data repository · 22 on sequential steps containing at least three steps and 60% of 39ar release...

12
Folco, 1 DATA REPOSITORY 1 Bulk chemistry 2 The major element composition of 39 sectioned spherules (Table DR1) from Victoria Land 3 Transantarctic Mountains (TAM) was obtained by averaging multiple electron microprobe 4 analyses (EMPA). EMPA were carried out using a CAMECA SX50 electron microprobe at the 5 IGG CNR in Padova. Running conditions were 15 kV accelerating voltage, 10 nA beam current. 6 Counting time was 7 s for Na, K and Si, and 10 s for the other analyzed elements. A 15 μm- 7 diameter defocused beam was employed to reduce migration of volatile elements. The 8 manifacturer-supplied PAP procedure was employed for raw data reduction. Synthetic, mineral 9 and glass standards were used for instrumental calibration. 10 The trace element composition of 6 sectioned particles was determined by averaging 11 multiple laser ablation - inductively coupled plasma mass spectrometry (LA-ICP-MS) analyses 12 performed at the CNR Istituto di Geoscienze e Georisorse in Pavia. The adopted instrument 13 couples a Nd:YAG laser operating at 266 nm with a quadrupole ICP-MS (Drc-e, Perkin Elmer). 14 Analyses were carried out with a spot 50 μm in diameter and NIST SRM 610 and 29 Si as external 15 standards (see also Tiepolo et al., 2003). 16 17 40 Ar- 39 Ar dating 18 Analytical methods. 40 Ar- 39 Ar dating experiments were carried out on a selection of TAM 19 spherules from three different sample sites (Frontier Mountain, Miller Butte and Timber Peak). 20 Thirty-six of the freshest (i.e., devoid of weathering products) spherules in the 400 to 600 μm 21 diameter range were chosen under the stereomicroscope and the scanning electron microscope. 22 The aim of the experiments was twofold: i) to further check that the studied spherules belong to 23 DR2008070

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Page 1: DATA REPOSITORY · 22 on sequential steps containing at least three steps and 60% of 39Ar release (see Ludwig, 2003, for 23 more details). In practice, the Plateau-Isochron age is

Folco, 1

DATA REPOSITORY 1

Bulk chemistry 2

The major element composition of 39 sectioned spherules (Table DR1) from Victoria Land 3

Transantarctic Mountains (TAM) was obtained by averaging multiple electron microprobe 4

analyses (EMPA). EMPA were carried out using a CAMECA SX50 electron microprobe at the 5

IGG CNR in Padova. Running conditions were 15 kV accelerating voltage, 10 nA beam current. 6

Counting time was 7 s for Na, K and Si, and 10 s for the other analyzed elements. A 15 μm-7

diameter defocused beam was employed to reduce migration of volatile elements. The 8

manifacturer-supplied PAP procedure was employed for raw data reduction. Synthetic, mineral 9

and glass standards were used for instrumental calibration. 10

The trace element composition of 6 sectioned particles was determined by averaging 11

multiple laser ablation - inductively coupled plasma mass spectrometry (LA-ICP-MS) analyses 12

performed at the CNR Istituto di Geoscienze e Georisorse in Pavia. The adopted instrument 13

couples a Nd:YAG laser operating at 266 nm with a quadrupole ICP-MS (Drc-e, Perkin Elmer). 14

Analyses were carried out with a spot 50 μm in diameter and NIST SRM 610 and 29Si as external 15

standards (see also Tiepolo et al., 2003). 16

17

40Ar-39Ar dating 18

Analytical methods. 40Ar-39Ar dating experiments were carried out on a selection of TAM 19

spherules from three different sample sites (Frontier Mountain, Miller Butte and Timber Peak). 20

Thirty-six of the freshest (i.e., devoid of weathering products) spherules in the 400 to 600 μm 21

diameter range were chosen under the stereomicroscope and the scanning electron microscope. 22

The aim of the experiments was twofold: i) to further check that the studied spherules belong to 23

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Folco, 2

one single microtektite population; ii) to date their formation event. Spherules were washed with 1

methanol and rinsed many times in an ultrasonic bath always using distilled water. The sample 2

was irradiated for 5 hours in the core of the TRIGA reactor, Pavia University, with FCT biotite as 3

flux monitor (see Laurenzi et al., 2007 for more details). 40Ar-39Ar analyses were performed at 4

the Ar Geochronology Laboratory, IGG, CNR, Pisa. Laser 40Ar-39Ar step-heating and total fusion 5

analyses were performed with a Quanta System diode pumped Nd-YAG laser, operated in 6

continuous mode at 1064 nm. Evolved gas was purified using two AP-10 SAES getters operated 7

at about 200 and 400 °C. Argon was measured with a MAP (Mass Analyzer Products) 215-50 8

mass spectrometer, in static mode, using a Balzer SEV-217 multiplier as collector. Raw data 9

were corrected for blanks, mass discrimination, and nuclear interferences through the ArArCALC 10

software (Koppers, 2002). Ages were calculated using the Isoplot 3.0 software (Ludwig, 2003). 11

Results. We first performed laser 40Ar-39Ar single-spherule total fusion (TF) dating on 25 12

spherules (Table DR2). These analyses provide apparent ages, calculated assuming an initial 13

atmospheric 40Ar/36Ar ratio, ranging from 6.4 to 11.4 Ma, with two distinctly older ages of 23 and 14

34 Ma. A preliminary age estimate for the TAM microtektites (based on 6 spherules) published in 15

abstract form (Folco et al., 2007) proved to be erroneous because not corrected for the excess Ar 16

subsequently revealed by the improved data set. The K/Ca ratio of the spherules, calculated from 17

the K-derived 39Ar and the Ca-derived 37Ar, varies from 0.1 to 1, wider but consistent with 18

electron microprobe data (0.20-0.69). K/Ca ratios define an inverse correlation with apparent 19

ages. The radiogenic 40Ar yields (corresponding to the ratio between radiogenic 40Ar and total 20

40Ar) display narrow variations, with an average percentage value of 31.9 ± 2. This strengthens 21

the argument that the studied spherules belong to a single population as hypothesized previously 22

on the basis of geochemical data. In the 40Ar/36Ar vs. 39Ar/36Ar isotope correlation diagram, 23 23

data points define a rough linear correlation (MSWD = 0.87) with an isochron age of 1.4 ± 1.5 24

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Ma and a trapped initial 40Ar/36Ar = 409 ±28. The difference between the apparent age from the 1

TF experiments and the isochron age value is due to the automatic correction for the trapped 2

component that the isochron calculation involves. In this paper we will use the normal isochron 3

approach in the place of the more common inverse isochron approach in order to give a more 4

immediate vision of the 40Ar/36Ar ratio. 5

We then performed stepwise heating (SH) 40Ar-39Ar analysis (Table DR2). In order to 6

obtain a sufficiently high signal to background ratio, 11 spherules (430 to 500 μm in diameter) 7

were used in a single multi-grain laser incremental heating experiment (Table DR3). As 8

previously noticed (Laurenzi et al., 2003), grains tend to join together well before final fusion, 9

with the result that the numbers and dimensions of the analysed objects change continuously 10

during the step-heating experiment. The age spectrum (Fig. DR2a) shows: i) high apparent ages 11

for low temperature steps; ii) an apparent age plateau (3.40 ± 1.1 Ma) that comprises four 12

concordant incremental heating steps totalling 67% of the whole amount of 39Ar gas released. 13

The integrated age, 9.00 ± 0.63 Ma, falls in the range of the total fusion apparent ages of the 14

individual spherules. The K/Ca ratio (weighted mean = 0.49 ± 0.07; Fig. DR2a) is consistent with 15

the average obtained from the TF analyses and suggests that the K carrier is solely the glass, 16

consistently with the observation of the total lack of weathering minerals and mineral inclusions 17

in the analyzed spherules. Isochrons with a statistically acceptable MSWD (~ ≤ 1) can be 18

calculated using the 4 plateau points only or by iteratively adding the other contiguous steps one 19

at the time, provided that the mathematical solutions gives good statistics. A more rigorous 20

approach involves the use of the “Plateau-Isochron” procedure to perform an isochron regression 21

on sequential steps containing at least three steps and 60% of 39Ar release (see Ludwig, 2003, for 22

more details). In practice, the Plateau-Isochron age is the isochron age defined by the set of 23

contiguous steps with the greatest amount of argon that defines a true isochron. The isochron 24

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regression accepted 9 out of 10 steps, including 96.8 % of the released 39Ar, with a result of 0.76 1

± 0.98 Ma (MSWD = 0.29; probability = 0.96, initial 40Ar/36Ar = 422 ± 18) (Fig. DR2b). 2

Both TF and SH experiments give poorly determined age values (errors exceeding 100%) 3

and initial 40Ar/36Ar higher than the atmospheric ratio (295.5), evidencing the presence of 40Ar 4

not derived from in-situ decay of 40K. Both experiments display a very narrow interval of 5

variation of the 40Ar/36Ar ratios: 434 ± 13 (standard deviation) for the TF, and 444 ± 29 for the 6

SH. These values are slightly above, but within error, of the trapped components obtained from 7

the isochron diagrams, evidencing that the amount of radiogenic 40Ar formed by in-situ decay of 8

40K was too small to be detected with such a high background. The apparent age variations 9

displayed by the TF data might in part be due to the difference in the K content of the spherules. 10

Despite the poorly resolved age values, however, the whole data set indicates that the Quaternary 11

age of TAM microtektites is plausible. 12

As the spherules are totally glassy, two processes might be responsible for the initial 13

radiogenic trapped component: the decrepitation of fluid inclusions, as microbubbles were indeed 14

observed under the stereomicroscope in some of the analysed spherules, and/or Ar dissolved into 15

the glass, due to incomplete degassing of the melt formed by the impact. The last process might 16

be further affected by the correlation between SiO2 content, that shows variability in the analysed 17

spherules, and Ar solubility in melts (see Kelley, 2002 and references therein). 18

19

REFERENCES CITED 20

Folco, L., Rochette, P., Perchiazzi, N., D’Orazio, M., Laurenzi, M. A., and Tiepolo, M., 2007, 21

Microtektites from the Transantarctic Mountains: Abstracts, Meteoritics and Planetary 22

Science, 2007, v. 42 (Suppl.), p. A50. 23

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Glass, B. P., Huber, H., and Koeberl, C., 2004, Geochemistry of Cenozoic microtektites and 1

clinopyroxene-bearing spherules: Geochimca et Cosmochimica Acta, v. 68, p. 3971-4006, 2

doi: 10.1016/j.gca.2004.02.026. 3

Glass, B.P., and Koeberl C., 2006, Australasian microtektites and associated impact ejecta in the 4

South China Sea and the Middle Pleistocene supereruption of Toba: Meteoritics and 5

Planetary Science, v. 41, p. 305-326. 6

Kelley, S., 2002, Excess argon in K-Ar and Ar-Ar geochronology: Chemical geology, v.188, p. 7

1-22. 8

Koeberl, C., Bottomley, R., Glass, B. Y., and Storzer, D., 1997, Geochemistry and age of Ivory 9

Coast tektites and microtektites: Geochimica et Cosmochimica Acta, v. 61, p. 1754-1772. 10

Koppers, A.A.P., 2002, ArArCALC – software for 40Ar/39Ar age calculations. Computer and 11

Geosciences, v. 28, p. 605-619. 12

Laurenzi, M. A., Balestrieri, M. L., Bigazzi, G., Hadler Neto, J. C., Junes, P. J., Norelli, P., 13

Oddone, M., Osorio Araya, A. M., and Viramonte, J.G., 2007, New constraints on ages of 14

glasses proposed as reference materials for fission-track dating: Geostandards and 15

Geoanalytical Research, v. 31, p. 105-124. 16

Laurenzi, M. A., Bigazzi G., Balestrieri M. L., and Bouška, V., 2003, 40Ar/39Ar laser probe dating 17

of the Central European tektite-producing impact event: Meteoritics and Planetary Science, 18

v. 38, p. 887-893. 19

Ludwig, K. R., 2003, User’s manual for Isoplot 3.00: Berkeley Geochronology Center, Special 20

Publication No. 4, p. 70. 21

Tiepolo, M., Bottazzi, P., Palenzona, M., and Vannucci, R., 2003, A laser probe coupled with 22

ICP – Double-focusing sector-field mass spectrometer for in situ analysis of geological 23

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samples and U-Pb dating of zircon: Canadian Mineralogist, v. 41, p. 259-272, doi: 1

10.2113/gscanmin.41.2.259. 2

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Table DR1. Bulk chemistry of TAM microtektites by means of EMP (major elements) and LA-1 ICP-MS (trace elements) analyses. Data for Australasian microtekties (normal type) available 2 from the literature (Glass t al., 2004) are shown for comparison. 3 TAM

(this work) Australasian (normal)

(Glass et al., 2004) Average‡ Silica-poor§ Silica-rich§ Average Range #2.9-03 #2.9-04 Major elements (wt %) SiO2 71.6 ± 3.2 67.8 77.0 69.6 ± 4.4 60.5 - 78.1 TiO2 0.88 ± 0.09 1.00 0.73 0.82 ± 0.12 0.64 - 1.18 Al2O3 15.3 ± 1.8 17.8 12.3 14.9 ± 2.5 10.3 - 21.5 FeO† 4.07 ± 0.60 4.26 3.33 5.08 ± 1.10 2.90 - 7.23 MnO 0.09 ± 0.02 0.11 0.06 MgO 2.91 ± 0.58 3.65 1.95 3.23 ± 1.05 1.67 - 5.07 CaO 3.43 ± 0.47 4.09 2.80 3.52 ± 1.19 1.63 - 6.56 Na2O 0.27 ± 0.04 0.30 0.29 0.92 ± 0.44 0.22 - 1.70 K2O 0.97 ± 0.15 0.88 1.18 1.83 ± 0.81 0.67 - 3.21 Total 99.5 ± 0.3 99.89 99.64 Trace elements (μg g-1) Li 36 ± 6 33 29 Sc 17 ± 2 19.4 14.3 14.3 ± 3.7 7.4 - 21.9 V 32 ± 5 25 31 Cr 60 ± 39 61 47 128 ± 105 22 - 402 Co 6 ± 2 5.0 5.8 12 ± 7 2.9 - 31.3 Rb 45 ± 14 33 56 76 ± 46 9 - 184 Sr 206 ± 27 219 176 200 ± 78 102 - 468 Y 34 ± 4 32.5 27.0 Zr 307 ± 25 278 297 315 ± 81 171 - 508 Nb 20 ± 2 19.7 17.0 Cs 2.8 ± 1.0 1.92 2.9 4.30 ± 3.11 0.98 - 12.1 Ba 527 ± 60 533 432 475 ± 113 259 - 669 La 51 ± 6 49.8 40.6 48.3 ± 9.5 30.9 - 69.9 Ce 103 ± 12 101 84 95.5 ± 25.6 56 - 172 Pr 11 ± 1 10.8 9.0 Nd 43 ± 5 41.7 33.9 43.9 ± 10.6 27.0 - 68.1 Sm 9 ± 1 8.0 6.4 8.54 ± 2.00 5.4 - 12.2 Eu 1.6 ± 0.2 1.60 1.25 1.56 ± 0.43 0.86 - 2.70 Gd 7.0 ± 0.9 6.9 5.5 7.20 ± 1.52 4.6 - 10.4 Tb 1.0 ± 0.1 0.97 0.81 1.19 ± 0.32 0.72 - 2.24 Dy 6.7 ± 1.0 6.3 5.3 Ho 1.3 ± 0.2 1.2 1.0 Er 3.8 ± 0.5 3.5 3.0 Tm 0.5 ± 0.1 0.5 0.4 0.58 ± 0.12 0.4 - 0.8 Yb 3.9 ± 0.5 3.7 3.0 3.87 ± 0.83 2.4 - 5.5 Lu 0.6 ± 0.1 0.51 0.43 0.57 ± 0.13 0.35 - 0.83 Hf 8.2 ± 0.9 7.2 7.8 9.07 ± 2.3 6.0 - 14.9 Ta 1.7 ± 0.2 1.60 1.36 1.57 ± 0.32 0.96 - 5.00 Pb 0.02 ± 0.01 0.02 0.03 Th 19 ± 3 18.0 14.9 16.0 ± 4.3 7.4 - 23.8 U 0.6 ± 0.2 0.36 0.8 1.76 ± 1.34 0.28 - 4.85 ‡Average composition and s. d. (1σ) calculated on the basis of the bulk composition of 39 and 6 individual particles for major 4 and trace elements, respectively. 5 §Bulk composition of Si-poor and Si-rich representative particles #2-9-03 and #2.9-04. 6 †All iron given as FeO. 7 8 9

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Table DR2. Argon isotopic analytical data for TAM microtektites. Argon isotopes are in moles. J= 0.0004996 ± 1 0.00000145. 2

3 Laser total fusion analyses

Apparent age ± 2σ 40Ar(r) #ID 36Ar(a) 37Ar(Ca) 38Ar(Cl) 39Ar(K) 40Ar(r) (Ma) (%) K/Ca ± 2σ

#1 4.41E-17 6.48E-16 1.22E-18 8.57E-16 5.86E-15 6.15 ± 0.48 31.0 0.701 ± 0.041#2 1.70E-17 2.60E-16 9.78E-19 2.82E-16 2.28E-15 7.27 ± 1.25 31.2 0.575 ± 0.038#3 2.50E-17 5.08E-16 1.60E-18 4.69E-16 3.83E-15 7.35 ± 0.73 34.1 0.489 ± 0.029#4 1.99E-17 2.85E-16 b.d.l. 3.02E-16 2.79E-15 8.30 ± 1.08 32.2 0.561 ± 0.036#5 1.48E-17 2.59E-16 1.27E-18 2.22E-16 2.12E-15 8.57 ± 1.30 32.6 0.455 ± 0.030#6 4.53E-17 7.73E-16 2.40E-18 6.81E-16 6.70E-15 8.85 ± 0.62 33.3 0.467 ± 0.027#7 2.59E-17 5.73E-16 4.13E-19 4.35E-16 4.34E-15 8.95 ± 1.04 36.1 0.403 ± 0.023#8 3.54E-17 7.77E-16 4.56E-19 4.40E-16 4.40E-15 8.99 ± 0.95 29.6 0.300 ± 0.017#9 1.45E-17 2.62E-16 2.22E-19 2.14E-16 2.24E-15 9.41 ± 2.06 34.3 0.432 ± 0.027#10 3.07E-17 5.65E-16 1.03E-18 1.98E-16 5.01E-15 22.67 ± 1.62 35.6 0.186 ± 0.012#11 3.54E-17 5.76E-16 1.63E-18 1.25E-16 4.80E-15 34.29 ± 2.92 31.5 0.115 ± 0.008 #12 2.31E-17 3.27E-16 1.23E-18 3.91E-16 2.76E-15 6.35 ± 0.94 28.8 0.633 ± 0.117#13 1.92E-17 1.97E-16 9.30E-19 3.63E-16 2.62E-15 6.50 ± 0.69 31.6 0.974 ± 0.350#14 1.55E-17 2.12E-16 9.60E-19 3.04E-16 2.34E-15 6.94 ± 0.78 33.9 0.759 ± 0.328#15 1.79E-17 2.44E-16 1.24E-18 3.21E-16 2.61E-15 7.32 ± 0.69 33.0 0.696 ± 0.254#16 3.40E-17 6.19E-16 1.23E-18 5.54E-16 4.53E-15 7.36 ± 1.07 31.1 0.474 ± 0.071#17 1.65E-17 2.11E-16 5.02E-19 2.64E-16 2.19E-15 7.45 ± 0.98 31.0 0.666 ± 0.273#18 1.90E-17 2.41E-16 7.51E-19 3.08E-16 2.66E-15 7.74 ± 0.87 32.1 0.677 ± 0.205#19 2.14E-17 3.84E-16 8.19E-19 3.34E-16 2.91E-15 7.82 ± 0.88 31.5 0.461 ± 0.110#20 1.57E-17 2.26E-16 2.07E-19 2.38E-16 2.11E-15 7.95 ± 1.15 31.2 0.560 ± 0.231#21 1.45E-17 1.71E-16 3.43E-19 2.30E-16 2.16E-15 8.44 ± 1.49 33.6 0.714 ± 0.332#22 1.52E-17 2.70E-16 5.57E-19 1.94E-16 1.96E-15 9.06 ± 1.57 30.3 0.381 ± 0.094#23 1.94E-17 4.09E-16 1.25E-18 2.04E-16 2.23E-15 9.80 ± 1.49 28.0 0.265 ± 0.040#24 1.79E-17 3.29E-16 1.01E-19 2.15E-16 2.39E-15 10.00 ± 2.22 31.1 0.346 ± 0.095#25 1.91E-17 2.37E-16 6.76E-19 1.81E-16 2.29E-15 11.39 ± 1.77 28.9 0.403 ± 0.112

4 Laser step-heating experiment

39Ar(K) Apparent Age ± 2σ 40Ar(r) Laser Intensity (W)

36Ar(a) 37Ar(Ca) 38Ar(Cl) 39Ar(K) 40Ar(r) (%) (Ma) (%) K/Ca ± 2σ

1.5 1.94E-17 5.06E-17 2.05E-18 6.91E-17 3.27E-15 3.19 42.18 ± 6.08 36.3 0.723 ± 0.9072.5 3.75E-17 1.24E-16 1.33E-18 1.30E-16 4.93E-15 6.01 33.82 ± 4.66 30.8 0.555 ± 0.3603.5 1.78E-17 9.41E-17 1.28E-18 7.90E-17 2.41E-15 3.65 27.31 ± 6.71 31.5 0.445 ± 0.4295.0 1.64E-17 5.96E-17 5.32E-19 1.13E-16 2.12E-15 5.20 16.92 ± 3.41 30.4 1.001 ± 1.4097.0 1.58E-17 1.62E-16 4.43E-19 1.71E-16 2.02E-15 7.90 10.6 ± 2.28 30.2 0.561 ± 0.3119.0 8.28E-18 1.82E-16 b.d.l. 1.51E-16 1.27E-15 6.96 7.59 ± 2.57 34.2 0.438 ± 0.23811.0 6.96E-18 1.83E-16 5.30E-19 1.70E-16 7.82E-16 7.84 4.15 ± 2.24 27.5 0.491 ± 0.25713.0 5.86E-18 2.81E-16 4.43E-19 2.79E-16 1.28E-15 12.86 4.15 ± 1.41 42.5 0.525 ± 0.18616.0 1.13E-17 6.92E-16 1.07E-18 5.93E-16 2.01E-15 27.40 3.05 ± 0.77 37.5 0.454 ± 0.087fuse 1.05E-17 5.19E-16 1.20E-18 4.11E-16 1.57E-15 18.99 3.44 ± 1.10 33.6 0.420 ± 0.095

Column headings are as follows: 36Ar (a) = atmospheric 36Ar; 37Ar(Ca) = Ca-derived 37Ar; 38Ar (Cl) = Cl-derived 38Ar; 39Ar (K) = 5 K-derived 39Ar; 40Ar(r) = radiogenic 40Ar; 40Ar(r) (%) = ratio (%) of radiogenic 40Ar over total 40Ar. 6 The correction factors for reactor induced interfering reactions were: 39Ar/37Ar (Ca) = 0.00075 ± 0.00008; 36Ar/37Ar (Ca) = 0.00024 7 ± 0.00002; 40Ar/39Ar (K) = 0.0093 ± 0.00093. 8

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Laser total fusion analyses are divided into two sets by a blank row, and each set of data is listed in order of increasing ages. The set 1 #1 to #11 was analysed before the failure of the mass spectrometer filament. The set #12 to #25 and the step heating experiment 2 were performed five months later, after replacing the filament. 3

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1

2 3

4

Fig. DR1. Trace element compositional diagrams for TAM microtektites relative to literature 5 data (Koeberl et al., 1997; Glass et al., 2004) for Ivory Coast, Australasian, and North American 6 microtektites. TAM microtektites show a geochemical affinity to Australasian microtektites. In 7 the refractory element ratio diagram (A), TAM microtektites plot within the compositional field 8 of Australasian and North American microtektites, whereas they distinctly overlap with 9 Australasian microtektites at the high end of a common Zr/Rb versus Th/Cs volatilization trend 10 (B). 11

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1 2

Fig. DR2. Multi-grain (n=11) 40Ar-39Ar step heating experiment of a Transantarctic Mountain 3

microtektite sample. A: Apparent age spectrum with K/Ca ratio. B: Isochron plot; the nine data 4

points used for age calculation are shaded. 5

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1 2

Fig. DR3. Map showing the TAM microtektite find location in Victoria Land, Antarctica, relative 3

to the Australasian tektite strewn field (dashed line; modified after Glass and Koeberl, 2006) 4

which is outlined by tektite finds on land and microtektites finds in cored deep-sea sediments. 5

The square, circle and triangle are the locations of the hypothetical source crater of the 6

Australasian tektites proposed by Glass and Pizzuto (1994), Prasad et al. (1997) and Glass and 7

Koeberl (2006), respectively. 8

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