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Supplemental Material -- Petrogenesis and structure of oceanic crust in the Lau back-arc basin
1. Methods
1.1 Model Starting Compositions
Because the primary magma composition cannot be known precisely, we tested
multiple starting compositions (C0) shown below in Table S1. Starting compositions
include: a representative high MgO sample (RC028), a modified version of this
composition adjusted by hand to yield improved fits for total oxide suite (MOD3), and
the starting composition chosen by the alphaMELTS amoeba minimization routine, which
varies the parental melt composition from an initial estimate to best fit the suite of data by
isobaric forward fractionation (Antoshechkina et al., 2010). We also note that the trends
in lava composition also indicate small differences in starting composition for the
different domains in certain major element oxides (e.g., FeO*, TiO2, Na2O). In order to
assess the effects of this, we also tested a fourth C0 (MOD4wet) estimated from the
highest MgO sample compositions available for the Domain II and transitional crust. For
all starting compositions, we fix relative abundances of all oxides except initial water
composition (H2Oi), which is allowed to vary (0.0 to 3.0 wt. % H2Oi).
Example model runs are shown in Figs. S1-3 on the following pages. Model results
are relatively insensitive to these minor variations in starting composition, all of which
constitute reasonable choices for a primitive magma of this dataset. Because the general
results show little dependence on starting composition, we present results for a single
starting composition throughout the manuscript. We have selected starting composition
MOD3 since these runs show slightly lower misfits overall.
Table S1: Starting compositions for MELTS fractionation runs.
C0 RC028 MOD3 amoeba MOD4wet
SiO2 49.87 50.9 50.74 51.8
TiO2 0.88 0.88 0.88 0.80
Al2O3 15.3 14.6 14.7 15.98
FeO* 9.31 9.10 8.65 9.20
MgO 9.03 9.10 9.51 7.25
CaO 13.08 12.4 12.6 12.09
Na2O 2.10 1.80 1.82 2.0
K2O 0.019 0.08 0.08 0.12
P2O5 0.05 0.08 0.08 0.10
1.2 Methods – Model Misft Calculations
In order to compare model results across these multiple components, we calculate an
overall misfit for each model run and each oxide-MgO pairing, and then combine these
misfits into a total misfit for all oxides of interest. We first calculate a mean absolute
deviation for each oxide-MgO pairing by calculating the minimum distance (Euclidean
distance in MgO-oxide space) from each sample data point to the model run trend line
and taking the average for all samples. Because some oxide-MgO trends show
significant scatter (e.g., FeO*, P2O5) while others exhibit very tight trends (e.g., CaO), we
then scale them by a parameterization of spread. To calculate this scaling parameter, we
construct an ‘ideal’ fractionation trend for each oxide-MgO pair by calculating regression
lines through every sample subset of interest while taking into account inflections in
oxide trends due to phase appearances when necessary. We then calculate the standard
deviation of each sample subset from this idealized fractionation trend divided by the
square root of the number of samples in that dataset (equivalent to a standard error, but of
the fractionation trend rather than of the mean, which is a better accounting of “spread” in
this case). We normalize the mean absolute deviation for each oxide-MgO pairing by this
standard error. The resulting mean scaled absolute deviation (MSAD) for a given model
run can be thought of as the number of standard errors from the sample trend for any
given oxide. This allows us to directly compare model fits across different oxides with
different average concentrations and different amounts of scatter, and combine them into
a total average MSAD for all oxides for a given set of model conditions. Independent of
the starting composition, SiO2 and K2O consistently show poor model fits for all
conditions and contribute little to the understanding of this system. We omit them from
the total average MSAD.
Table S2. Calculated spread parameters for each MgO-oxide pairing.
(MgO-) ELSC1 ELSC2 ELSC3-4 VFR Al2O3 0.119 0.142 0.496 0.365 TiO2 0.031 0.058 0.258 0.336 FeO* 0.119 0.234 0.348 0.484 CaO 0.083 0.070 0.410 0.357 Na2O 0.129 0.084 0.267 0.392 P2O5 0.011 0.010 0.254 0.294
Supplemental Figures:
Figure S1. Major element variation diagrams showing MELTS model runs with MOD3
starting composition (0.01 GPa, FMQ-2).
Figure S2. Major element variation diagrams showing MELTS model runs with amoeba
starting composition for comparison (0.01 GPa, FMQ-2).
Figure S3. Major element variation diagrams showing MELTS model runs with
MOD4wet starting composition (0.01 GPa, FMQ-2). Runs with H2Oi < 0.7 wt. % have
plagioclase on the liquidus (and therefore not in equilibrium with a peridotite mantle),
leading to initial increases in MgO.
Figure S4. MELTS model misfits as a function of pressure and H2Oi content for Domain
III OSC samples (calculation as in Fig. 6 of text). On average, Domain III OSC samples
are best matched by model runs with slightly higher initial water contents (~0.4 wt. %)
and higher pressures than samples from segment centers.
5052
5456
58S
iO2
ELSC1ELSC2ELSC3ELSC4VFR
0.8
1.2
1.6
TiO
2
1415
16A
l2O
3
911
13Fe
O*
79
1113
CaO H2O (wt. %)
0.00.20.40.60.81.0
2.0
2.5
3.0
3.5
Na2
O
3 4 5 6 7 8 9
0.2
0.4
MgO
K2O
3 4 5 6 7 8 9
0.05
0.15
0.25
MgO
P2O
5
Fig. S1
5052
5456
58S
iO2
ELSC1ELSC2ELSC3ELSC4VFR
0.8
1.2
1.6
TiO
2
13.5
14.5
15.5
Al2
O3
911
13Fe
O*
810
12C
aO 0.00.20.40.60.81.0
H2Oi (wt. %)
2.0
2.5
3.0
3.5
Na2
O
3 4 5 6 7 8 9
0.1
0.3
0.5
MgO
K2O
3 4 5 6 7 8 9
0.1
0.2
0.3
MgO
P2O
5
Fig. S2
5052
5456
58S
iO2
ELSC1ELSC2ELSC3ELSC4VFR
0.8
1.2
1.6
TiO
2
1415
16A
l2O
3
911
13Fe
O*
79
1113
CaO H2O (wt. %)
0.00.20.40.60.81.0
2.0
2.5
3.0
3.5
Na2
O
3 4 5 6 7 8 9
0.2
0.4
MgO
K2O
3 4 5 6 7 8 9
0.05
0.15
0.25
MgO
P2O
5
Fig. S3
3.0
3.5
4.0
4.5
5.0
0.0 0.2 0.4 0.6 0.8 1.0 1.20.05
0.10
0.15
0.20Domain III - OSC samples
H2O (wt. %)
P (G
Pa)
Fig. S4
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