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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