Electronic Appendix 1: Supplementary text to accompany the manuscript, “
Mantle
melting as a function of water content beneath the Mariana arc
.”
Mariana Arc Whole Rock Data, Melt Inclusion Data and Primary Melt Compositions
Whole
-
rock major and trace eleme
nt data for the host scoria samples used for
melt inclusion work in this study are presented in Electronic Appendix 2. Major and trace
elements for samples AGR19 and GUG
-
79
-
1 were analyzed by using the JY Ultima C
ICP
-
AES and VG PQ ExCell ICP
-
MS at Boston
University, following methods outlined
by
Kelley
et al.
(2003)
. Select major elements for samples AGR
-
Kimi, PB14, PB62 and
PB64, in addition to trace elements, we analyzed using the The
rmo X
-
Series II ICP
-
MS
at the Graduate School of Oceanography, University of Rhode Island, also following
techniques outlined by
Kelley
et al.
(2003)
. Major and trace elements for sampl
e SA93
are from the study of
Meijer & Reagan (1981)
.
The
complete data set for olivine
-
hosted melt inclusions from the Mariana arc is
presented in Electronic Appendix 3. See the main text for analytical details.
Electronic Appendix 4 presents the modeled primary melt compositions for the
least
-
fractionated, und
egassed melt inclusions (see main text for screening criteria and
reconstruction method), in addition to modeled pressures and temperatures of
equilibration calculated using the thermobarometer of
Lee
et al.
(2009)
. Averages for
each island are given, and are also reported in the main text in Table 2.
Mariana Trough Data an
d Correction Scheme to Reconstruct Primary Melts
Figure A1 shows examples of liquid lines of descent preserved in glasses from the
Mariana trough back
-
arc basin (see main text for data references). In order to accurately
capture and correct for variations
in LLD’s due to variations in H
2
O, the data have been
split into three groups by H
2
O content: <1 wt.%, 1.0
-
1.5 wt.%, and >1.5 wt.% H
2
O. The
point of plagioclase
-
in was chosen either by visible kink in the LLD (>1.5 wt.% group;
7.1 wt.% MgO), the most MgO
-
rich sample in the group (1.0
-
1.5 wt.% group; 7.4 wt.%
MgO), or by analogy with MORB (<1 wt.% group; 8.5 wt.% MgO). Ol+plag±cpx
crystallization trends were determined empirically using linear regression of data in each
group with MgO<MgO @ plag
-
in. Electro
nic Appendix 5 presents the average slopes
used to correct each data point back to the composition at plag
-
in.
Sensitivity Test of Batch Model Results to Uncertainties in Individual Variables
The method used to invert melt composition for melt fraction (
F
) and
concentration of H
2
O in the mantle source (
!
C
H
2
O
o
) is sensitive to errors and uncertainties
in model inputs. Here we present a sensitivity test of model results for a subset of data to
isolated variables in the inversion model.
• F
orsterite content of mantle olivine
The method presented in the main text references all reconstructed primary melt
compositions to equilibrium with mantle olivine at Fo
90
. If the residual mantle is more
fertile, the Fo content of residual olivine could b
e lower (e.g., Fo
89
), or if it is left
significantly depleted by high extents of melting, the Fo content of the residual olivine
may be higher (e.g., Fo
91
). Figure A2 shows the sensitivity of model results to different
reference Fo contents, ranging from F
o
89
to Fo
91
. Differences in model results between
Fo
89
and Fo
90
are small, yielding differences of 0 to 1% (absolute) in calculated F, and 0
-
0.01 wt.% (absolute) in
!
C
H
2
O
o
.
Differences in model results between Fo
90
and Fo
91
are
slightly gr
eater, yielding differences of 0 to 2% (absolute) in calculated F, and 0
-
0.01
wt.% (absolute) in
!
C
H
2
O
o
. The net effect of this variable on data arrays is a slight
horizontal translation of 0
-
2% F (absolute).
• Concentration of TiO
2
in th
e Mariana Arc Mantle Source
Uncertainties in the absolute value of
!
C
TiO
2
o
applied for the Mariana arc (0.123
wt.% TiO
2
; see main text) and in the assumption of constant
!
C
TiO
2
o
among the four arc
volcanoes may have signifi
cant impact on the modeling results. Figure A3a shows the
sensitivity of model results to ±10% variations in
!
C
TiO
2
o
(from 0.111 to 0.135 wt.% TiO
2
),
assuming a constant source beneath all volcanoes. Errors in
F
and
!
C
H
2
O
o
due to
uncertainties in
!
C
TiO
2
o
are highly correlated on Figure A3a, showing differences of ±1
-
3%
F (absolute) and ±0.03
-
0.10 wt.%
!
C
H
2
O
o
(absolute). Figure A3b shows the sensitivity of
model results to volcano
-
specific var
iations in
!
C
TiO
2
o
, which are constrained here using the
TiO
2
/Y model outlined in the main text. The four islands are within ±10% of each other
in
!
C
TiO
2
o
calculated using this model, with Guguan and Agrigan nearly identical
to the
average used for the whole arc (0.125 wt.%
!
C
TiO
2
o
), Sarigan more depleted (0.110 wt.%
!
C
TiO
2
o
), and Pagan more enriched (0.135 wt.%
!
C
TiO
2
o
). The net effect of this variable is
movement of model poin
ts in or out of the origin on Figure A3, yielding a small
influence on the slopes/shapes of data trends, but significant differences in the absolute
values of
F
or
!
C
H
2
O
o
.
Allowing the mantle source to vary with each volcano would create
s
lightly more spread among the data arrays for each island, distinguishing Pagan and
Sarigan more clearly from Agrigan and Guguan.
• Mantle
-
Melt Partition Coefficients for H
2
O and TiO
2
Uncertainties in the absolute values of mantle/melt partition coeffici
ents
D
H2O
and
D
TiO2
and in the assumption of constant
D
H2O
and
D
TiO2
over a large range of residual
peridotite compositions may also have significant impact on the modeling results.
Partition coefficients have been shown to decrease by ~50% from relatively
fertile to
depleted perido
tite
(McDade
et al.
, 2003)
, a
nd sensitivity of the model results to such
variations is thus important to constrain. Recent determinations of
D
H2O
have yielded
smaller values than the
D
H2O
used by this study (0.012, this s
tudy; 0.009,
Aubaud
et al.
,
2004
; 0.007,
Hauri
et al.
, 2006
). Figure A4 shows the sensitivity of model results to
variations in
D
H2
O
at the lowest determined value of 0.007. Differences in model results
even over this large variation in
D
H2O
are practically indistinguishable (0.01
-
0.02 wt.%
!
C
H
2
O
o
, absolute). This outcome shows that the model results are essentially i
nsensitive to
the value used for
D
H2O
, within ±50%, justifying both the value of
D
H2O
used and the
assumption of constant
D
H2O
. The model results are more sensitive to the value of
D
TiO2
used. Figure A5a shows the impact of ±25% variation in
D
TiO2
(0.03 to
0.05), assumed
constant among all samples. As with
!
C
TiO
2
o
, errors resulting from uncertainty in
D
TiO2
are
correlated, causing model points to move in or out of the origin, and giving differences of
±1% F (absolute) and ±0.02
-
0.05 wt.%
!
C
H
2
O
o
(absolute). Figure A5b shows the result of a
simple model allowing
D
TiO2
to decrease by 50% as F increases from 10% to 22%. The
values applied for
D
TiO2
were 0.04 for F
≤
10%, 0.03 for 10%<F<15%, and 0.02 for
F
≥
15%. In all cases, the net
effect of allowing
D
TiO2
to vary with
F
on data trends from
each island would be a slight shallowing of the slopes on Figure A5.
Monte Carlo Error Analysis of Batch Melting Model
Here we present a comprehensive Monte Carlo random error analysis on the
va
riables input to the batch melting inversion, to show the combined effects of
uncertainties and errors on the model output. The error analysis incorporates uncertainties
of ±5% in the raw concentrations of TiO
2
and H
2
O in the melt inclusions (assumed to be
analytical error), ±25% in the amount of olivine added back to reach Fo
90
(equivalent to
the difference between Fo
89
and Fo
91
, as explored above
), ±10% in
!
C
TiO
2
o
as explored
above, and ±25% in
D
TiO2
and
D
H2O
as explored above. A Monte Car
lo simulation of the
batch model was run through 1000 iterations, allowing for random variation of each
variable within the set boundaries of uncertainty. The 900 intermediate solutions were
used to generate error ellipses (90% confidence) around the model
ed data points
presented in the main text of this work, which are shown on Figure A6. Within each
island, the error ellipses for the selected points do not overlap within error, indicating that
the model points within the data arrays from each island are s
tatistically distinguishable.
Figure Captions
Figure A1. Liquid lines of descent for Mariana trough basalts. Symbols are colored to
indicate water content groups 0
-
1.0 wt.% H
2
O (red), 1.0
-
1.5 wt.% H
2
O (brown), and >1.5
wt.% H
2
O (blue). Darker blue symbols
within this group have MgO greater than MgO at
plagioclase
-
in. (a) Al
2
O
3
vs. MgO, with least
-
squares linear regressions through data
points withn each group with MgO<MgO at plag
-
in. (b) FeO* vs. MgO, where FeO* is
total Fe reported as FeO, with least
-
squa
res linear regressions through data points within
each group with MgO<MgO at plag
-
in. See Electronic Appendix 5 for average slopes for
all the major elements, used to correct fractionated Mariana trough basalts back to MgO
at plag
-
in.
Figure A2. Plot of
!
C
H
2
O
o
vs. melt fraction (
F
), showing the effect on select model points
of referencing reconstructed primary melts to different values of the forsterite content of
mantle olivine. Each point is labeled with the Fo content of the reference
olivine used,
larger symbols are the model points presented in the main text of the paper, referenced to
Fo
90
.
Figure A3. Plots of
!
C
H
2
O
o
vs. melt fraction (
F
), showing
(a)
the effect on select model
points of ±10% variations in
!
C
TiO
2
o
and (b) the effect of volcano
-
specific variations in
!
C
TiO
2
o
. Each point is labeled with the value of
!
C
TiO
2
o
used. Larger symbols between labeled
points are the model points presented in the main text of the
paper, using
!
C
TiO
2
o
=0.123.
Figure A4. Plot of
!
C
H
2
O
o
vs. melt fraction (
F
), showing the effect on select model points
of varying
D
H2O
. Each point is labeled with the
D
H2O
used, larger symbols are the model
points presente
d in the main text of the paper, using
D
H2O
=0.012
.
Figure A5. Plots of
!
C
H
2
O
o
vs. melt fraction (
F
), showing
(a)
the effect on select model
points of ±25% variations in
D
TiO2
and (b) the effect of a simple model allowing
D
TiO2
to
decrease
with increasing
F
. Each point is labeled with the value of
D
TiO2
used. Larger
symbols are the model points presented in the main text of the paper, using
D
TiO2
=0.04.
Figure A6. Plot of
!
C
H
2
O
o
vs. melt fraction (
F
), showing the effect on
select model points
of combined random uncertainties in model input variables, using a Monte Carlo
simulation. Solid filled symbols are the model points presented in the main text of the
paper. Shaded ellipses surrounding each model point show the errors a
ssociated with
each model point (90% confidence).
References
Aubaud, C., Hauri, E. H. & Hirschmann, M. M. (2004). Hydrogen partition coefficients
between nominally anhydrous minerals and basaltic melts.
Geophysical Research Letters
31
.
Hauri, E. H., Gaetani, G. A. & Green, T. H. (2006). Partitioning of water during melting
of the Earth's upper mantle at H2O
-
undersaturated conditions.
Earth and Planetary
Science Letters
248, 715
-
734.
Kelley, K. A., Plank, T., Ludden, J. N. & Staudigel,
H. (2003). Composition of altered
oceanic crust at ODP Sites 801 and 1149.
Geochemistry Geophysics Geosystems
4,
doi:10.1029/2002GC000435.
Lee, C.
-
T. A., Luffi, P., Plank, T., Dalton, H. & Leeman, W. P. (2009). Constraints on the
depths and temperatures of
basaltic magma generation on Earth and other terrestrial
planets using new thermobarometers for ma.
Earth and Planetary Science Letters
279,
20
-
33.
McDade, P., Blundy, J. D. & Wood, B. J. (2003). Trace element partitioning between
mantle wedge peridotite
and hydrous MgO
-
rich melt.
American Mineralogist
88, 1825
-
1831.
Meijer, A. & Reagan, M. K. (1981). Petrology and geocehmistry of the island of Sarigan
in the Mariana arc: Calc
-
alkaline volcanism in an oceanic setting
Contributions to
Mineralogy and Petrolo
gy
77, 337
-
354.
y = 0.6752x + 12.499
R
2
= 0.5711
y = -0.7859x + 12.773
R
2
= 0.4745
y = 0.6403x + 12.358
R
2
= 0.6099
y = 0.8453x + 10.131
R
2
= 0.3992
y = -0.5x + 12.715
R
2
= 0.2875
14.00
15.00
16.00
17.00
18.00
Al
2
O
3
(wt. %)
y = -0.7061x + 13.003
R
2
= 0.6436
6.00
7.00
8.00
9.00
10.00
5.00
6.00
7.00
8.00
9.00
FeO* (wt. %)
MgO (wt. %)
a
b
Figure A1
MgO @ plag-in
<1 wt.% H2O
MgO @ plag-in
1-1.5 wt.% H2O
MgO @ plag-in
>1.5 wt.% H2O
Melt Fraction (
F
), %
, wt.%
C
H
2
O
o
89
90
91
89
90
91
89
90
91
89
90
91
89
90
91
89
89
89
90
90
90
91
91
91
0.0
0.2
15
20
25
30
10
5
0
0.4
0.6
0.8
1.0
Figure A2
, wt.%
C
H
2
O
o
0.111
0.111
0.111
0.111
0.111
0.111
0.111
0.111
0.135
0.135
0.135
0.135
0.135
0.135
0.135
0.135
0.0
0.2
0.4
0.6
0.8
1.0
Melt Fraction (
F
), %
, wt.%
C
H
2
O
o
0.110
0.110
0.125
0.135
0.125
0.125
0.125
0.135
0.0
0.2
15
20
25
30
10
5
0
0.4
0.6
0.8
1.0
Figure A3
a
b
Melt Fraction (
F
), %
, wt.%
C
H
2
O
o
0.012
0.007
0.0
0.2
15
20
25
30
10
5
0
0.4
0.6
0.8
1.0
Figure A4
0.012
0.007
0.012
0.007
0.012
0.007
0.012
0.007
0.012
0.007
0.012
0.007
0.012
0.007
, wt.%
C
H
2
O
o
0.05
0.04
0.03
0.0
0.2
0.4
0.6
0.8
1.0
Figure A5
0.05
0.04
0.03
0.05
0.04
0.03
0.05
0.04
0.03
0.05
0.04
0.03
0.05
0.04
0.03
0.05
0.04
0.03
0.05
0.04
0.03
Melt Fraction (
F
), %
, wt.%
C
H
2
O
o
0.04
0.02
0.0
0.2
15
20
25
30
10
5
0
0.4
0.6
0.8
1.0
0.04
0.02
0.04
0.02
0.04
0.03
0.04
0.03
0.04
0.03
0.04
0.03
0.04
a
b
Melt Fraction (
F
), %
, wt.%
C
H
2
O
o
SA93D
SA93B
PB64G
AGRI2-54
GUG C
AGRI2-31
GUGXa
PB14Ka
0.0
0.2
15
20
25
30
10
5
0
0.4
0.6
0.8
1.0
Figure A6