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TRANSCRIPT
313
International Geology Review, Vol. 49, 2007, p. 313–328.Copyright © 2007 by V. H. Winston & Son, Inc. All rights reserved.
0020-6814/07/925/313-16 $25.00
Continuous Metamorphic Zircon Growth and Interpretation of U-Pb SHRIMP Dating: An Example from the Western Himalaya
MARY L. LEECH,1 Department of Geosciences, San Francisco State University, San Francisco, California 94132
S. SINGH, AND A. K. JAIN
Department of Earth Sciences, Indian Institute of Technology, Roorkee, 247667, India
Abstract
Ultrahigh-pressure (UHP) rocks in the northwest Himalaya are some of the youngest on earth,and allow testing of critical questions of UHP metamorphism and exhumation and the India-Asiacollision. The Tso Morari Complex (TMC) is a UHP subduction-zone complex in eastern Ladakh inthe western Himalaya, south of the Indus-Yarlung suture zone. U-Pb SHRIMP dating of zircon showsthe TMC has a Proterozoic protolith, preserves a Pan-African magmatic history, and shows continu-ous metamorphic zircon growth during the Early to Middle Eocene, hence constraining the timing ofcollision, subduction, and exhumation in the western Himalaya. Zircon dating indicates that UHPmetamorphism occurred at 53.3 ± 0.7 Ma, followed by 8 m.y. of continual zircon crystallization toamphibolite-facies metamorphic conditions at 45.2 ± 0.7 Ma. Similar continuous zircon growth dur-ing UHP metamorphism and through early exhumation to amphibolite-facies conditions occurs inother UHP subduction complexes, including the Sulu terrane, where coesite-bearing inclusionswithin dated zircon prove conclusively that zircon dates record UHP metamorphism. U-Pb SHRIMPdating of zircon for both the TMC and the Sulu belt demonstrate that zircon continues to crystallizeat temperatures 400° ± 50°C based on 40Ar/39Ar dating yielding the same ages.
Introduction
THE TSO MORARI COMPLEX formed as a result ofUHP metamorphism during subduction of theIndian subcontinent beneath Asia in the EarlyEocene. The continent-continent collision isthought to have begun at 55 ± 1 Ma in the northwestHimalaya based on stratigraphy of collision-relatedsediments on both sides of the Indus-Yarlung suturezone (IYSZ) and a slowing of convergence rates(Klootwijk et al., 1992; Guillot et al., 2003). TheUHP eclogites from Tso Morari, India, and Kaghan,Pakistan (e.g., Pognante and Spencer, 1991; Jain etal., 2003; Kaneko et al., 2003), are evidence that theleading edge of the entire northwestern part of theIndian continental margin was subducted beneaththe Kohistan-Ladakh arc to a minimum of 90 km.Previously published age estimates for peak meta-morphism for the TMC are based on Sm-Nd, Lu-Hf,and U-Pballanite dating with significant errors (55 ± 7Ma, 55 ± 12 Ma, and 55 ± 17 Ma, respectively; seede Sigoyer et al., 2000) and do not allow preciseanalysis of the geologic evolution in such a young
mountain belt. Our U-Pb SHRIMP dating of zirconsfrom the TMC better defines the ages of peak UHPand retrograde metamorphism, thus constraining theP-T-t path and exhumation history of the TMC, andhelps resolve the timing of subduction and collisionin the northwest Himalaya.
The UHP Tso Morari Complex
The TMC is a 100 × 50 km NW-SE–trendingUHP eclogitic subduction zone complex in the east-ern Ladakh area near the western syntaxis of theHimalaya, south of the Indus-Yarlung suture zone(Fig. 1). The TMC was first described by Berthelsen(1953), and subsequently mapped by Srikantia andBhargava (1976); it is comprised of Proterozoic toPaleozoic quartzofeldspathic orthogneiss andmetasedimentary rocks, Paleozoic intrusive grani-toids, and small eclogite bodies and their retro-gressed equivalents (e.g., de Sigoyer et al., 1997;2000; Guillot et al., 1997; Girard and Bussy, 1999;Jain et al., 2003). The TMC is tectonically bound bythe IYSZ along its entire northeastern margin and bythe Tethyan sedimentary zone along its southwest-ern margin.1Corresponding author; email: [email protected]
314 LEECH ET AL.
Sachan et al. (2001) first reported coesite inclu-sions in garnet from TMC eclogites. Peak P-T condi-tions for the TMC were 750° to 850°C and aminimum of 2.7 GPa based on conventional thermo-barometric calculations, Thermocalc estimates(Powell and Holland, 1988), and the minimum pres-sure for coesite formation (Jain et al., 2003 and ref-erences therein). Retrograde HP eclogite-facies (2.0
GPa, 600°C) and amphibolite-facies metamorphism(1.3 GPa, 600°C) was followed by greenschist-faciesmetamorphism (0.4 GPa, 350°C) and final exhuma-tion to the upper crust (Jain et al., 2003; Schlup etal., 2003; de Sigoyer et al., 2000). The P-T paths forTso Morari metapelites and eclogites are similar,indicating they followed the same tectonometamor-phic history (de Sigoyer et al., 1997). Table 1 shows
FIG. 1. Regional tectonic map of the western Himalaya showing the Tso Morari Complex (pale grey) and the Indus-Yarlung suture zone (dark grey) (adapted from de Sigoyer et al., 2000; Guillot et al., 2003; Jain et al., 2003; Lacassin etal., 2004). Simplified modern cross-section A-A' (modified after Jain et al., 2003; approximate location on map) showsthe Tso Morari Complex in the footwall of the Indus-Yarlung suture zone and the ~10° modern subduction angle (truescale below sea level; topography is exaggerated). Abbreviations: BNS = Bangong-Nujiang suture; GF = Gozha fault;GHZ = Greater Himalayan zone; IGP = Indo-Gangetic plain; IYSZ = Indus-Yarlung suture zone; KBC = Karakorambatholith complex; KMF = Karakoram fault; KXF = Karakax fault; LBC = Ladakh batholith complex; LHZ = LesserHimalayan zone; MBT = Main Boundary thrust; MCT = Main Central thrust; MHT = Main Himalayan thrust; MKT =Main Karakoram thrust; MMT = main mantle thrust; SHZ = Sub-Himalayan zone; SSZ = Shyok suture zone; STDS =South Tibetan detachment system; THZ = Tethyan Himalayan zone.
METAMORPHIC ZIRCON GROWTH 315
P-T estimates based on thermobarometry and min-eral closure temperature data.
Previous dating de Sigoyer et al. (2000) reported an eclogitization
age for the TMC of 55 Ma and syn-exhumation retro-grade metamorphic events at ~47 Ma (amphibolite-facies) and 30 Ma (greenschist-facies) using multi-ple thermochronological techniques (Table 1); theseages are interpreted to record eclogite-facies meta-
morphism (2.0 ± 3 GPa, not UHP metamorphism) atabout 55 Ma (55 ± 7 Ma, 55 ± 12 Ma, and 55 ± 17Ma from Sm-Nd, Lu-Hf, and U-Pb on allanite,respectively) and overlap considerably with agesrecording amphibolite-facies metamorphism (48 ± 2Ma, 47 ± 11 Ma, and 45 ± 4 Ma from 40Ar/39Ar,Sm-Nd, and Rb-Sr, respectively); this leaves openthe question of exactly when UHP eclogite-faciesmetamorphism and the subsequent amphibolite-facies metamorphism occurred. The 55 Ma age for
TABLE 1. Summary of Geochronologic Data for the Tso Morari Complex1
Rock type Age (Ma) Method Mineral P-T or Tc estimate Reference
Proterozoic protolith ages
Gneiss 748 ± 11–1744 ± 24 SHRIMP Zircon This study
Pan-African ages
Granite 482 ± 1 U-Pb Zircon Girard and Bussy, 1999
Metagranite 479 ± 2 U-Pb Zircon Girard and Bussy, 1999
Gneiss 479 ± 2 U-Pb Zircon Girard and Bussy, 1999
Gneiss 462 ± 9–477 ± 10 SHRIMP Zircon This study
UHP eclogite-facies event ~800°C/!2.9 GPa
Eclogite? 55 ± 17 U-Pb Allanite de Sigoyer et al., 2000
Eclogite 55 ± 12 Lu-Hf Grt-Omp-WR 600–750°C de Sigoyer et al., 2000
Metapelite 55 ± 7 Sm-Nd Grt-Gl-WR 600 ± 30°C de Sigoyer et al., 2000
Gneiss 53.3 ± 0.7 SHRIMP Zircon !900°C This study
Eclogite-facies event ~600°C/2.0 GPa
Gneiss 50.0 ± 0.6 SHRIMP Zircon This study
Amphibolite-facies event ~600°C/1.3 GPa
Gneiss 53.8 40Ar/39Ar Phengite 350-450°C Schlup et al., 2003
Gneiss 51.1 40Ar/39Ar Biotite 350°C Schlup et al., 2003
Metapelite 48 ± 2 40Ar/39Ar Phengite 350–450°C de Sigoyer et al., 2000
Gneiss 47.5 ± 0.5 SHRIMP Zircon This study
Eclogite 47 ± 11 Sm-Nd Grt-Amp-WR 600 ± 30°C de Sigoyer et al., 2000
Metapelite 45.5 ± 4.4 Rb-Sr Ap-Ph-WR de Sigoyer et al., 2000
Gneiss 45.2 ± 0.7 U-Pb Zircon This study
Greenschist-facies event/late-stage exhumation
Gneiss 34 ± 2–45 ± 2 FT Zircon ~240°C/0.4 GPa Schlup et al., 2003
Metapelite 31.1 ± 0.3 40Ar/39Ar Muscovite 350°C de Sigoyer et al., 2000
Metapelite 29.3 ± 0.3 40Ar/39Ar Biotite 350°C de Sigoyer et al., 2000
Metapelite 29 ± 0.4 40Ar/39Ar Biotite 350°C de Sigoyer et al., 2000
Gneiss 21 ± 3–26 ± 3 FT Apatite ~110°C/0.2 GPa Schlup et al., 2003
1See text for references for P-T and Tc estimates. Abbreviations: Amp = amphibole; Ap, = apatite; FT = fission-track; Grt, = garnet; Gl, = glaucophane; Ph = phengite; Tc, = closure temperature; WR = whole-rock.
316 LEECH ET AL.
peak metamorphism in the TMC is also the samedate that is commonly cited for the timing of the ini-tial India-Asia collision; UHP metamorphism couldnot have occurred at 55 Ma if the TMC was part ofthe Indian continent and, in fact, must be later.
The sometimes large analytical errors and dis-crepancies in mineral closure temperatures (Tc) formetamorphic ages shown in Table 1 require carefulevaluation before interpretation. Sm-Nd ages record~200°C below the peak UHP metamorphismtemperatures for the TMC (Mezger et al., 1992). TheLu-Hf system may record similar temperatures toSm-Nd, but results are quite variable; Tc can vary upto 150°C, from ~600°–750°C (Scherer et al., 2000;2003). The Tc for U-Pb in zircon is about 1000°C(Cherniak and Watson, 2001, 2003), close to peakmetamorphic temperatures for the TMC, so U-PbSHRIMP dating of zircons presented here addressesthe problem of these overlapping ages.
U-Pb Zircon SHRIMP Data
Dated zircons for this study are from two samplesof quartzofeldspathic gneiss (T18 [78°16'40" E,33°4'4" N] and T38 [78°21'33" E, 33°9'5" N]) fromthe UHP eclogitic country rock.
Sample preparation and analytical technique
A total of 78 analyses were completed for sampleT38 and 14 analyses for sample T18 (see Table 2 forU-Th-Pb data for all analyses). Zircons were sepa-rated and mounted using standard sample-prepara-tion methods for ion-microprobe analysis (Williams,1998), and U-Pb SHRIMP analyses, data reductionusing Squid, and plotting using Isoplot followedstandard techniques (Williams, 1998; Ludwig,1999). No morphologic or color differentiation wasmade during handpicking for the sample mount. Zir-cons include both subrounded and irregular-shapedgrains that display clear core/mantle/rim zoningrelationships under cathodoluminescence (CL)imaging (Fig. 2). SHRIMP analyses targeted rimsthat appeared to be metamorphic based on CL imag-ing (i.e., lack of oscillatory zoning, rounded grainmorphology); analysis of zircon mantles and coreswas performed for comparison and to establish dif-ferent growth domains within the zircons. Pb/Uratios were calibrated with reference standard R33(419 Ma; Black et al., 2004), which was analyzedafter about every fourth unknown analysis. Zirconswere analyzed using the SHRIMP-RG (-reversegeometry) at the Stanford-USGS Microanalysis
Center. U-Th-Pb data for each ~30 µm spot werecollected in five scans.
Results of dating
Figure 3 shows Tera-Wasserburg concordiadiagrams for analyses from both samples; theseconcordia plots include some discordant data, anddisplay mixing trends and discordance due tocommon Pb (all concordia plots show data uncor-rected for common Pb). All weighted mean ages(95% confidence level) described for dating in thisstudy are 207Pb-corrected 206Pb/238U ages from con-cordant data or data within 1–2% of concordance;high U (>3000 ppm, Williams and Hergt, 2000,cited in Ireland and Williams, 2003), high commonPb, and discordant analyses were excluded from agecalculations. Zircon rims yielding Eocene ages areonly from sample T38 (Figs. 3A and 3B; Table 2).Out of 26 analyses that yielded Late Paleocene toMiddle Eocene ages in sample T38, 11 wereexcluded from age calculations because they weremore than 5% discordant. Both samples T18 andT38 give ~500–400 Ma ages from zircon cores andmantles (Figs. 3C and 3D). Thirteen analyses in T38yielded ages in the Early Ordovician to Early Devo-nian; 11 of those analyses were concordant (2 wereexcluded because of high common Pb). Sample T18yielded eight concordant analyses from the MiddleOrdovician to the Early Devonian. Four zircon anal-yses in T38 indicate an inherited component withLate Proterozoic ages; two analyses were concordantat 1744 ± 24 Ma and 748 ± 11 Ma, corresponding tothe Indian craton (DeCelles et al., 2000).
Pan-African Magmatism
Zircons from both samples T18 and T38 yieldedages between ~400 and 480 Ma (Fig. 4); it is likelythese zircons record magmatism that was part ofwidespread late Pan-African magmatism alongnorthern India (Singh and Jain, 2003). Girard andBussy (1999) described late Pan-African magma-tism ages (479 ± 2 to 482 ± 1 Ma) recorded by inher-ited zircons from the TMC using conventional U-Pbdating (Table 1). Pan-African granitic magmatismoccurred in the Himalaya from 580 to 450 Ma, withan eastward progression over time (Girard andBussy, 1999). The ~400–480 Ma ages from TsoMorari zircons were analyzed in zircon cores andmantles; the morphology of the zircons, the oscilla-tory zoning patterns, and Th/U ratios indicate thatthese ages result from igneous domains.
METAMORPHIC ZIRCON GROWTH 317TA
BLE
2. S
HR
IMP
U-P
b A
naly
ses
of Z
irco
n fr
om th
e Ts
o M
orar
i Com
plex
1
Spot
U(p
pm)
Th(p
pm)
Th/U
204 P
b/20
6 Pb
Com
mon
206
Pb
(%)
238 U
/ 206
Pb*
207 P
b/20
6 Pb*
207 P
b/23
5 U#
206 P
b/23
8 U A
ge†
(Ma)
T18-
115
07 5
00.
03—
0.3
15.
6384
± 1
.410
30.
0572
± 1
.042
90.
5046
± 1
.754
0 3
98.3
± 5
.5T1
8-2
2205
53
0.02
0.00
00 0
.2 1
5.53
97 ±
1.3
999
0.05
65 ±
1.0
951
0.49
83 ±
1.7
917
401
.2 ±
5.5
T18-
325
39 6
60.
030.
0000
0.1
14.
2586
± 1
.395
20.
0565
± 0
.800
50.
5419
± 1
.644
1 4
36.5
± 6
.0T1
8-4
2113
64
0.03
— 0
.2 1
5.48
47 ±
1.3
970
0.05
64 ±
0.8
496
0.50
20 ±
1.6
351
402
.6 ±
5.5
T18-
529
3011
70.
040.
0000
0.8
36.
6296
± 1
.782
50.
0557
± 1
.141
10.
2063
± 2
.249
8 1
72.3
± 3
.1T1
8-6
2093
46
0.02
0.00
00 0
.7 2
4.20
33 ±
1.4
127
0.05
67 ±
1.1
830
0.31
46 ±
1.9
713
259
.3 ±
3.6
T18-
725
38 4
20.
020.
0000
0.6
21.
9682
± 1
.408
20.
0567
± 0
.974
20.
3514
± 1
.791
3 2
85.3
± 4
.0T1
8-8
2770
29
0.01
— 0
.7 2
7.18
44 ±
1.4
093
0.05
64 ±
1.1
034
0.28
59 ±
1.7
899
231
.3 ±
3.2
T18-
928
28 7
40.
030.
0000
0.4
17.
4286
± 1
.389
90.
0569
± 0
.746
60.
4471
± 1
.598
6 3
58.3
± 4
.9T1
8-10
705
37
0.05
— 0
.1 1
4.73
55 ±
1.4
413
0.05
62 ±
1.3
091
0.52
62 ±
1.9
471
422
.8 ±
6.0
T18-
11 9
27 5
30.
060.
0000
1.3
44.
1422
± 1
.634
10.
0594
± 2
.861
40.
1571
± 7
.709
8 1
42.5
± 2
.3T1
8-12
3350
95
0.03
0.00
00 0
.1 1
3.52
19 ±
1.4
113
0.05
68 ±
0.9
379
0.57
27 ±
1.7
499
459
.6 ±
6.4
T18-
1317
24 6
20.
040.
0000
0.2
14.
5686
± 1
.418
50.
0571
± 0
.781
30.
5343
± 1
.664
1 4
27.1
± 5
.9T1
8-14
4776
78
0.02
0.00
00 0
.1 1
5.43
04 ±
1.3
860
0.05
60 ±
0.5
241
0.49
73 ±
1.4
880
404
.2 ±
5.5
T38-
116
92 8
70.
050.
0000
0.2
8.8
534
± 1.
509
0.06
63 ±
1.6
497
0.55
65 ±
1.7
732
448
.8 ±
6.2
T38-
2 5
2514
80.
280.
0000
1.7
17.
4707
± 1
.555
90.
0566
± 2
.095
93.
2778
± 1
.613
213
41.2
± 1
9.3
T38-
3 2
6311
30.
430.
0003
0.5
131.
1379
± 1
.644
50.
0525
± 3
.625
50.
9595
± 3
.075
5 6
86.8
± 1
0.1
T38-
4 3
65 4
80.
130.
0004
0.4
25.
0738
± 1
.446
50.
0569
± 1
.501
30.
3929
± 5
.031
4 3
57.5
± 5
.5T3
8-5
1411
10
0.01
0.00
06 0
.7 1
7.21
24 ±
1.4
711
0.05
69 ±
1.5
485
0.04
53 ±
13.
0028
48.
6 ±
0.8
T38-
611
20 4
30.
040.
0000
0.7
13.
4602
± 1
.395
70.
0568
± 0
.756
90.
3057
± 2
.223
7 2
50.4
± 3
.6T3
8-7
773
24
0.03
0.00
01 0
.413
5.46
67 ±
2.1
873
0.05
42 ±
6.7
433
0.43
60 ±
2.5
589
362
.7 ±
5.3
T38-
820
58 3
40.
020.
0000
0.1
140.
9974
± 2
.245
70.
0605
± 6
.640
50.
5767
± 1
.605
4 4
61.6
± 6
.3T3
8-9
40
8 5
0.01
0.00
00 0
.9 1
4.49
42 ±
2.4
568
0.05
78 ±
6.2
480
0.05
52 ±
7.0
892
47.
0 ±
1.0
T38-
10 7
94 7
0.01
0.00
34 1
.7 1
4.23
10 ±
1.4
221
0.05
68 ±
1.1
420
— 4
4.8
± 1.
0T3
8-11
38
14
0.37
0.00
06 0
.3 1
5.31
77 ±
1.4
399
0.05
67 ±
1.3
542
0.46
57 ±
13.
8045
428
.9 ±
10.
5T3
8-12
922
24
0.03
0.00
00 0
.1 1
4.72
65 ±
1.3
841
0.07
13 ±
0.5
055
0.54
05 ±
1.9
469
437
.2 ±
6.1
T38-
13 7
30 2
70.
040.
0001
0.2
13.
0916
± 1
.596
30.
0576
± 2
.391
80.
4938
± 2
.328
7 4
06.8
± 5
.8T3
8-14
4155
30
0.01
0.00
09 2
.011
1.24
12 ±
1.8
618
0.12
04 ±
7.1
091
0.53
67 ±
3.8
399
415
.3 ±
5.7
T38-
15 1
86 5
80.
310.
0000
0.1
135.
3161
± 2
.199
70.
0644
± 6
.301
50.
6071
± 2
.875
6 4
73.9
± 7
.4
Tabl
e co
ntin
ues
318 LEECH ET AL.
TAB
LE 2
. Con
tinue
d
Spot
U(p
pm)
Th(p
pm)
Th/U
204 P
b/20
6 Pb
Com
mon
206
Pb
(%)
238 U
/ 206
Pb*
207 P
b/20
6 Pb*
207 P
b/23
5 U#
206 P
b/23
8 U A
ge†
(Ma)
T38-
1658
0 7
70.
130.
0062
9.3
13.
4268
± 1
.520
10.
0583
± 1
.143
5—
52.
4 ±
1.3
T38-
1750
8 2
0.00
0.00
25 2
.2 1
8.59
01 ±
1.4
025
0.05
68 ±
1.2
363
0.02
63 ±
50.
7294
46.
4 ±
1.1
T38-
1813
96 2
30.
020.
0000
0.3
171.
5470
± 2
.735
50.
0990
± 6
.750
90.
5828
± 2
.160
9 4
61.9
± 6
.9T3
8-19
1998
48
0.02
0.00
00 0
.4 6
5.93
98 ±
1.8
869
0.24
54 ±
2.5
881
0.41
31 ±
1.9
782
336
.3 ±
4.7
T38-
20 5
29 7
0.01
0.01
20 6
.611
8.77
48 ±
2.1
319
0.05
81 ±
6.2
166
— 3
5.0
± 1.
1T3
8-21
361
18
0.05
0.01
5825
.0 8
7.52
73 ±
1.7
442
0.13
40 ±
14.
2193
— 7
2.9
± 3.
4T3
8-22
493
40.
010.
0030
1.4
131.
6984
± 2
.108
10.
0567
± 1
0.07
34—
53.
3 ±
1.2
T38-
23 5
00 3
80.
080.
0051
10.9
122.
6140
± 2
.004
80.
0708
± 5
.132
50.
0864
± 4
7.86
56 6
5.3
± 2.
3T3
8-24
424
10.
000.
0000
1.2
8.1
187
± 1.
5489
0.06
51 ±
1.7
870
0.05
94 +
10.
2917
48.
2 ±
1.1
T38-
2550
7 3
0.01
0.00
28 3
.0 3
.225
4 ±
1.42
010.
1051
± 0
.542
00.
0301
± 5
5.93
27 5
0.8
± 1.
1T3
8-26
178
130
0.73
0.00
01 0
.1 1
2.95
43 ±
1.4
597
0.05
66 ±
1.5
690
1.07
64 ±
2.5
375
748
.0 ±
11.
3T3
8-27
489
188
0.38
0.00
00 -
0.2
123.
4885
± 1
.974
50.
0695
± 4
.993
04.
4758
± 1
.535
417
43.7
± 2
4.2
T38-
28 4
48 5
30.
120.
0000
0.0
136.
3644
± 2
.152
80.
0622
± 6
.110
80.
5904
± 2
.418
2 4
79.4
± 6
.9T3
8-29
370
20.
010.
0009
2.8
118.
4879
± 2
.102
40.
0705
± 5
.545
80.
0620
± 1
0.11
19 5
0.5
± 1.
0T3
8-30
599
30.
000.
0000
1.9
92.
6446
± 1
.917
10.
2682
± 2
.812
40.
0629
± 6
.479
0 4
6.2
± 1.
0T3
8-31
440
45
0.10
0.00
28 3
.0 1
4.11
34 ±
0.3
652
0.05
71 ±
1.2
060
0.03
08 ±
80.
1297
52.
6 ±
1.2
T38-
32 3
01 9
0.03
0.02
0327
.9 1
1.72
06 ±
0.3
992
0.12
85 ±
1.0
672
— 5
0.0
± 2.
7T3
8-33
410
33
0.08
0.00
00 0
.1 2
0.93
61 ±
0.5
469
0.05
77 ±
1.1
332
0.54
99 ±
1.3
535
440
.6 ±
1.6
T38-
34 3
18 6
50.
210.
0047
8.5
59.
6268
± 0
.330
10.
0548
± 1
.342
80.
6443
± 1
8.38
66 4
82.6
± 6
.1T3
8-35
849
45
0.05
0.00
04 0
.7 5
3.79
13 ±
0.4
935
0.05
89 ±
2.2
335
0.34
17 ±
2.8
917
298
.8 ±
1.6
T38-
3614
75 3
40.
020.
0002
0.3
134.
3868
± 2
.361
00.
1864
± 2
1.18
380.
1205
± 2
.419
9 1
06.4
± 0
.4T3
8-37
653
40.
010.
0003
0.5
131.
6593
± 0
.912
70.
0731
± 3
.395
40.
1387
± 4
.958
7 1
17.2
± 0
.6T3
8-38
562
80.
010.
0039
7.0
15.
6648
± 0
.338
80.
0583
± 1
.153
50.
0679
± 7
2.04
15 4
7.2
± 0.
5T3
8-39
562
80.
010.
0077
7.0
126.
1916
± 1
.066
50.
0628
± 2
.641
3—
47.
2 ±
0.5
T38-
40 5
8626
70.
470.
0005
1.0
31.
4252
± 0
.547
90.
0587
± 3
.420
80.
4393
± 5
.031
3 3
97.2
± 1
.4T3
8-41
961
20.
000.
0016
3.0
150.
3122
± 0
.956
70.
0628
± 3
.852
30.
0404
± 1
9.45
44 4
9.9
± 0.
7T3
8-42
384
19
0.05
0.00
09 1
.612
5.11
64 ±
1.1
462
0.07
14 ±
9.3
085
0.19
80 ±
8.6
671
199
.8 ±
1.2
T38-
43 5
38 8
0.01
0.00
22 4
.113
3.32
84 ±
0.9
303
0.05
29 ±
4.0
177
0.02
54 ±
38.
0814
41.
9 ±
0.4
T38-
44 3
36 1
0.00
0.00
15 2
.812
3.04
97 ±
0.9
423
0.09
61 ±
3.0
535
0.05
32 ±
21.
1635
49.
8 ±
0.7
T38-
45 4
19 2
0.00
0.00
06 1
.1 8
7.67
34 ±
0.8
520
0.05
84 ±
3.4
805
0.04
46 ±
12.
1739
47.
8 ±
0.5
METAMORPHIC ZIRCON GROWTH 319T3
8-46
371
10.
000.
0037
6.8
12.
8848
± 0
.329
60.
0576
± 1
.068
30.
0413
± 3
7.34
53 4
9.1
± 0.
6T3
8-47
348
10.
000.
0004
0.7
124.
6407
± 0
.902
50.
0754
± 5
.739
20.
0824
± 7
.354
7 7
2.1
± 0.
6T3
8-48
514
30
0.06
0.00
00 0
.0 6
3.05
56 ±
0.6
498
0.06
04 ±
2.5
458
0.61
46 ±
1.1
331
481
.3 ±
1.6
T38-
49 8
72 7
0.01
0.00
6712
.2 6
9.16
42 ±
0.8
252
0.07
04 ±
3.0
476
— 4
9.7
± 0.
6T3
8-50
472
12
0.03
0.00
10 1
.911
4.72
99 ±
0.7
298
0.06
04 ±
2.9
250
0.09
61 ±
11.
0007
99.
9 ±
0.7
T38-
51 3
90 6
00.
160.
0021
3.7
63.
0724
± 1
.221
10.
0598
± 2
.257
10.
0758
± 2
5.01
72 9
0.0
± 0.
8T3
8-52
1164
60.
000.
0013
2.3
51.
5326
± 0
.565
90.
0561
± 3
.011
00.
0482
± 1
4.82
85 5
5.0
± 0.
4T3
8-53
1359
16
0.01
0.00
25 4
.512
2.41
00 ±
1.0
409
0.07
62 ±
7.1
467
0.04
57 ±
38.
2616
99.
9 ±
1.2
T38-
54 5
40 1
90.
040.
0007
1.2
103.
0441
± 1
.332
40.
2918
± 6
.542
80.
1221
± 8
.591
4 1
22.7
± 0
.7T3
8-55
47
7 8
0.02
0.00
38 6
.813
9.09
00 ±
0.8
572
0.06
49 ±
3.3
765
— 5
0.6
± 0.
7T3
8-56
430
10
0.02
0.02
0837
.613
0.86
56 ±
0.9
004
0.10
66 ±
3.0
644
— 4
3.7
± 2.
8T3
8-57
530
20.
000.
0029
5.3
117.
8033
± 0
.657
80.
0643
± 2
.610
30.
0186
± 6
0.64
76 4
5.2
± 0.
4T3
8-58
555
50.
010.
0076
13.7
68.
7304
± 0
.701
10.
0623
± 2
.711
9—
45.
5 ±
0.6
T38-
59
836
50.
010.
0029
5.3
23.
8414
± 1
.270
00.
0566
± 1
.351
00.
0220
± 5
7.51
81 5
3.3
± 0.
4T3
8-60
510
20.
000.
0029
5.2
46.
9308
± 1
.193
30.
0716
± 2
.378
70.
0342
± 6
6.64
67 9
1.5
± 0.
7T3
8-61
831
40
0.05
0.00
05 1
.0 7
2.92
58 ±
0.7
315
0.06
75 ±
2.9
066
0.27
69 ±
4.8
455
263
.3 ±
3.3
T38-
62 4
08 1
60.
040.
0020
3.6
66.
5008
± 0
.867
90.
4692
± 5
.063
20.
1186
± 2
0.09
13 1
32.1
± 1
.7T3
8-63
577
60.
010.
0020
3.6
105.
5547
± 0
.843
20.
0701
± 3
.167
50.
0684
± 2
3.12
49 8
5.7
± 0.
7T3
8-64
665
12
0.02
0.02
6948
.5 6
6.70
73 ±
0.9
952
0.10
99 ±
7.3
660
— 4
6.7
± 6.
7T3
8-65
586
12
0.02
0.00
32 5
.7 6
4.23
28 ±
1.0
008
0.06
69 ±
2.8
173
0.02
66 ±
62.
9750
59.
1 ±
0.6
T38-
66 4
06 2
0.00
0.01
3123
.6 9
0.90
37 ±
0.9
429
0.08
34 ±
3.2
342
— 8
8.7
± 1.
6T3
8-67
651
90.
010.
0005
0.8
152.
9934
± 1
.422
60.
0677
± 4
.913
40.
1280
± 5
.939
1 9
7.3
± 1.
0T3
8-68
418
56
0.14
0.00
25 4
.5 2
5.87
52 ±
0.5
559
0.06
23 ±
2.0
052
0.06
74 ±
24.
5217
67.
4 ±
0.8
T38-
69 3
96 7
0.02
0.00
45 8
.1 2
5.88
93 ±
0.5
119
0.05
92 ±
1.8
867
— 4
0.9
± 0.
6T3
8-70
350
120
0.35
0.00
20 3
.6 3
3.05
98 ±
0.8
019
0.07
18 ±
1.7
593
0.16
72 ±
25.
0025
241
.1 ±
1.4
T38-
71 3
47 1
90.
050.
0005
1.0
62.
0157
± 0
.628
90.
0645
± 2
.393
40.
2682
± 6
.008
1 2
41.9
± 1
.3T3
8-72
632
40
0.06
0.00
21 3
.810
9.77
61 ±
1.6
477
0.14
60 ±
8.9
024
0.16
14 ±
18.
8451
187
.0 ±
1.6
T38-
73 5
70 1
60.
030.
0011
2.0
63.
3291
± 0
.606
40.
0628
± 3
.241
00.
1046
± 6
.788
4 1
01.0
± 0
.7T3
8-74
67
5 4
40.
070.
0245
44.2
26.
9720
± 0
.485
20.
0574
± 1
.614
1—
51.
4 ±
1.5
T38-
75 6
34 8
0.01
0.00
46 8
.4 7
7.78
67 ±
0.9
407
0.09
40 ±
8.6
446
— 9
9.2
± 0.
7T3
8-76
524
10
0.02
0.00
02 0
.3 2
2.53
82 ±
0.3
730
0.08
38 ±
2.7
228
0.27
94 ±
2.0
116
232
.8 ±
1.2
T38-
77 4
88 7
0.01
0.00
7413
.4—
——
77.
7 ±
1.2
T38-
78 9
75 2
60.
030.
0016
2.9
——
0.35
79 ±
9.8
150
269
.0 ±
1.8
1 1"
erro
r un
less
not
ed o
ther
wis
e; *
= u
ncor
rect
ed; e
rror
giv
en a
s pe
rcen
tage
; # =
cor
rect
ed fo
r 20
4 Pb;
err
or g
iven
as
perc
enta
ge; †
= c
orre
cted
for
207 P
b.
320 LEECH ET AL.
FIG. 2. Cathodoluminescence images of Tso Morari zircons showing individual SHRIMP analysis spots (U-Pb datingand REE analyses). All zircon rims yielding Eocene metamorphism ages, and representative zircon mantles and coreswith Pan-African or protolith ages, are shown. Sample and spot numbers are listed with 207Pb-corrected ages (in Ma).
METAMORPHIC ZIRCON GROWTH 321
Sample T38 yields 11 concordant analyses withcorrected ages ranging from 397.2 ± 1.4 to 481.3 ±1.6 Ma; weighted mean averages yield several agegroups (based on cumulative probability curves) at480.9 ± 3.0 Ma (three spots) and 440.6 ± 2.9 Ma(four spots), and a single spot at 397.2 ± 1.4 Ma.Eight concordant analyses in sample T18 have cor-rected ages ranging from 398.3 ± 5.5 to 459.6 ± 6.4Ma; best ages include weighted mean averages of402.7 ± 6.2 Ma (three spots) and 424.9 ± 8.3 Ma(two spots), and a single spot age of 459.6 ± 6.4 Ma.
The 480.9 ± 3.0 Ma weighted mean average agein T38 corresponds well to the 479 ± 2 to 482 ± 1Ma ages from Girard and Bussy (1999) (Table 1).Several of the younger Pan-African ages with rea-
sonably small analytical errors (see Table 4 inGirard and Bussy, 1999) fall within the range of460–470 Ma and correspond to the ages seen inboth T18 and T38. The lower limits of errors on agesfor Pan-African magmatism reach 398 Ma (Girardand Bussy, 1999, and references therein), thereforethe younger ages seen in both T18 and T38 from 397to 449 Ma may represent very late stage Pan-Africanmagmatism.
Eocene Zircon Growth
Nineteen concordant zircon analyses from sam-ple T38 yield ages from a 10 m.y. period in the Earlyto Middle Eocene from about 55 to 45 Ma (Fig. 4A,
FIG. 3. Tera-Wasserburg concordia diagrams showing U-Pb SHRIMP data for samples T18 and T38 from the TsoMorari Complex. A. All analyses for sample T38. B. Near-concordant Tertiary analyses for T38. C. Concordant and near-concordant Paleozoic zircon ages. D. Concordant and near-concordant analyses for T18. Data are uncorrected for com-mon Pb (error ellipses are 2"); all data shown are greater than 95% concordant, and analyses high in common Pb wereexcluded. Discordance was estimated by using a mixing line between the common Pb ratio (207Pb/206Pb = 0.86) and theconcordia line.
322 LEECH ET AL.
FIG. 4. Weighted mean age plots for the Tso Morari Complex (A) and the Sulu terrane (B) showing continuous meta-morphic zircon growth from UHP conditions through early exhumation. A. Four “snapshots” of metamorphic zircongrowth at ~53, 50, 47, and 45 Ma correspond to—and are bracketed by—multiple thermochronometers (see Table 1). B:A similar example of continuous metamorphic zircon growth from the Sulu terrane, China (from Liu et al., 2004) whereinthe older ages are from coesite-bearing zircon domains, and the younger ages correspond to quartz-bearing zircondomains. All weighted mean ages (95% confidence level) described for dating in this study are 207Pb-corrected 206Pb/238U ages from concordant data or data within 1–2% of concordance. High U, high common Pb, and discordant analyseswere excluded from age calculations.
METAMORPHIC ZIRCON GROWTH 323
Table 2); morphological and CL characteristics, andU-Th-Pb concentrations do not allow us to distin-guish zircons from each of these three age groups(Figs. 2 and 3; Table 2). Analyses that yieldedEocene ages were from thin, bright rims (under CL)with darker cores/mantles; these metamorphic rimshad very low Th/U ratios (<0.14 with most <0.02).There are only rare inclusions in these rims, andincluded minerals do not allow for thermobaromet-ric estimates. Most metamorphic rims were too thinto yield sufficient U for analysis or the beam over-lapped into older growth domains within the zirconand yielded an older apparent (mixed) age.
Because of the small amount of radiogenic Pb inTertiary zircon, 207Pb/206Pb and 207Pb/235U agesdetermined by the ion microprobe have high uncer-tainties and cannot be use to evaluate discordance.However, assuming common Pb is the most signifi-cant factor in producing discordance toward a com-mon-Pb 207Pb/206Pb ratio (0.86 ± 0.6; Cumming andRichards, 1975), then a common-Pb correction pro-vides acceptable estimates of true ages (DeGraaff-Surpless et al., 2003). This is a reasonable assump-tion for zircons in this study because the data thatplot above concordia fit a mixing line toward a207Pb/206Pb ratio for common Pb and do not fit amixing line toward older ages (Figs. 3A and 3B).
The Tera-Wasserburg concordia diagram pro-vides a graphical estimate of discordance in youngzircon grains by showing uncorrected 207Pb/206Pbratios plotted against uncorrected 238U/206Pb ratios(Fig. 3B). Discordance of Eocene grains was esti-mated by determining where data fall on a mixingline from the common-Pb value through the data toconcordia. Eocene zircon data shown in Figure 3Bonly includes grains more than 95% concordant;analyses with high common Pb were excluded.
REE Analyses of Triassic Zircon Domains
Rare-earth-element (REE) data were collectedusing the SHRIMP-RG in the same analysis spotsfor which U-Pb dating was done in an attempt to dis-tinguish between eclogite-facies zircon growth andlower-grade metamorphic zircon growth.
Analytical technique
The lack of well-characterized zircon crystals forREE calibration standards requires calibration toother REE and zircon standards. For our analyses,we calibrated to: NIST SRM 611 and NIST SRM 613(REE-spiked) glasses; SL13 standard zircon (REE
concentrations based on SL13-LA-CH in Hoskin,1998); and CZ3 (U-concentration standard). NISTglasses and SL13 zircon were analyzed at the begin-ning and end of the SHRIMP session. Rare-earthdata were collected in three scans, with the CZ3standard repeated after every twelfth analysis;multiple CZ3 and SL13 standards were run beforeand after each sample. Details of data reductionwere as described by Hoskin (1998); data werenormalized to the chondrite values of McDonoughand Sun (1995).
Summary and interpretation of REE data
Sample T38 was analyzed for REEs and showconsistent patterns of depleted LREEs with slightnegative Eu anomalies and enriched HREEs withrespect to MREEs. Figure 5 shows REE patterns forzircons yielding Eocene ages (see Fig. 2, Table 2).Although patterns for all analyses are broadly simi-lar, those REE patterns for the older dates (~53 Ma)are more enriched in the LREEs, specifically Laand Ce, with concentrations roughly two orders ofmagnitude higher, whereas La and Ce concentra-tions for younger ages are much lower and morevariable.
Zircon growing in the presence of garnet shouldshow a depleted HREE pattern because garnet pref-erentially incorporates HREEs; in contrast, mag-matic zircon grown in the presence of plagioclaseshould have elevated HREEs and a negative Euanomaly (example in Fig. 5; Hermann et al., 2001;Rubatto, 2002; Rubatto and Hermann, 2003). Ourage and REE data for zircons are from quartzofelds-pathic gneisses that have abundant feldspar andonly rare to minor garnet; consequently the REEpatterns are generally consistent with zircon grow-ing in association with feldspar. These REE patternsdo not rule out zircon crystallization at eclogite-facies in a largely garnet-free rock, but may reflectzircon growth under amphibolite-facies conditionsfor some zircons based on our interpretation of theage data for these samples below.
Interpreting UHP versus RetrogradeZircon Crystallization Ages
Sorting the Eocene-age data by age yields whatappears to be continuous zircon crystallization from~55 to 45 Ma (Fig. 4A). It is inappropriate to esti-mate the timing of peak metamorphism by calculat-ing a weighted mean age from these 19 analysesspanning 10 m.y.; this would result in a young
324 LEECH ET AL.
apparent age with a large amount of uncertainty(49.7 ± 1.6 Ma; MSWD = 26). We separate thesedata into four age groups (Fig. 4A) with overlapping1" error bars, and include the maximum number ofanalyses that yield ages with small errors and lowMSWD values: 53.3 ± 0.7 Ma (MSWD = 0.20), 50.1± 0.6 Ma (MSWD = 0.37), 47.5 ± 0.6 Ma (MSWD =0.61), and 45.2 ± 0.7 Ma (MSWD = 0.55). Theseages are effectively snapshots in time during contin-uous metamorphism from UHP conditions throughearly exhumation.
Our Eocene U-Pb SHRIMP ages correspond wellto—and are in part bracketed by—existing thermo-chronometric data for peak and retrograde metamor-phic events in the TMC at ~55 ± 11 Ma and 47 ± 3Ma, respectively (de Sigoyer et al., 2000; Table 1).We interpret the oldest Eocene age (53.3 ± 0.7 Ma)to date UHP metamorphism in the TMC because itcorresponds to three different radiometric datingsystems that shows peak metamorphism took placeat ~55 Ma (de Sigoyer et al., 2000; Fig. 4A, Table 1).The 47.5 ± 0.6 Ma age from this study is equivalentto the 45–48 Ma ages obtained by de Sigoyer et al.(2000) for the amphibolite-facies retrograde meta-morphism using 40Ar/39Ar, Rb-Sr, and Sm-Nd datingmethods. Well-established 40Ar/39Ar closure tem-peratures exist for biotite, muscovite, and phengite,ranging from 350 to 400° ± 50°C (McDougall and
Harrison, 1999); these ages therefore record syn-exhumation cooling in UHP terranes.
The 50.0 ± 0.6 Ma age, intermediate between theUHP and the amphibolite-facies metamorphism(Fig. 4A, Table 1), corresponds to metamorphismthat is recorded by several thermobarometric calcu-lations (see Guillot et al., 1997; de Sigoyer et al.,2000; Jain et al., 2003) and falls on the exhumationpath between the UHP and amphibolite-faciesevents (Fig. 6). Similar to other UHP terranes (e.g.,Leech and Willingshofer, 2004), standard thermo-barometric calculations (using Fe-Mg exchange ingarnet and omphacite [de Sigoyer et al., 2004])record retrograde P-T conditions rather than peakmetamorphic conditions; temperature estimates willalso be too low if the estimated pressure used in thecalculation is too low (de Sigoyer et al., 2004 uses2.0–2.5 GPa despite the occurrence of coesite).Analytical errors were too large with previous datingmethods to distinguish this metamorphic event. Thefinal group of ages at 45.2 ± 0.7 Ma must record thelowest-temperature zircon growth (~350–450°C,corresponding to the lower limit of closure tempera-tures in phengite for the 40Ar/39Ar system).
Abundant examples exist of low-temperaturezircon crystallization, including amphibolite-facieszircon growth in diamondiferous UHP rocks fromthe Kokchetav massif (Hermann et al., 2001). Similar
FIG. 5. Chondrite-normalized (McDonough and Sun, 1995) REE patterns of zircons yielding Tertiary U-Pb ages forsample T38. Two typical patterns for magmatic zircon and eclogite-facies zircon (from Rubatto and Hermann, 2003) areshown for comparison.
METAMORPHIC ZIRCON GROWTH 325
to the multiple stages of Eocene zircon growthdescribed in this study, Hermann et al. (2001) dem-onstrated that coesite-and diamond-bearing zircon(their Domain 2) looks identical under CL to growthdomains recording upper amphibolite- to granulite-facies zircon growth (their Domain 3). U-Th-Pbconcentrations for Domains 2 and 3 in Kokchetavzircons are indistinguishable, just as are U-Th-Pbconcentrations in TMC zircon rims.
Continuous Metamorphic Zircon Growth
In the Sulu terrane, China, coesite-bearingzircon domains (cores and mantles) unquestionablyyield the timing for UHP metamorphism, whereasyounger quartz-bearing zircon rims record retro-grade zircon growth (Liu et al., 2004). Sorting theSulu U-Pb data (from Liu et al., 2004) by age showsthe same continuum of zircon growth from UHP to
FIG. 6. Age-depth diagram showing conditions for the Tso Morari Complex during UHP metamorphism, and subse-quent exhumation with results of various radiometric dating methods (see Table 1; de Sigoyer et al., 2000, Schlup et al.,2003; Leech et al., 2005) plotted in appropriate temperature ranges for those methods (modified after Fig. 17 in Massonneand O’Brien, 2003). The exhumation P-T-t path shown is modified from de Sigoyer et al. (2000) to account for the morerecent discovery of coesite and other mineralogical evidence for UHP metamorphism (Sachan et al., 2001, 2004; Mukher-jee and Sachan, 2003; Leech et al., 2006a). The vertical bar represents a 3 m.y.–wide period corresponding to the garnetdiffusion modeling of Konrad-Schmolke et al. (2005) and Massonne and O’Brien (2003), stopping at about 450°C, atwhich point garnet diffusion ends; this 3 m.y.–period fits all high- and intermediate-temperature geochronometry withinerror. White symbols correspond to U-Pb SHRIMP dating of zircon from this study as outlined in Figure 4A.
326 LEECH ET AL.
retrograde metamorphic conditions (Fig. 4B). Leechet al. (2006b) demonstrate that U-Pb ages on differ-ent zircons from the same area, but lacking UHPindex mineral inclusions, record the same span ofages for peak and retrograde zircon growth asdescribed by Liu et al. (2004); 40Ar/39Ar datingrecords retrograde metamorphism in the same rocks(Webb et al., 2006). Similar examples of continuousmetamorphic zircon growth are seen in UHP rocksfrom eastern Greenland (McClelland et al., in press)and the Ural Mountains, Russia (Beane and Leech,in press).
Comparing our U-Pb SHRIMP dating of zirconto results from several other radiometric datingsystems indicates that metamorphic zircon growthcan continue essentially uninterrupted from UHPconditions (ca. #1000°C) through exhumation to themid-crust at significantly lower temperatures (ca.350–450°C); this is a reliable method to help inter-pret U-Pb age dating when internal evidence islacking (see the section on Eocene Zircon Growth).
A new model for diffusion in garnet (Konrad-Schmolke et al., 2005) from the Tso Morari Complexdescribes a rapid exhumation period from peakthrough retrograde metamorphism to no more than 3m.y., ending with garnets cooling below about 450°Cwhen measurable diffusion in garnet ends. Theresults of dating from this study and multiple inter-mediate- to high-temperature geochronometers(!450°C) reported in de Sigoyer et al. (2000) all fit,within error, this 3 m.y. period from 53 to 50 Ma.Figure 6 illustrates how zircon continued to growfrom peak metamorphic conditions through muchlower temperatures during exhumation (to about400°C).
Timing of UHP Metamorphismand the India-Asia Collision
The timing of UHP metamorphism (53.3 ± 0.7Ma) in the TMC is ~2 m.y. younger than estimatesfor the timing of the initial collision between Indiaand Asia at 55 ± 1 Ma (see discussion in Guillot etal., 2003 and Leech et al., 2005). In order to recon-cile the short period of time available for Tso Morariprotoliths to enter the subduction zone along theleading edge of the Indian continent and then torecrystallize under UHP conditions, subductionmust have been vertical. Leech et al. (2005) pre-sented a subduction model using this U-PbSHRIMP dating to quantify the timing and angle ofsubduction; the model considers the geometry of a
subduction zone, accounting for the strength of thecontinental lithosphere, and recalculates the timingof the initial collision between continental India andAsia from 55 Ma to 57 Ma. Zircon geochronologyusing the precision of SHRIMP and other ion micro-probe analyses have applicability beyond constrain-ing complex metamorphic histories; tectonic modelsof continental collision, subduction, and exhuma-tion result from careful U-Pb dating (e.g., Guillot etal., 2004, 2006; Leech et al., 2005) and give insightinto much larger scale processes.
Acknowledgments
This work was supported in part by U.S. NSF-EAR 0003355 to J. G. Liou. Field work was fundedby a NSF-AAAS WISC program travel grant and theDepartment of Science and Technology (DST) ofIndia under its HIMPROBE program. We are grate-ful to Kailash Chandra and T.K. Ghosh for use of theEPMA facilities at the Institute InstrumentationCentre, IIT Roorkee. We thank Joe Wooden andJeremy Hourigan (now at University of California atSanta Cruz) for help in the Stanford/USGS SHRIMPlab, Ruth Zhang for help analyzing samples, andKathy DeGraaff-Surpless for help with data analysis.Laura Webb (Syracuse University) helped to inter-pret 40Ar/39Ar data. Thanks also to George Changand Guenther Walther in Stanford’s StatisticsDepartment. James Crowley and one anonymousreviewer provided several suggestions on an earlyversion of this manuscript that helped to improvethis work.
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