

invariance of the TiO

/Y ratio with extent of melting at mid-

ocean ridges. Regional MORB averages (samples with 7.5–

8.5 wt % MgO) are from the following regions: the

Kolbeinsey ridge [

Devey et al.

, 1994], the Australian-

Antarctic discordance [

Klein et al.

, 1991], the Indian Ocean

triple junction [

Price et al.

, 1986], the Tamayo region

[

Bender et al.

, 1984], the Pacific seamounts [

Niu and

Batiza

, 1997], the Cayman rise and the Reykjanes ridge

(www.petdb.org), and the Mid-Atlantic Ridge between the

Kane and Hayes fracture zones (www.petdb.org). Error

bars are one standard deviation of the regional average.

(b) TiO

/Y versus Na

O in ridge and back-arc regions with

enriched mantle (Table 1) showing high TiO

/Y, attributed

here to source enrichment. The points shown are

individual glass samples. The bold line is the MORB

batch melting model curve from Figure 8a.

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geochemical range recorded, for example, along the Lau

basin (Figure 7l) would correlate with variations in H

concentration along the length of the basin, and indeed in

global basins. The Lau basin mantle composition clearly

varies along strike regardless of how we model it, but there

is no strong argument for why large variations of H

concentrations in the source regions of arcs and back arcs

should correlate globally with the extent of prior mantle

depletion [

Eiler et al.

, 2000]. Water concentrations more

sensibly correlate with additions of slab-derived compo-

nents and with

. We therefore elect to constrain variations

in the water-poor, MORB-like component of the mantle

beneath back-arc basins using the approach described above

whereby this component is assumed to have been derived

from DMM by variable amounts of prior batch melt

extraction, and where the amount of this prior melt extrac-

tion is constrained using a fit to the HFSE that assumes they

are truly conservative (i.e., uninfluenced by the addition of

water-rich, slab-derived components). To the degree that

these conservative elements might have been influenced by

addition from the slab, the absolute magnitude of their

variations in the MORB-like component in the sources of

back-arc magmas may require modification, and the source

constraints we present (Table 1) would represent the min-

imum amount of depletion (and therefore the maximum

)

necessary to explain the geochemistry of these back-arc

basins.

2.5. Modeling Enriched Mantle Source Compositions

[

] The melt removal–based source model also only

succeeds in regions where the mantle is similar to, or more

depleted than, the initial DMM composition. In regions

where the mantle is more trace element–enriched than

DMM, the trace element patterns have steeper negative

slopes than unmodified DMM and cannot be explained by

prior melt removal from this MORB-like source. In such

cases we employed another approach to approximating the

O-poor mantle sources. In the case of the Gala

́pagos

spreading center, we adopted the source constraints of

Cushman et al.

[2004], but in other regions where enriched

mantle source characteristics have not been so rigorously

evaluated, we applied a simple model based on TiO

systematics. The ratio of TiO

to Y varies little during

mantle melting at mid-ocean ridges (TiO

/Y = 0.04–0.05

for regionally averaged MORB (Figure 8)) because these

elements have similar mantle/melt

s. On the other hand,

regions near hot spots or having previously recognized,

isotopically enriched mantle have high TiO

/Y ratios

(e.g., FAZAR, N. Fiji basin (Figure 8) [

Eissen et al.

, 1994;

Asimow et al.

, 2004]). Some of the high ratios could arise

from a higher

in these sources (which could contain

garnet), but we elect to treat TiO

/Y ratios in excess of

mean MORB entirely as TiO

enrichment of the H

O-poor

mantle source, in order to provide a maximum constraint

; that is,

TiO

ðÞ

sample

TiO

ðÞ

MORB

DMM

;

where (TiO

/Y)

sample

is the TiO

/Y ratio of the glass,

(TiO

/Y)

MORB

is 0.04, and

DMM

is 0.133 (Table 2). This

likely overestimates

and leads to maximum values for

and

. We thus present the results below using a

range of

values, but in all cases comparing results

using the constant source model (DMM [

Salters and

Stracke

, 2004]) to maximum

constraints from TiO

in enriched regions and CE constraints for depleted

regions (Table 1).

2.6. Uncertainties and Errors

[

] The effects of uncertainties in measurements and

model assumptions on the final calculations of

and

require careful consideration. We first addressed the

confidence level of each source of uncertainty. For analyti-

cal measurements (TiO

and H

O), we used the standard

deviation of replicate measurements on any given sample to

reflect the uncertainty in the data (±5% for TiO

, ±10% for

O). For

, both the correction for crystal fractionation

and the possibility of slab-derived TiO

in the melt contrib-

ute to errors in this value, and we used an uncertainty of

±20%. Minimum errors in the mantle source composition

(

) arise from analytical uncertainties in the measurement

of the CEs used to constrain the source characteristics.

Uncertainties on

were thus constrained by allowing

10% variation in all of the CEs in the melt removal model

for each region and by constraining the full range of

values

(as shown by pattern shapes in Figure 7) permissible by any

pair of CEs within this 10% concentration variation (see

Table 1). On average, this analysis results in

10% error in

. We explored the effect of a ±50% variation in

(0.02–0.06), which encompasses the range over which the

instantaneous value of

may vary along a polybaric path

(see section 2.3 [

Langmuir et al.

, 1992]). The

(0.012)

used here originates from S&N94 and is consistent with the

used here (Table 2), but recent experiments suggest

lower values for both

and

during batch melting of

spinel lherzolite (0.007–0.009 [

Aubaud et al.

, 2004;

Hauri

et al.

, 2006]. Studies of MORB and OIB data also suggest a

lower value for

, closer to

(0.01 [

Dixon et al.

2002]), and we thus also evaluated the effect of lowering

in our error analysis but use

= 0.012 for the final

calculations to remain consistent with S&N94. An addition-

al test of the modeling outcome, using Na

O instead of TiO

as a proxy for

, is provided in the auxiliary material

Using this alternate proxy for

yields results similar to

those for TiO

. Our results are thus not dependent on the use

of TiO

as a proxy for

, nor on factors specific to TiO

(e.g., the presence of rutile, ilmenite, and Ti-clinohumite in

the mantle).

[

] We used a Monte Carlo error analysis, which allows

each parameter to vary simultaneously within its assigned

uncertainty during the calculation of

and

,to

evaluate the effects of these uncertainties on the model

trends. This technique produces error ellipses around the

modeled points in

versus

, which represent the

outcome of 90% of the trial calculations (Figure 9a).

Elongation of the ellipses relative to the origin is largely a

product of the uncertainties in

and

, but also serves to

emphasize that errors on this diagram are highly correlated.

is used to calculate

, and any error contributing to

the determination of

therefore propagates into error in

Auxiliary materials are available in the HTML. doi:10.1029/

2005JB003732.

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. This analysis results in up to 30% uncertainty in the

-intercept (melt fraction at zero

) of a regressed line

but relatively little variation in the slope (

10%), which

indicates that the slopes of the model trends are more robust

than the intercepts.

[

] Both the S&N94 method and the procedure outlined

here result in similar trends despite employing different

geochemical constraints and data sets for determining

and

in the Mariana trough. Figure 9b compares the results

from S&N94 with the results from this study. For the two

best-fit lines shown in Figure 9b (one regressed through

the S&N94 points and the other through the points from

this work), the absolute difference in

-intercept is large

(3.4 versus 7.0%), owing in part to the extra steps taken here

to correct for crystal fractionation, which result in lower

TiO

in the modeled melt compositions. The slopes of the

two trends, however, differ by only 28% (1.63 versus 2.08).

This difference in slope translates into relatively small dif-

ferences in

at a given

(e.g., 0.07 versus 0.10 wt %

= 10%), and is probably within the analytical

uncertainty in the H

Omeasurement.Weregardthis

comparison as a successful reproduction of the original

S&N94 trend, using the TiO

proxy for

2.7. Mantle Temperature, Axial Depth, Crustal

Thickness, and Melt Production

[

] Mantle potential temperature (

) is a primary factor

in melt production at mid-ocean ridges, and it likely

strongly influences melt generation beneath back-arc basins

as well. At ridges, mantle

controls the depth/pressure at

which melting initiates (

) and thus the overall extent of

melting (

), which relates to the length of the melting

column [

Klein and Langmuir

, 1987;

McKenzie and Bickle

1988]. The FeO concentration of a melt is sensitive to

whereas the concentrations of incompatible elements such as

OorTiO

vary inversely with

[

Klein and Langmuir

1987;

Kinzler and Grove

, 1992]. In Figure 2, the correlation

of global MORBs in Na

(Fo90)

versus Fe

(Fo90)

(i.e., Na

O and

FeO concentrations corrected for crystal fractionation to

equilibrium with Fo

; see section 2.1) is consistent with

variations in

and

[

Langmuir et al.

, 1992;

Kinzler

1997;

Asimow et al.

, 2001]. We used the pooled, accumu-

lated fractional melting model of

Langmuir et al.

[1992] to

calculate

from dry, MORB-like back-arc basin melts

0.5 wt % (Figure 2, Tables 3 and 4)) using Na

(Fo90)

and Fe

(Fo90)

parameterized as follows:

ðÞ¼

4381

Fo90

ðÞ

154

Fo90

ðÞ

1088

ðÞ¼

164

Fo90

ðÞ

336

Fo90

ðÞ

1956

Values of

were calculated for each mid-ocean ridge and

back-arc basin by averaging

(Fe) and

(Na) for each

sample, then averaging

(sample) for all samples in each

basin (Table 4). In the few cases where the standard

deviation between the two

calculations from a single

glass composition was >50

C, then only

(Na) was used in

the regional average because the correction of Fe concen-

trations in high-Fe glasses to Fo

has greater error than the

Na correction.

[

] Axial depth and crustal thickness at mid-ocean ridges

are also linked to total melt production, reflecting the

integrated effects of mantle temperature, wet melting, and

melt removal. High mantle temperature and large extents of

melting combine to generate thick oceanic crust that, due to

isostasy, lies at shallower water depths (i.e., lower axial

depth) than regions with thinner crust. Axial depth and

crustal thickness relate quantitatively to the extent of

melting as reflected, for example, by the correlation of

depth with melt fraction proxies (e.g., Na

8.0

[

Klein and

Langmuir

, 1987]; see Figure 1). In order to explore the

extent to which the chemical and physical relationships

observed at mid-ocean ridges extend to back-arc basins, we

determined mean axial depths at back-arc basins either from

Figure 9.

O concentration of the mantle source)

versus

(mantle melt fraction) showing (a) error ellipses for

10 example points in the Mariana trough (MT). The bold

line is a linear regression through the full MT data set,

as shown in Figure 10a. The equation of the line is

2.082

– 0.142 (

= 0.798), errors on the slope are ±10%,

and errors on the intercept are ±30%. (b) Comparison

between results of S&N94 and this study. The black circles

and short-dashed line are the results and linear best fit from

S&N94 (

= 1.628

– 0.055;

= 0.840). The open

diamonds are the results from this study, utilizing a larger

initial glass data set than S&N94, and the solid line is the

best fit line to these points (

= 2.082

– 0.142;

= 0.798).

This study filtered the data differently than did S&N94,

which is why this study plots fewer points.

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the axial profiles of

Taylor and Martinez

[2003] for the four

basins they examined or from averaging the sample collec-

tion depths for the other basins we have examined in our

study (see Table 4). We also estimated crustal thickness (see

Table 4) from seismic profiles of the few basins where

detailed geophysical data exist [

Bibee et al.

, 1980;

LaTraille

and Hussong

, 1980;

Ambos and Hussong

, 1982;

Turner et

al.

, 1999;

Crawford et al.

, 2003;

Martinez and Taylor

2003].

2.8. Summary of Methods

[

] We have described in detail the several steps in our

treatment of glass compositions from back-arc basins, and

we summarize them here. The compiled basalt data were

first screened to exclude fractionated compositions (MgO <

7.0 wt %) and degassed samples (pure H

O saturation

pressure <30 bars from eruption pressure). All remaining

glasses were then corrected for the effects of crystal

fractionation, adjusting the melt compositions to olivine-

enriched compositions that would be in equilibrium with

. The extent of melting of a peridotitic mantle source

(

) required to produce each corrected back-arc basin glass

composition was calculated based on its TiO

content

relative to its mantle source using the batch melting equa-

tion and a constant

. The concentration of H

O in the

mantle source of each sample was then calculated using this

value of

and a constant

. Note that the calculations of

require knowledge of the TiO

content of the mantle

source (

) of each sample prior to melting. We have

shown that TiO

contents of most back-arc mantle sources

(prior to addition of slab-derived components) can be

modeled using the DMM composition of

Salters and

Stracke

[2004], but in some cases the deviation from this

end-member appears to be significant. For mantle lower in

TiO

than DMM, we adjusted

for each spreading

segment using conservative elements (Nb, Ta, Zr, TiO

Y), assuming that the concentrations of these elements

deviate from DMM due to a previous episode of melt

extraction (assumed to be batch melting). For sources

enriched in trace elements relative to DMM (again, prior

to addition of slab-derived components), we modeled

based on their TiO

/Y ratios. The total variation in

from region to region is a little more than a factor of 2.

A Monte Carlo error analysis reveals uncertainties on the

linear regression through the modeled Mariana trough data

30% on the

-intercept and

10% on the slope of the

line, and the trend of

and

determined using this

procedure is similar to that first shown in this region by

S&N94 (see Figure 9b).

3. Results

[

] Here we present a summary of the modeling outcome

for back-arc basins and mid-ocean ridges. Detailed discus-

sions of the results for each specific region are presented in

the auxiliary material. The correlation of TiO

2(Fo90)

and

(Fo90)

in the fractionation-corrected glass data illustrate

the first-order observations suggesting a relationship be-

tween H

O and mantle melting in back-arc basin settings.

Most of the back-arc basin data show dominant trends of

decreasing TiO

2(Fo90)

with increasing H

(Fo90)

(Figure 4).

Because TiO

is incompatible during mantle melting, and

we assume TiO

originates only from the mantle, we

expect that its concentration in the melt will be progres-

sively diluted as the melt fraction (

) increases. The

relationships shown in Figures 4a, 4c, and 4d thus suggest

Table 3.

Geochemical Variables at Back-Arc Basins

Basin

Segment

Dry Samples Only (H

O < 0.5 wt %)

All Samples

CaO/Al

(Fo90)

CaO/Al

(Fo90)

Small-Scale Averages

East Scotia ridge

E2–E4

0.69

0.02 7.48 0.46 2.66 0.13

0.68

0.01 6.62 0.25 2.62 0.07

E5–E8

0.73

0.01 8.18 0.11 2.69 0.07

0.73

0.01 8.07 0.15 2.70 0.07

0.71

0.02 7.03 0.08 3.06 0.04

0.71

0.02 6.49 0.41 2.85 0.20

Lau basin

MTJ

0.76

0.02 9.08 0.18 2.20 0.04

0.79

0.02 8.24 0.27 2.17 0.07

CLSC

0.82

0.02 9.51 0.25 1.92 0.03

0.82

0.02 9.51 0.25 1.92 0.03

ILSC

0.76

0.03 8.22 0.47 1.84 0.18

0.76

0.03 8.22 0.47 1.84 0.18

ELSC

0.79

0.01 8.76 0.40 1.55 0.04

0.80

0.01 8.73 0.23 1.57 0.07

VFR

0.86

0.01 10.34 0.41 1.12 0.06

Manus basin

0.76

0.09 8.35 0.00 1.28 0.00

MSC-ETZ

0.85

0.00 10.46 0.08 1.68 0.04

0.83

0.02 9.54 0.41 1.63 0.04

Mariana trough

–17

0.69

0.07 8.04 0.14 2.68 0.12

0.68

0.01 7.01 0.30 2.52 0.08

–19

0.69

0.05 7.22 1.08 2.79 0.07

0.66

0.01 6.45 0.23 2.54 0.06

–21

0.67

0.01 6.70 0.49 2.39 0.15

North Fiji basin

N160

0.73

0.00 8.60 0.00 2.30 0.00

0.67

0.03 6.11 0.57 2.53 0.14

0.73

0.04 8.59 0.37 2.17 0.02

0.73

0.04 8.59 0.37 2.17 0.02

Woodlark basin D’Entrecasteaux

0.66

0.00 6.24 0.06 2.73 0.02

center

0.76

0.00 8.71 0.06 2.32 0.03

0.76

0.00 8.71 0.06 2.32 0.03

east

0.71

0.02 8.46 0.14 2.77 0.04

0.67

0.03 7.74 0.73 2.58 0.18

Basin-Scale Averages

East Scotia ridge

whole

0.72

0.01

0.70

0.01

Lau basin

north

0.79

0.01 8.98 0.17 2.04 0.04

0.80

0.01 8.73 0.21 2.04 0.05

south

0.79

0.01 8.76 0.40 1.55 0.04

0.85

0.01 9.91 0.34 1.24 0.06

Manus basin

whole

0.85

0.00 10.46 0.08 1.68 0.04

0.81

0.03 9.32 0.38 1.60 0.04

Mariana trough

whole

0.69

0.04 7.66 0.36 2.72 0.09

0.67

0.01 6.69 0.18 2.50 0.05

Sumisu rift

whole

0.70

0.03 9.27 0.59 2.04 0.02

North Fiji basin

whole

0.74

0.01 8.59 0.33 2.19 0.03

0.70

0.01 7.97 0.49 2.28 0.07

Woodlark basin

whole

0.74

0.01 8.61 0.07 2.49 0.07

0.74

0.03 7.93 0.33 2.49 0.07

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