Text S1: Ti-in-quartz methods
S1. Methods
Samples were chosen to ensure a complete spread across both the carapace and core
structural zones of Goodenough, Mailolo, Morima, and northwest Normanby dome.
The quartz grains analyzed by this study were >75 μm in diameter, which is the
resolution of the LA-ICP-MS. Analytical spots were scattered as far apart as possible
in the mount, in an attempt to obtain a spatially-averaged mean Ti concentration for
the sample as a whole.
In 54% of the samples, less than the full suite of eight spot analyses was included in
the mean Ti concentrations. On average, seven spots were analyzed per sample.
Wherever possible, spot analyses were taken from both the rim and core of up to four
different quartz grains to yield eight spot analyses. This was successfully undertaken
on 22% of the samples analyzed here. On average six quartz grains were analyzed per
sample (Table 1). The high number of quartz grains that do not include separate core
and rim spot analyses resulted from several analytical limitations: (1) rejection of
contaminated signal (~42%), (2) fracturing during ablation destroying the rim or core
of the grain analyzed (~32%), and (3) small grain size (<125 μm) allowing only one
ablation pit per grain (~26%).
The LA-ICP-MS was tuned before every analytical run to ensure a high stability and
sensitivity of the NIST 612 standard. Each analytical run was arranged using
standard-sample bracketing; four unknown analyses were bracketed by two NIST 612
standard analyses. Consistency of 47Ti/29Si and 43Ca/29Si were monitored during data
processing as variations in these ratios suggest ablation of an undesirable mineral
phase.
The New Wave 193 μm solid-state Nd-YAG laser at VUW causes trace element-poor
and Si-rich material to fracture during interaction of the laser with the target. Ideally,
this interaction should create a round crater. This fracturing results in the creation of
mineral shards in the first few seconds of laser ablation that are subsequently blown
away by the gas flow, and may result in unwanted mineral phases being incorporated
into the signal and the destruction of the area immediate to the shot. Laser settings
(such as optional gas flow, extract voltage, and torch position) were tuned during
ablation of the NIST 612 standard to ensure that: (1) the quartz ablated as well as
possible, and (2) the ICP-MS was at optimum sensitivity and low internal errors
(Table S1). The switch between pulse (P; <1 x 106 counts per second; 43Ca, 47Ti, 49Ti,
27
Al) and analog (A; >1 x 106 counts per second;
29
Si) counting modes was carried
out by the ICP-MS. The P/A factor was measured on all analyzed elements during
tuning to ensure the switch between high and low signal was performed correctly.
Elemental oxide production was maintained below 1.5% by tuning the conditions of
the plasma torch, and was monitored by ThO+/Th+.
Table S1. Analytical conditions of the LA-ICP-MS
ICP-MS
System
Agilent 7500CS
Acquisition mode
Peak-hopping
pulse (43Ca, 47Ti, 48Ti, 27Al) and analogue
Detection mode
(29Si)
Laser ablation
New Wave 193 nm (deep UV) solid state
System
laser
Laser power
65% for NIST 612, ~85% for quartz grains
Ablation mode
Static spot analysis
Repetition rate
10 Hz
Standards
Bracketing/Calibration standards
NIST 612
Analysis method
Standard/sample acquisition
60 seconds
Wash out/background acquisition
90 seconds
Measured isotopes and integrations
29
times
Si, 43Ca, 47Ti, 49Ti, 27Al; all 0.01 seconds
Tuning
Tuning standards
NIST 612
29
Monitored isotopes during tuning
Si, 43Ca, 47Ti, 49Ti, 27Al
Ablation mode
50 μm diameter spots
Monitored isotopes during ablation 29Si, 43Ca, 47Ti, 49Ti, 27Al
47
Background
Ti <400 counts per second*
Oxides
<1.5% (checked during tuning)
Carrier gas (Ni)
0.75 -0.85 L min-1
Optional gas (He)
75 - 85%
RF Power
1500 W
RF matching
1.96 V
Sample depth
3 – 4 mm
*Counts per second or signal measure by the LA-ICP-MS
Ti concentration was internally corrected during data reduction with respect to Si. The
equations used for this correction can be written as:
[ Si] Smpl = [ Si] Std ´
and
CPSSmpl
CPSStd
[Ti] Smpl = [Ti] Std ´
CPSSmpl
CPSStd
where [i]Smpl is the concentration of the element of interest in the sample or unknown,
[i]Std is the concentration of the element of interest in the standard, and CPSi is the
counts per second or signal of the sample or standard. SiO2 is by far the major oxide
in quartz and therefore has an assumed value of 100% for a pure quartz grain. If the
measured Si concentration is less than 100% during analysis, this secondary internal
correction for Si increases the Ti concentration of the unknown by a proportional
amount.
The background-corrected signal for each spot analysis was corrected to the
bracketing NIST 612 using GeoReM preferred values. The background for all beams
was measured and subtracted from the signal of each spot analysis prior to calculation
of the Ti concentration. The mean Ti concentration in quartz for each sample quoted
in Table 1 was calculated as the weighted mean of all analyses (up to eight) of the
sample (weight equal to std dev-2). The uncertainty of the mean Ti concentration
(standard error) was calculated by pooling the weighted residuals. The 95%
confidence interval of the mean Ti concentration (quoted as 2σ in Table 1) is given
by: ±t × (weighted standard error), where t is the Student’s t statistic for 95% with (n1) degrees of freedom (n is the number of data).
S2. Errors and uncertainties calculations
The total uncertainty related to the Ti-in-quartz apparent temperature (Table 1) is
derived from three sources. First, there is an uncertainty in the slope and intercept of
the least-squares regression-analysis carried out during calibration of the thermometer
(~5 °C of uncertainty; Thomas et al., 2010).
Secondly, there is the analytical
uncertainty, which is a 95% confidence interval of the average Ti concentration.
Thirdly, there is an assigned uncertainty of ±0.2 in the Ti activity ( aTiO2 ). We suggest
that the three sources of uncertainty are independent of each other as they arise from
different contributions. Thomas et al., (2010) determined the calibration uncertainty.
The analytical uncertainty is calculated from the ICP-MS measurement statistics. The
aTiO uncertainty is an assigned value.
2
The combination of the three sources of uncertainties into the single value was
determined as a 95% confidence interval of the quotient. The calibration uncertainty
(c1 = ±3122, c2 = ±0.04, c3 = ±63), the analytical uncertainty (εj), and the Ti activity
uncertainty (α) were all incorporated into the original Thomas et al. (2010) equation:
T (°C) =
(60952 ± c1 ) + (1741± c3 )P
- 273.15
Qtz
(1.520 ± c 2 ) - R(ln XTiO
±
e
)
+
R(ln
a
±
a
)
j
TiO
2
2
.
Expanding the denominator gives
ìï æ X Qtz ö
æ
æ
ej ö
a öüï
TiO2
2
ç
÷
ç
÷
ç
1.520
±
c
R
ln
+
ln
1+
ln
1+
í
(
) ï ç a ÷ ç X Qtz ÷ ç a ÷÷ýï .
TiO2 ø
TiO2 øþ
è
è
î è TiO2 ø
Approximating Ln(1+x) by the first term of its power series is valid if x2<<x. If
and
a
<<1, the denominator is approximately
aTiO
2
ìï æ X Qtz ö e
a üï
TiO2
j
ç
÷
1.520
±
c
R
ln
+
í
(
) ï ç a ÷ X Qtz a ýï .
TiO2
TiO2 þ
î è TiO2 ø
2
So the variance of the denominator is
se
Qtz
XTiO
2
ìï æ e ö
æ a öüï æ c 2 ö2
j
÷÷ý + ç ÷
= -R ívar çç Qtz ÷÷ + var çç
a
ïî è XTiO2 ø
è TiO2 øïþ è 2 ø ,
2
which expands to
2 ü
ì
2
a
ï æ c2 ö
1
2ï
2
2
=R í
se +
+
÷ .
2ý ç
Qtz 2
2
è
ø
a
ï ( XTiO
ï
(
)
TiO2
2)
î
þ
( )
The variance of the numerator is
æ c1 ö æ c 3 ö
= ç ÷ +ç ÷
è2ø è2ø ,
2
2
where we have taken the ranges c1, c2, and α to be 2σ, and c3 to be <<c1. The two
variances were then input in the equation for the 95% confidence interval of a
quotient:
æ Aö 1
A2
varç ÷ = 2 var A + 4 var B,
è Bø B
B
in order to determine the combined uncertainty, with the same requirements as before.
S3. One-sided t distribution
A one-sided t distribution was used to determine the probability that the slopes for the
linear regressions in Figure 11 were negative or zero (Table S2). We assume that the
uncertainties or scatter in the data, and hence the slope estimates, are
Normal/Gaussian random variables.
Table S2. Results of one-sided t distribution
Standard
No.
Slope
Deviation
of
Fault
(m)
m (sd)
dataa
Wakonai 0.01157
0.00383
21
Mwadeia 0.00301
0.00213
14
Morima 0.00166
0.00042
5
NW Norm. 0.00071
0.00165
5
SE Norm. 0.00370
0.00126
5
a
df = no. of data -2
b
Probability slope is negative or zero
m/sd
3.01810
1.41544
3.94945
0.42839
2.92843
p0b
0.00353
0.09118
0.01448
0.34863
0.03054
p0
< 1%
< 10%
< 2%
< 35%
< 4%