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Hf^Nd isotopic evolution of the lower crust
Je¡ D. Vervoort a;*, P. Jonathan Patchett a, Francis Albare©de b,Janne Blichert-Toft b, Roberta Rudnick c, Hilary Downes d
a Department of Geosciences, University of Arizona, Tucson, AZ 85721, USAb Ecole Normale Superieure de Lyon, UMR CNRS 8515, 69364 Lyon Cedex 7, France
c Department of Earth and Planetary Sciences, Harvard University, 20 Oxford St., Cambridge, MA 02138, USAd School of Earth Science, Birkbeck College, London WC1E 7HX, UK
Received 22 November 1999; received in revised form 23 May 2000; accepted 25 May 2000
Abstract
We report Hf isotopic data for over 50 well studied lower crustal samples from three Proterozoic and Phanerozoicregions in southwest Europe, eastern Australia and southern Mexico. We use these data to characterize the Lu^Hfisotopic composition of the lower crust and, in combination with existing Sm^Nd data, to constrain coupled Hf^Ndisotopic behavior and evolution within this reservoir. Although most of these samples have present-day parent/daughter(p/d) ratios consistent with Hf^Nd evolution within the terrestrial Hf^Nd array, some samples have divergent p/d ratiosthat would evolve out of the terrestrial array in 1 Ga or less. The present-day 176Hf/177Hf and 143Nd/144Nd isotopiccompositions of all samples, with one lone exception, plot within the terrestrial array. This indicates that (1) somepresent-day p/d ratios may be a relatively recently acquired characteristic through magmatic or metamorphic processesnot related to the time-integrated Sm/Nd and Lu/Hf ratios of their sources, and/or (2) the Lu/Hf and Sm/Nd p/dvariations exist on a small hand-size scale but not necessarily on a larger scale. The lower crust, from this initial data set,is broadly similar to the upper crust in terms of both its present-day p/d values and time-integrated Lu^Hf and Sm^Ndevolution. As a result, the lower crust appears to have a Hf and Nd isotopic composition similar to that of all othercrust and mantle reservoirs so far characterized. ß 2000 Elsevier Science B.V. All rights reserved.
Keywords: hafnium; isotope ratios; lower crust; isotope fractionation; composition; xenoliths; granulites
1. Introduction
Although the detailed nature of the lower crustis not well known, there are increasingly tighterconstraints on its bulk chemical and isotopic com-
position from recent geochemical studies of xeno-liths (e.g. [1] and references therein) and exposedgranulite terranes (e.g. [2] and references therein),as well as P-T-t (e.g. [3^5]) and integrated geo-physical studies [6^8]. This multidisciplinarywork demonstrates that the lower crust is highlyheterogeneous, generally in the granulite meta-morphic grade, and is overall more ma¢c anddepleted in incompatible and heat producing ele-ments (HPE: e.g. K, U, Th) than the upper andmiddle crust [8]. The Hf isotopic composition and
0012-821X / 00 / $ ^ see front matter ß 2000 Elsevier Science B.V. All rights reserved.PII: S 0 0 1 2 - 8 2 1 X ( 0 0 ) 0 0 1 7 0 - 9
* Corresponding author. Tel. : +1-520-626-9122;Fax: +1-520-621-2672; E-mail: [email protected]
EPSL 5527 2-8-00
Earth and Planetary Science Letters 181 (2000) 115^129
www.elsevier.com/locate/epsl
evolution of the lower crust, however, is not wellconstrained.
There are several fundamental reasons why weshould be interested in the Hf isotopic composi-tion of the lower crust and why constraining theisotopic composition of the lower crust is essentialfor our understanding of the Hf^Nd isotopic be-havior in the bulk silicate Earth (BSE).
First, the lower crust is depleted in incompat-ible elements and HPE compared with the uppercrust, suggesting the former has been reworked bymelting and intracrustal di¡erentiation. A mineralthat may leave a distinctive ¢ngerprint of this pro-cess is garnet, which occurs in basaltic [9] andpelitic [10] lower crustal lithologies. If garnet inthese rocks is a purely metamorphic phase, thenits formation will not produce signi¢cant bulkrock fractionation of Lu/Hf and Sm/Nd ratios.If, however, garnet is residual from melting ordi¡erentiation events, it will impart an elevatedLu/Hf ratio to the bulk rock due to the veryhigh partition coe¤cients of garnet for Lu com-pared to Hf. Such high Lu/Hf ratios have beenreported for two garnet^granulite xenoliths fromKilbourne Hole, New Mexico [11]. If such highLu/Hf lithologies are typical of lower crust, then itwill rapidly evolve toward highly radiogenic Hfisotopic compositions and should be recognizablein xenoliths and magmas that are derived from orinteract with the lower crust.
Second, the overwhelming majority of mantleand upper crustal lithologies examined thus farlie along a single, well correlated 176Hf/177Hf^143Nd/144Nd isotopic array. This includesMORBs, OIBs, IAVs and continental crust of awide range of lithologies, Archean to recent (dataof many authors, see [12,13] for a compilation ofsources and [14^18] for recent data). This indi-cates that, to a ¢rst approximation, Lu^Hf andSm^Nd fractionate in a similar fashion in all ter-restrial reservoirs. However, if the lower crustcontains widespread residual or cumulate garnet,it might develop `decoupled' Hf^Nd isotopic com-positions that will evolve out of the terrestrial Hf^Nd array.
Third, an outstanding problem with respect tothe Hf^Nd isotopic systematics of the silicateEarth is that the terrestrial Hf^Nd array appears
to lie signi¢cantly above the BSE compositionbased on the chondritic Sm^Nd and Lu^Hf valuescurrently in use [19^21]. If the chondritic Hf^Ndvalues accurately represent BSE Hf^Nd isotopiccompositions, then the BSE composition shouldlie along a mixing hyperbola between bulk crustand depleted mantle [21]. It has been suggested[21], however, that the most plausible mixing hy-perbolae pass above BSE and that this indicatesthe existence of a hidden reservoir to balance theterrestrial array with BSE. If the lower crust ischaracterized by high time-integrated Lu/Hf ratiosand hence anomalously radiogenic Hf isotopiccompositions, the problem is exacerbated becausethe bulk crust will plot even further above theterrestrial array.
In this paper, we characterize the Hf isotopiccomposition of the lower crust and, in conjunc-tion with published Sm^Nd isotopic data, exam-ine coupled Hf^Nd behavior and evolution in thisrelatively inaccessible region. We report Hf iso-tope data for several suites of lower crustal sam-ples that have been thoroughly characterized byprevious geochemical, petrological and isotopicstudies (references below). These include: xeno-liths from Mesozoic to recent volcanic rocks inthe Massif Central (France) and the Iberian belt(Spain); xenoliths within the McBride and Chud-leigh volcanic provinces in north Queensland,Australia; and xenoliths and exposed Proterozoicgranulite and eclogite terranes in southern Mexi-co. The geological setting of each of these suiteshas been described in detail elsewhere (see below)but brief geological summaries are given belowto provide background for the data presentedherein.
2. Geological overview of analyzed samples
2.1. Massif Central, France
The lower crustal xenoliths we analyzed fromthe Massif Central occur in Neogene (ca. 4^7 Maold) volcanic conduits or breccia `pipes' fromBournac and Roche Pointue in France [22]. Thesevolcanic conduits cut through late Paleozoic gran-ites and Hercynian gneisses [22,23] and contain
EPSL 5527 2-8-00
J.D. Vervoort et al. / Earth and Planetary Science Letters 181 (2000) 115^129116
xenoliths that are well characterized (e.g. [22^26]).Zircon ages for the Massif Central xenoliths areapproximately 300 Ma [27] and it is thought thatthe ma¢c granulites were produced during a Her-cynian underplating event that caused the pre-ex-isting metasedimentary crust to melt and form theabundant granites exposed in the Massif Central[28]. We analyzed metaigneous (ma¢c and inter-mediate-felsic) and metasedimentary xenolithsfrom both localities. All the Massif Centralxenoliths contain garnet with the exception ofthree ma¢c metaigneous samples (Table 1). Thegeochemistry (including Nd and Sr isotopes) ofthe Massif Central xenoliths analyzed for Hf iso-topes in this paper has been previously describedin [23].
2.2. Spanish central system
The xenoliths from the Hercynian central re-gion of Spain [29] occur in an Early to MiddleJurassic alkaline dike swarm [30]. These dikes in-trude Hercynian (ca. 300 Ma [27,31]) granites andLate Proterozoic to Paleozoic metamorphic rocks[29] and carry xenoliths of mainly felsic metaig-neous compositions (V95%) and rare ma¢c meta-igneous and metapelitic compositions. Thermo-barometric calculations on mineral assemblagesin these samples [29] indicate lower crustal equili-bration conditions (V850³^950³C, 7^11 kbar).We analyzed six felsic metaigneous xenolithsfrom two locations (La Paramera and Peguerinos)in the Spanish central system [31], all of whichcontain garnet as a major phase [29]. Villasecaet al. [29] concluded that the felsic granulite xeno-liths represent restites following extraction of agranitic melt similar in composition to the Hercy-nian granites [31]. Major element and trace ele-ment as well as Nd and Sr isotopic data for thesamples we analyzed are reported in [29].
2.3. McBride and Chudleigh volcanic provinces,Queensland, Australia
The xenoliths from northeast Australia arehosted by basalts in two Pliocene^Pleistocene(6 3 Ma) volcanic provinces in north Queensland[32]. The basalts from both provinces were
erupted through diverse rock types ranging fromthe Proterozoic granites and metamorphic rocksof the Georgetown Inlier [33] to Paleozoic vol-canic, plutonic and sedimentary rocks of the Tas-man fold belt [34].
Xenoliths from the McBride Province are pre-dominantly ma¢c, but a signi¢cant number (20^30%) of felsic to intermediate compositions alsooccur [35]. The latter are mostly metaigneous withlesser amounts of metapelites. All McBride xeno-liths underwent high-grade metamorphism about300^200 Ma ago and the protoliths for many ofthe xenoliths are Permo^Triassic in age, with theexception of a few xenoliths with Proterozoiccrystallization ages (V1.5 Ga) as indicated byU^Pb ages of zircons [36]. These later ages corre-spond approximately to the age of the George-town Inlier, which was overprinted by the wide-spread Permo^Triassic metamorphic orogenicevent. We analyzed eight ma¢c metaigneous andthree metasedimentary/felsic metaigneous xeno-liths from the McBride suite, all but two of whichare garnet-bearing.
Xenoliths from the Chudleigh volcanic provinceare exclusively ma¢c in composition [34]. The xe-noliths have been interpreted to be young (Ceno-zoic) cumulates formed from a ma¢c magmaevolving by fractional crystallization and assimi-lation of deep crustal rocks [34,37], which crystal-lized at mid to lower crustal levels [38,39]. Weanalyzed 11 ma¢c xenoliths from the Chudleighvolcanic province, four of which are garnet-bear-ing.
Major and trace element, Nd, Sr, Pb, O and Osisotopic data for McBride and Chudleigh are re-ported in [34,35,37,40^42]. These xenolith suitesthus represent the most completely characterizedsamples of lower crust currently described in theliterature.
2.4. Mexican lower crustal granulites
Samples of the lower crust of Mexico exist asboth tectonic slivers exposed throughout the Mex-ican Cordillera [43] and as xenoliths carried inrecent volcanic rocks [44]. We analyzed threeMexican lower crustal granulites. Two of theseare garnet-bearing metapelites from exposures in
EPSL 5527 2-8-00
J.D. Vervoort et al. / Earth and Planetary Science Letters 181 (2000) 115^129 117
Tab
le1
Hf
and
Nd
isot
opic
data
Sam
ple
Gt?
176H
f/17
7H
f17
6L
u/17
7H
f14
3N
d/14
4N
d14
7Sm
144N
dC
once
ntra
tion
sO H
f�0�
O Nd�
0�t H
fÿD
Mt N
dÿD
Mf L
u=H
ff S
m=N
dF
Nd
data
sour
ceL
uH
fSm
Nd
Mas
sif
Cen
tral
Ma¢
cm
etai
gneo
usH
229A
0.28
2860
þ5
0.02
230.
5125
11þ
107
0.15
210.
322.
013.
4513
.75
3.11
32.
481.
181.
583
0.33
30.
231.
46[1
9]17
B1
0.28
2716
þ5
0.01
830.
5124
33þ
200.
1407
0.45
3.48
5.48
23.5
93
1.98
34.
001.
311.
503
0.45
30.
281.
59[1
9]R
P-8
Gt
0.28
2799
þ5
0.02
860.
5123
80þ
220.
1382
0.68
3.36
7.83
34.2
50.
953
5.03
2.25
1.55
30.
153
0.30
0.49
[19]
RP
-10
Gt
0.28
2502
þ5
0.01
840.
5121
59þ
120.
1309
0.24
3.70
9.55
44.1
23
9.55
39.
341.
861.
823
0.45
30.
331.
34[1
9]R
P-1
10.
2829
35þ
110.
0395
0.51
2611
þ24
0.16
830.
260.
942.
298.
235.
763
0.53
^1.
810.
183
0.14
31.
27[1
9]B
OU
-13
Gt
0.28
2501
þ5
0.00
332
0.51
2178
þ21
0.10
770.
104.
274.
7926
.90
39.
583
8.97
1.07
1.40
30.
903
0.45
1.99
[19]
Fel
sic^
inte
rmed
iate
met
aign
eous
BA
L-7
15G
t0.
2825
83þ
80.
0175
0.35
2.80
36.
681.
593
0.48
BA
L-7
15.2
Gt
0.28
2536
þ3
0.01
040.
334.
533
8.35
1.27
30.
69B
AL
-104
6G
t0.
2825
18þ
50.
0075
00.
5121
70þ
200.
1132
0.57
10.7
313
.19
70.4
43
8.98
39.
131.
181.
483
0.78
30.
421.
83[1
9]M
etas
edim
ents
830
Gt
0.28
2333
þ5
0.00
325
0.51
2048
þ21
0.08
940.
2510
.82
10.1
068
.31
315
.52
311
.51
1.31
1.35
30.
903
0.55
1.66
[19]
831
Gt
0.28
2496
þ5
0.01
060.
5121
37þ
210.
0934
0.51
6.78
7.31
47.6
73
9.76
39.
771.
351.
283
0.68
30.
531.
30[1
9]83
10G
t0.
2824
34þ
50.
0134
0.51
2094
þ45
0.11
950.
606.
346.
2431
.54
311
.95
310
.61
1.63
1.71
30.
603
0.39
1.53
[19]
8330
Gt
0.28
2435
þ4
0.01
450.
5120
38þ
210.
1210
0.62
6.02
8.15
40.7
23
11.9
23
11.7
01.
711.
823
0.56
30.
391.
47[1
9]83
40G
t0.
2824
88þ
70.
0129
0.51
2274
þ33
0.13
250.
647.
026.
7830
.95
310
.04
37.
101.
491.
643
0.61
30.
331.
88[1
9]83
20G
t0.
2825
02þ
90.
0170
0.51
2215
þ22
0.12
570.
413.
444.
3120
.76
39.
553
8.25
1.74
1.62
30.
493
0.36
1.36
[19]
17B
AG
t0.
2825
02þ
60.
0239
0.51
2206
þ26
0.14
950.
482.
863.
3313
.47
39.
553
8.43
2.56
2.23
30.
293
0.24
1.19
[19]
Spa
nish
cent
ral
syst
emF
elsi
cm
etai
gneo
usU
-145
Gt
0.28
2636
þ6
0.01
650.
5123
79þ
80.
1396
0.67
5.74
6.25
27.1
03
4.81
35.
051.
391.
583
0.51
30.
291.
74[2
5]U
-146
Gt
0.28
2484
þ5
0.01
330.
5121
67þ
120.
1113
0.58
6.21
4.07
22.1
03
10.1
83
9.19
1.52
1.46
30.
603
0.43
1.39
[25]
U-1
47G
t0.
2824
47þ
60.
0175
0.51
2122
þ5
0.14
870.
554.
466.
6427
.00
311
.49
310
.07
1.92
2.40
30.
483
0.24
1.95
[25]
U-1
52G
t0.
2824
87þ
60.
0105
0.51
2217
þ7
0.13
070.
587.
778.
1337
.60
310
.08
38.
211.
371.
713
0.68
30.
342.
04[2
5]U
-155
Gt
0.28
2594
þ5
0.01
660.
5123
33þ
40.
1378
0.71
6.06
6.02
26.4
03
6.29
35.
951.
501.
643
0.50
30.
301.
68[2
5]U
-157
Gt
0.28
2566
þ5
0.01
580.
5122
48þ
40.
1335
0.65
5.83
6.14
27.8
03
7.29
37.
611.
501.
713
0.53
30.
321.
64[2
5]M
exic
anga
rnet
-bea
ring
pelit
esM
OL
-5-8
6G
t0.
2821
59þ
50.
0008
230.
5118
33þ
90.
1097
0.02
2.56
0.14
0.76
321
.68
315
.70
1.46
1.93
30.
983
0.44
2.21
[40]
OA
X-5
-86
Gt
0.28
2288
þ4
0.01
310.
5119
62þ
60.
1102
0.79
8.59
6.51
35.7
13
17.1
23
13.1
91.
901.
753
0.61
30.
441.
38[4
0]T
-18-
87G
t0.
2826
52þ
50.
0261
0.51
2580
þ6
0.18
710.
673.
647.
8925
.51
34.
243
1.13
2.41
3.25
30.
223
0.05
4.47
[40]
Mex
ican
garn
et-b
eari
ngec
logi
tes
D-7
814
Gt
0.28
2772
þ6
0.00
983
0.51
2797
þ9
0.15
210.
324.
576.
2524
.84
0.00
3.10
0.82
0.88
30.
713
0.23
3.11
[0]
M-7
Gt
0.28
3154
þ13
0.03
900.
5131
64þ
110.
2300
0.41
1.49
2.14
5.63
13.5
110
.26
^0.
120.
170.
170.
99[0
]M
P-3
Gt
0.28
2775
þ6
0.01
020.
5128
15þ
160.
1539
0.24
3.39
4.68
18.3
80.
113.
450.
830.
863
0.69
30.
223.
19[0
]M
I-6
Gt
0.28
3194
þ15
0.04
020.
5131
43þ
80.
2302
0.42
1.47
2.14
5.63
14.9
29.
85^
^0.
200.
171.
19[0
]
EPSL 5527 2-8-00
J.D. Vervoort et al. / Earth and Planetary Science Letters 181 (2000) 115^129118
Tab
le1
Hf
and
Nd
isot
opic
data
Sam
ple
Gt?
176H
f/17
7H
f17
6L
u/17
7H
f14
3N
d/14
4N
d14
7Sm
144N
dC
once
ntra
tion
sO H
f�0�
O Nd�
0�t H
fÿD
Mt N
dÿD
Mf L
u=H
ff S
m=N
dF
Nd
data
sour
ceL
uH
fSm
Nd
Chu
dlei
ghvo
lcan
icpr
ovin
ceM
a¢c
met
aign
eous
83-1
070.
2829
16þ
470.
0404
0.51
2421
þ16
0.12
360.
020.
050.
311.
595.
093
4.23
^1.
230.
213
0.37
30.
56[3
0]83
-112
0.28
2676
þ10
0.00
825
0.51
2598
þ26
0.16
270.
132.
151.
666.
173
3.39
30.
780.
941.
653
0.75
30.
174.
36[3
0]83
-112
.20.
2826
29þ
50.
0078
90.
5125
98þ
260.
1627
0.11
2.02
1.66
6.17
35.
063
0.78
1.01
1.65
30.
763
0.17
4.42
[30]
83-1
14G
t0.
2827
57þ
110.
0244
0.51
2507
þ18
0.18
600.
100.
551.
103.
593
0.53
32.
561.
743.
523
0.27
30.
054.
93[3
0]83
-125
Gt
0.28
3024
þ15
0.03
010.
5126
81þ
200.
1752
0.08
0.37
0.94
3.26
8.91
0.84
1.27
1.86
30.
103
0.11
0.91
[30]
83-1
270.
2830
29þ
160.
0182
0.51
2638
þ32
0.12
010.
020.
140.
301.
539.
090.
000.
500.
843
0.46
30.
391.
17[3
0]83
-131
Gt
0.28
2962
þ18
0.02
310.
5125
94þ
200.
1645
0.05
0.33
0.62
2.26
6.72
30.
860.
891.
723
0.31
30.
161.
89[3
0]83
-140
0.28
2812
þ18
0.02
550.
5123
25þ
320.
1528
0.06
0.35
0.89
3.53
1.41
36.
111.
662.
063
0.24
30.
221.
06[3
0]83
-110
0.28
3019
þ10
0.03
580.
5129
16þ
360.
2541
0.27
1.06
1.73
4.13
8.73
5.42
^^
0.07
0.29
0.25
[30]
83-1
150.
2829
97þ
70.
0330
0.51
2756
þ14
0.23
960.
321.
362.
466.
207.
962.
302.
24^
30.
010.
223
0.06
[30]
83-1
260.
2829
61þ
80.
0254
0.51
2693
þ38
0.18
230.
120.
651.
665.
526.
681.
071.
062.
213
0.24
30.
073.
25[3
0]B
CG
t0.
2832
08þ
90.
0302
0.51
3126
þ36
0.23
750.
170.
811.
293.
3815
.42
9.52
0.11
^3
0.10
0.21
30.
47[3
0]M
cBri
devo
lcan
icpr
ovin
ceM
a¢c
met
aign
eous
83-1
58G
t0.
2831
56þ
90.
0467
0.51
2885
þ11
0.23
040.
551.
673.
108.
1313
.58
4.82
^^
0.40
0.17
2.32
[32]
85-1
06G
t0.
2830
62þ
60.
0186
0.51
2964
þ7
0.19
540.
292.
213.
6211
.20
10.2
66.
360.
431.
553
0.44
30.
0167
.10
[32]
85-1
000.
2824
21þ
80.
0121
0.51
1956
þ4
0.12
730.
232.
694.
2820
.32
312
.41
313
.30
1.57
2.10
30.
643
0.35
1.81
[32]
85-1
08G
t0.
2830
36þ
80.
0358
0.51
2146
þ4
0.13
830.
311.
234.
4719
.49
9.34
39.
604.
012.
020.
073
0.30
30.
24[3
2]85
-108
.2G
t0.
2830
34þ
80.
0346
0.51
2146
þ4
0.13
830.
301.
214.
4719
.49
9.27
39.
602.
742.
020.
043
0.30
30.
12[3
2]85
-120
0.28
2649
þ6
0.02
100.
5121
96þ
110.
1529
0.27
1.83
3.95
15.6
13
4.35
38.
621.
722.
383
0.37
30.
221.
66[3
2]83
-159
Gt
0.28
2100
þ7
0.00
798
0.51
1887
þ5
0.13
700.
468.
104.
3119
.02
323
.76
314
.65
1.90
2.50
30.
763
0.30
2.51
[32]
85-1
07G
t0.
2823
80þ
50.
0039
10.
5120
11þ
100.
1370
0.52
19.0
15.
7321
.49
313
.86
312
.23
1.26
2.26
30.
883
0.30
2.91
[32]
85-1
14G
t0.
2825
07þ
50.
0463
0.51
2430
þ25
0.18
800.
892.
721.
815.
823
9.37
34.
06^
^0.
393
0.04
38.
76[3
2]85
-114
.2G
t0.
2825
02þ
50.
0468
0.51
2430
þ25
0.18
800.
912.
751.
815.
823
9.55
34.
06^
^0.
403
0.04
39.
06[3
2]M
etas
edim
ents
/fel
sic
met
aign
eous
83-1
57G
t0.
2821
35þ
90.
0115
0.51
1724
þ5
0.13
191.
307.
696.
0027
.50
322
.53
317
.83
2.08
2.64
30.
663
0.33
1.99
[32]
83-1
60G
t0.
2826
68þ
70.
0210
0.51
2280
þ13
0.12
650.
624.
205.
1124
.40
33.
683
6.98
1.65
1.52
30.
373
0.36
1.04
[32]
83-1
62G
t0.
2827
36þ
90.
0360
0.51
2285
þ14
0.18
871.
254.
915.
8618
.80
31.
273
6.89
^^
0.08
30.
043
1.93
[32]
Sm^N
dis
otop
icda
tapu
blis
hed
prev
ious
lyw
ith
the
exce
ptio
nof
Mex
ican
garn
etec
logi
tes
([0]
,th
isst
udy)
.2c
erro
rsfo
rH
fco
ncen
trat
ions
are
60.
5%an
dfo
rL
uco
ncen
trat
ions
and
176L
u/17
7H
far
e6
1.0%
.17
6H
f/17
7H
fra
tios
corr
ecte
dfo
rm
ass
frac
tion
atio
nw
ith
179H
f/17
7H
f=0.
7325
.F
orca
lcul
atio
nof
O Hf
valu
es,
we
used
176H
f/17
7H
f CH
UR�0�=
0.28
2772
and
176L
u/17
7H
f CH
UR�0�=
0.03
32.O H
f�0�,
O Nd�
0�=
pres
ent-
dayO
Hf
and
Nd
valu
es.
f Lu=
Hf
=[(
176L
u/17
7H
f sam
ple)
/(17
6L
u/17
7H
f CH
UR
)31]
;f S
m=N
dis
anal
ogou
s.t H
fÿD
M=
(1/V
)Ln[
((17
6H
f/17
7H
f)sa
mpl
e3(17
6H
f/17
7H
f)D
M)/
((17
6L
u/17
7H
f)sa
mpl
e3(17
6L
u/17
7H
f)D
M)+
1];
t Ndÿ
DM
isan
alog
ous.
For
calc
ulat
ion
oft H
fÿD
Man
dt N
dÿD
M,
we
used
the
follo
win
gva
lues
for
the
pres
ent-
day
depl
eted
man
tle.
176H
f/17
7H
f=0.
2832
24;
176L
u/17
7H
f=0.
0381
3;
143N
d/14
4N
d=
0.51
3151
;14
7Sm
/144N
d=
0.21
37.
`Gt'
sign
i¢es
aga
rnet
-bea
ring
sam
ple.
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the Sierra Madre Oriental in central Mexico(MOL-5) and from the Oaxacan complex insouthern Mexico (OAX-5) [44,45]. A third sample(T-18) is a garnet-bearing metapelite xenolith oc-curring in a Quaternary volcanic vent (El Toro) incentral Mexico. The ages of the protoliths of theselower crustal samples [46] are not well constrainedbut are believed to be Grenvillian (ca. 1.1^1.0Ga). A Sm^Nd garnet whole-rock age of 0.96Ga has been reported by Patchett and Ruiz[46] for OAX-5. Major and trace element data[45] and Nd^Sr isotopic data [44,46] for some ofthese and related rocks have been reported else-where.
2.5. Acatlan complex eclogites, southern Mexico
We also analyzed four samples from the Acat-lan complex, a high P/T metamorphic belt insouthern Mexico. These samples include threeeclogites and one garnet-bearing metapelite fromthe Xayacatlan formation, an eclogitized sequenceof the Acatlan complex. The Xayacatlan forma-tion is interpreted to have formed from oceanicbasalts and associated rocks that were tectonicallyemplaced adjacent to the Grenville crust of south-ern Mexico [47] during the Devonian. Althoughthese and the Oaxacan complex samples are notxenoliths, they nevertheless represent an impor-
Fig. 1. Present-day Hf^Nd isotopic compositions of granulite samples (open symbols) analyzed in this study relative to the terres-trial Hf^Nd array [12]. Also shown are garnet granulites from Kilbourne Hole, New Mexico [11] (crossed circles). Most Hf^Nddata plotted here are from [12] and references therein. New data added to this diagram are from [15,16,18] and references there-in.
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tant lithologic type that may be volumetricallyimportant in the lower crust.
3. Analytical techniques
Whole-rock powders were dissolved with a HF/HNO3 mixture in steel jacketed Te£on dissolutionvessels for 7 days at 160³C [48]. This procedureyielded complete dissolution, with the exceptionof ¢ne black graphitic particulates in a few peliticsamples. Lu^Hf elemental separations followedthe procedure outlined in [13]. All samples werespiked with a mixed 176Lu^180Hf spike prior tochemical separation and analysis.
Lu and Hf isotopic compositions were analyzedon a VG Plasma 54 (P54) multicollector-in-ductively coupled plasma-mass spectrometer inLyon, France [13,49]. Isotopic analyses on theP54 in Lyon were carried out over two 8-day pe-riods in the Fall of 1998 and Spring of 1999. Theaverage 176Hf/177Hf value for the JMC 475 Hfstandard during these periods was 0.282161 þ 14(2c).
4. Results
The Hf^Nd isotopic data for the lower crustalsamples are given in Table 1. Present-day isotopicvalues for both Hf and Nd are given with theirassociated in-run (2c) errors. Also shown are thedepleted mantle model Hf and Nd ages and Lu/Hf and Sm/Nd fractionation factors. The param-eters used to calculate these values are given in thefootnotes to Table 1.
4.1. Present-day Hf^Nd isotopic composition
Present-day Hf^Nd isotopic values for all xeno-liths are plotted in Fig. 1 relative to the `terrestrialarray' of Vervoort and others [12] de¢ned by Hf^Nd isotopic values from a wide variety of crustand mantle samples (3.5 Ga to the present). Theterrestrial array as shown here consists of bothinitial (small gray circles) and present-day isotopiccompositions (large gray circles) : data sources ofthese data are given in the caption. The lower
crustal samples have present-day Hf^Nd isotopicvalues that (1) span the entire range of the terres-trial array and (2) plot entirely within the array,with one exception (85-108).
4.2. Possible parent/daughter (p/d) fractionations
The mean Lu/Hf ratio of the present sampleset is 0.119 þ 3 (176Lu/177Hf = 0.0169 þ 5) for amean Sm/Nd ratio of 0.247 þ 3 (147Sm/144Nd =0.150 þ 2). These values are estimated assuminga log-normal distribution and are insensitive tothe exclusion of extreme values. The mean Hf/Nd ratio is 0.189 þ 6, identical with the bulk con-tinental crust estimate (0.19) of Rudnick andFountain [8] but somewhat higher than their low-er crustal estimate of 0.17. Also shown in Table 1are the p/d ratios and fractionation (f) values forthe xenoliths, where fLu=Hf = [(176Lu/177Hfsample)/(176Lu/177HfCHUR)31] and fSm=Nd = [(147Sm/144Ndsample)/(147Sm/144NdCHUR)31]. CHUR is thechondritic uniform reservoir reference used to ap-proximate the bulk Earth's present-day composi-tion. These four general groups of f values (pos-itive and negative for Lu/Hf and Sm/Ndfractionations) will give rise to coupled Hf andNd isotopic evolution into the four quadrants ofthe OHf^ONd plot: negative fLu=Hf and fSm=Nd val-
Fig. 2. Potential p/d fractionation paths for the Sm/Nd^Lu/Hf isotopic system, superimposed on the terrestrial Hf^Ndarray [12]. Fractionation parallel to the terrestrial array isproduced by coupled Lu/Hf and Sm/Nd fractionation withfLu=Hf /fSm=Nd ratios of approximately 1.5. Large arrows showdominant fractionations in crust and mantle. Smaller arrowsillustrate potential fractionation paths for sources with highand low Lu/Hf relative to Sm/Nd.
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ues will produce isotopic evolution toward nega-tive OHf and ONd values and so on as illustrated inFig. 2.
Also shown in Table 1 is F, the ratio of fLu=Hf /fSm=Nd. This is essentially a measure of the slopeof the Hf^Nd evolution of each sample based onits present-day p/d ratio. Positive slopes with Fvalues of approximately 1.5 will evolve withinthe array. Negative slopes, due to either negativefLu=Hf or fSm=Nd, will evolve out of the array. Therate at which a sample can evolve out of the arrayis a function of not only the slope of the evolution(the di¡erence between F of the sample and thatof the array) but also the size of the fLu=Hf andfSm=Nd values. Samples with more strongly posi-tive or negative f values will evolve more quicklyaway from the array.
4.3. Lu/Hf and Sm/Nd ratios and Hf^Nd isotopicevolution
The p/d compositions of all lower crustal sam-
ples are shown in Fig. 3 relative to a compilationof crustal compositions [12]. The Hf^Nd isotopicevolution of the lower crustal samples resultingfrom these p/d ratios, if we assume closed systembehavior, is shown in Fig. 4. Most lower crustalsamples, as is the case with the vast majority ofcrustal samples in general, have subchondritic Sm/Nd and Lu/Hf ratios and plot in a broad band inthe lower left quadrant of Fig. 3. These coherentfractionations give rise to nearly parallel Hf^Ndisotopic trends within the array (Fig. 4a). Thistype of Sm/Nd and Lu/Hf fractionation in crustalsamples is ultimately produced by enrichment ofmore incompatible elements in magmas duringmelting processes. This is true regardless ofwhether the samples are mantle melts and arenew to the crust (e.g. [13]), are melts of existingcrust [48] or have had a long crustal history andare now part of the sedimentary record [12]. AllHf^Nd isotopic growth lines in Fig. 4a are pro-duced by F values (fLu=Hf /fSm=Nd) of 0.9^2.0 (de-limited by the hatched wedge in the lower leftquadrant of Fig. 3) and are representative of thetime-integrated Lu/Hf and Sm/Nd ratios of mostcrustal samples.
Other samples have negative fLu=Hf and fSm=Nd
but have slopes that cause them to diverge ob-liquely from the array (Fig. 4b). These have arbi-trarily been distinguished from the group of sam-ples having coherent fractionations on the basis ofF values 6 0.9 or s 2.0. Only one sample fromthis group (RP-8 from the Massif Central) has theshallower evolution (F6 0.9) toward the high OHf
side of the array. Ten other samples (three gran-ulites from the McBride and the Chudleigh prov-inces, two Mexican garnet-bearing metapelitesand two Mexican eclogites) have high F valuesand evolve toward the low OHf side of the array(Fig. 4b). All of these samples, however, havepresent-day O values that fall within the terrestrialarray.
The opposite p/d fractionation within the ter-restrial Hf^Nd array with superchondritic Sm/Ndand Lu/Hf values is shown in Fig. 3 by four sam-ples (83-110, 83-158, M-7 and MI-6). These sam-ples have positive fLu=Hf and fSm=Nd values andevolve toward positive OHf and ONd values (Fig.4c). Although this is the dominant composition
Fig. 3. Plot of 147Sm/144Nd vs. 176Lu/177HfCHUR compositionof granulite samples relative to recent and ancient muds [12],and continental crust [12]. This shows to a ¢rst approxima-tion that the fractionations of Lu/Hf and Sm/Nd in the low-er crust are broadly similar to that of the upper continentalcrust. Gray symbols represent garnet-bearing samples; opensymbols represent garnet free samples. Also shown on thisdiagram are four garnet granulites from Kilbourne Hole(crossed circles; data of [11]). Two samples have extremelyhigh Lu/Hf ratios, 1^2 orders of magnitude higher than allother lower crustal samples analyzed here. Dashed lines indi-cate present-day 147Sm/144Nd and 176Lu/177Hf CHUR values.
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and fractionation characteristic of the depletedmantle reservoir, it is rare among continentalcrustal samples because of the di¡erentiationprocesses inherent in their formation. Most crus-tal samples derived from the depleted mantle havepositive initial OHf and ONd values, indicative ofpositive time-integrated f values, but present-daysubchondritic p/d ratios (negative f values) thatnow cause them to evolve toward negative OHf
and ONd values. Also shown on Fig. 3 are twosamples from the Chudleigh Province (83-115and BC) that have superchondritic Sm/Nd valuesand near-chondritic Lu/Hf values, which cause
them to evolve below the array with slightly neg-ative F trajectories (Fig. 4c).
The samples with the largest deviation from`normal' Lu/Hf and Sm/Nd fractionations andthus with the greatest potential for evolving toHf and Nd compositions out of the terrestrialarray are those with superchondritic Lu/Hf andsub- or near-chondritic Sm/Nd (Fig. 4d). Thereare ¢ve examples of these: one each from theFrench Massif Central (RP-11) and ChudleighProvince (83-107) and three from the McBrideProvince (83-162, 85-114 and 85-108). Althoughall these samples have trajectories that will evolve
Fig. 4. Hf^Nd evolutionary paths for granulite samples based on their present-day Lu^Hf and Sm^Nd isotopic compositions.Open circles represent present-day compositions. The length of all arrows corresponds to 1 Ga of evolution assuming closed sys-tem behavior. Intermediate circles represent compositions at 0.5 Ga. Background samples of the terrestrial Hf^Nd array are thesame as in Figs. 1 and 2. The crossed circles in (d) are garnet granulites from Kilbourne Hole (data of [11]). The Hf^Nd growtharrows for these two samples are only 25 Ma with intermediate points at 10 Ma. The position of the present-day compositionsof these two samples still within the terrestrial Hf^Nd array in spite of the rapid radiogenic Hf growth of these samples demon-strates that the p/d ratios of these samples are recently acquired features, 6 25 Ma. See text for further description of individualpanels.
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toward anomalous Hf^Nd isotopic compositions,with one exception (85-108), all have present-dayisotopic compositions that are within the array(Fig. 4d).
5. Discussion
5.1. Residual garnet and high Lu/Hf reservoirs inthe lower crust?
Anomalously high Lu/Hf ratios in a source re-gion can be the result of two primary processes:melt extraction in the presence of garnet to pro-duce higher Lu/Hf in a restite, or crystallization of
garnet from a magma, resulting in high Lu/Hf ina cumulate. Both scenarios involve the role ofgarnet, which has a high partition coe¤cient forheavy rare-Earth elements and results in the pref-erential retention of Lu over Hf. Residual garnetwill thus have high Lu/Hf that will evolve tohighly radiogenic Hf isotope compositions overtime [48,50]. However, if the garnet in these sam-ples is instead a metamorphic phase, then enrich-ment of Lu/Hf will not occur, and we would notexpect production of radiogenic Hf.
The latter appears to be the case for most of thelower crustal samples analyzed in this study.Although more than three-fourths of the samplesare garnet-bearing, there is scant evidence that the
Fig. 5. Chondrite-normalized REE patterns of granulite samples: (a) samples with Hf^Nd evolution within array (Fig. 4a); (b)samples with �fLu=Hf and �fSm=Nd values (Fig. 4c); (c) samples evolving to compositions above terrestrial array (Fig. 4d); (d) Kil-bourne Hole garnet granulite samples [11] (Fig. 4d). Other REE data are from [23,29,34,35,45]. Hf generally behaves similar toLREEs in terms of partitioning between melts and solids appropriate to this study. The two xenoliths from this study that doshow a modest garnet e¡ect (83-162 and 85-114) are shown in Fig. 4d by the shaded circles.
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garnet in these samples is a residual phase from aprior melting event (Fig. 3). Garnet-bearing sam-ples exhibit the same range in p/d ratios as con-tinental crust. There is no correlation betweengarnet-bearing samples and elevated Lu/Hf ratios.
In a study of lower crustal granulite xenolithsfrom Kilbourne Hole, New Mexico, Scherer andothers [11] found extremely high Lu concentra-tions (7^8 ppm) and Lu/Hf ratios (176Lu/177Hfof 0.93 and 1.30) in two garnet-bearing granulitexenoliths, which clearly re£ect preferential parti-tioning of Lu over Hf in garnet (Fig. 3). Thesexenoliths also have slightly superchondritic Sm/Nd ratios (147Sm/144Nd of 0.297 and 0.301). Theextreme elevation of Lu/Hf in these samples rela-tive to all the lower crustal samples analyzed inthe present study (Fig. 3) results in steep and rap-id production of radiogenic Hf: Hf evolves by 64and 86 OHf units in 100 million years, with onlynegligible Nd growth (V1 ONd unit) over the sametime. This rapid radiogenic Hf growth is plottedin Fig. 4d for the Kilbourne Hole samples(CKH39 and CKH64). Note that, in contrast tothe growth trajectories for all the other sampleswhose total length corresponds to 1.0 Ga (withintermediate marks at 0.5 Ga), the growth linesillustrated for the KBH samples represent only 25Ma, with intermediate marks at 10 Ma. (Fig. 4d).These isotope systematics in the Kilbourne Holesamples suggest that garnet formed as a residualphase during early magmatic processes (6 25 Ma)in the Rio Grande Rift [11]. Clearly, if a sourcesuch as this was volumetrically signi¢cant in thelower crust and was allowed to evolve for hun-dreds of millions of years, it would be easily rec-ognizable by its Hf isotopic signature.
How volumetrically important might such lith-ologies be? The widespread occurrence of a highLu/Hf reservoir in the deep crust was what Ver-voort and Patchett [48] searched for in a varietyof Precambrian granites derived by melting ofpre-existing (s 300 Ma older) crust. All of thesesamples, however, had Hf and Nd isotopic com-positions that plotted within the terrestrial array.Vervoort and Patchett [48] concluded that eithergarnet is not a widespread residual phase in themid to lower crust, or that such high Lu/Hf gar-net-bearing assemblages do not contribute to
magmas originating from or passing through themid to lower crust [48].
Lower crustal samples from our study that aremost likely to exhibit a radiogenic Hf garnet e¡ectare those with 176Lu/177Hf ratios higher thanchondritic (i.e. positive fLu=Hf values). Of these,six also have positive fSm=Nd values (Fig. 4c) andof the ¢ve samples with �fLu=Hf and 3fSm=Nd val-ues (Fig. 4d), three (RP-11, 83-107 and 85-108)have superchondritic Lu/Hf ratios due to mainlylow Hf concentrations (all = 1.2 ppm), rather thanelevated Lu contents (all = 0.3 ppm Lu; Table 1).Two McBride Province samples (83-162 and 85-114) have modal garnet [35] and do show a mod-est garnet e¡ect. These samples have relativelyhigh Lu concentrations (V1 ppm) which resultin elevated Lu/Hf ratios (0.036 and 0.046). TheseLu/Hf ratios, however, are still only slightlysuperchondritic and are quite modest comparedto the two Kilbourne Hole garnet granulites [11].
The Lu^Hf and Sm^Nd systematics of thesesamples are re£ected in their REE patterns.Most granulite xenoliths (Fig. 5a) have broadlysimilar REE patterns with LREE enrichment,Eu anomalies (both positive and negative) and£at to HREE-depleted patterns. All of the sam-ples in Fig. 5a have Hf and Nd isotopic compo-sitions that plot within the array. In contrast, theKilbourne Hole garnet granulites with high Lu/Hfratios have pronounced LREE depletion andHREE enrichment, characteristic of residual gar-net (Fig. 5d). The two McBride samples with amodest garnet e¡ect (83-162 and 85-114) have £atto slightly enriched HREE, but with much lowerabundance of HREE than the Kilbourne Holegarnet granulites. Considering the lack of evi-dence for residual garnet in the samples in thisstudy, it is not surprising that these lower crustalsamples show no diversion from the terrestrialHf^Nd array.
The samples in this study were not selected tosearch for a radiogenic Hf garnet e¡ect but ratherto give a ¢rst-order view of Hf^Nd isotopic sys-tematics of the lower crust from well character-ized suites of samples. Based on this initial survey,residual garnet-bearing assemblages with hightime-integrated Lu/Hf ratios do not seem to bea widespread feature of the lower crust. Although
EPSL 5527 2-8-00
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most of the samples analyzed here are garnet-bearing, it is clear that most of this garnet isnot a residual phase. Of the 50 samples we haveanalyzed, only two samples exhibit a modest gar-net e¡ect and even in these samples the radiogenicHf growth is rather slow and has been insu¤cientfor the samples to evolve out of the terrestrial Hf^Nd array.
5.2. Coherent Hf^Nd behavior in the silicate Earth
There are three main observations that can bemade about the Hf^Nd data of the lower crustalxenoliths we have examined in this paper. First,the lower crustal samples span a wide range ofHf^Nd isotopic compositions that mirror the ter-restrial array. It appears, therefore, that we havesampled a representative range of Hf^Nd isotopiccompositions and p/d ratios in the lower crust.Second, these samples have a wide variety of p/dratios, which have produced Hf^Nd isotopic evo-lutionary paths in many divergent directions. Themajority of these samples, however, have isotopicgrowth that tracks along the terrestrial Hf^Ndarray. Third, in spite of this range of fractiona-tions and evolutionary trajectories, all granulitesamples, with one exception, have evolved topresent-day isotopic compositions within the ter-restrial array. Thus the lower crust appears to bebroadly similar to upper crustal samples in termsof overall Hf^Nd isotopic composition and evo-lution. We do not imply that there are no res-ervoirs with distinctive Hf^Nd isotopic com-positions. Indeed, ferromanganese crusts aredemonstrably radiogenic in Hf and plot along atrend at an oblique angle to the Hf^Nd array [51].Other reservoirs (e.g. lithospheric mantle [52] ; 1.4Ga anorogenic granites [50]) are suggested to haveHf^Nd isotopic compositions distinct from themantle OIB array. What we do imply is that, toa ¢rst order, the upper and lower crustal reser-voirs are similar.
This ¢rst-order coherency of Hf^Nd isotopesand parallel Lu/Hf and Sm/Nd fractionations inthe crust and mantle is a surprising outcome ofrecent Hf^Nd isotopic investigations of variousterrestrial reservoirs [12]. This contrasts markedlywith the Hf^Nd isotopic evolution of lunar [53,54]
and Martian [55] samples which record highly di-vergent Lu/Hf and Sm/Nd fractionations after theprimary di¡erentiation of these bodies. None ofthe minerals that account for substantial fraction-ation of Sm/Nd and Lu/Hf seems to achieve Hf^Nd decoupling in the terrestrial system. The over-all crust^mantle coherency in the terrestrial Hf^Nd array also seems to re£ect e¤cient mixingprocesses of a dynamic Earth: mantle convection,homogenization in the crust via sedimentary pro-cesses, and recycling of crustal materials back intothe mantle [12].
Within the lower crust, there seems to be arange of p/d fractionations capable of producingdivergent Hf^Nd evolution. The reason these donot result in signi¢cant isotopic divergence fromthe terrestrial array may simply be due to therecent timing of these p/d fractionations and/orthe scale of lower crustal heterogeneities.
A striking example of a young fractionationevent is in the contrast between the extreme176Lu/177Hf ratios in the Kilbourne Hole garnetgranulites and their rather normal 176Hf/177Hf ra-tios. In the Kilbourne Hole case, this inconsis-tency is explained if their elevated Lu/Hf ratioswere produced by very recent fractionation(6 25 Ma [11]). This age corresponds to the ini-tiation of ma¢c magmatism of the Rio GrandeRift but is much younger than the protolith age(ca. 1.6 Ga [56]) of most lower crustal xenoliths inthat region.
Perhaps the most signi¢cant reason we do notsee large Hf^Nd isotopic divergence from themantle array is due to the size of the xenolithsrelative to lower crustal heterogeneity. Most xe-noliths are small compared to the compositionallayering often present in these samples and arecertainly much smaller than the heterogeneity be-lieved to exist in the lower crust. Therefore, someof the divergence seen in coupled Hf^Nd evolu-tion (e.g. Fig. 4b,d) may re£ect p/d fractionationsand elemental variations that exist on the scale ofsmall xenolith samples, but not on a larger (res-ervoir) scale.
Some of the interest in the Hf^Nd isotopiccomposition of the lower crust has been in itsrelationship to the upper crust, mantle and theBSE reference. Blichert-Toft and Albare©de [21]
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have argued that the BSE lies signi¢cantly belowthe terrestrial array and hypothesized the exis-tence of a hidden reservoir in the Earth neededto balance terrestrial compositions. Others [12,57]have argued that the mismatch between BSE andthe terrestrial array may be an artifact due to theuncertainty in the Lu^Hf and Sm^Nd chondriticreference points.
Our data suggest that the lower crust is similarto the upper crust in terms of both its present-dayp/d values (Fig. 3), Hf/Nd ratios, and time-inte-grated Lu^Hf and Sm^Nd evolution (Fig. 4). Wehave examined only a few xenolith suites in thepresent paper and these may not be representativeof the entire lower crust. However, the lack ofsigni¢cant HREE enrichment in the vast majorityof lower crustal xenoliths [58] suggests that our¢ndings are globally relevant. As a whole, thelower crust does not appear to be a reservoirwith a unique Hf^Nd composition. Thus, as istrue for Sm/Nd, Lu/Hf ratios are not greatly frac-tionated by lower crustal processes and the lowercrust does not appear to be a reservoir with along-lived isotopic history distinct from the uppercrust.
In closing, we o¡er the caveat that the xenolithswe have examined are all from post-Archean ter-ranes and it is possible that the Hf isotopic com-position of the lower crust and its formation inthe Archean is fundamentally distinct from thepost-Archean. Evidence for this comes from theoccurrence of TTG (Trondhjemite^Tonalite^Granodiorite association) magmas in the Arche-an. The TTGs are characteristically depleted inHREEs, indicative of residual garnet in theirsources. It is possible that these magmas and theirsource regions will evolve to compositions belowand above the Hf^Nd terrestrial array, respec-tively. To our knowledge, there have been no Hfisotope analyses of TTG samples that have astrong HREE-depleted character. Nevertheless,we have not observed anomalous Hf isotopiccompositions, either initial or present-day, inany of the Archean samples examined thus farincluding Archean juvenile (mantle-derived) sam-ples [13], Archean shales [12], Archean komatiites[16,17] and Precambrian granitoids melted fromArchean crust [48].
Acknowledgements
We are grateful to Philippe Telouk for his ex-pertise in maintaining the P54 in top running con-dition and Joaquin Ruiz and Diana Meza-Figuer-oa for providing the Mexican samples. We thankChris Hawkesworth, Clark Johnson and VincentSalters for their constructive and helpful reviews.This research was funded by NSF Grants EAR-9526536 and EAR-9814885 and by the ProgramDynamique des Transports Terrestres of InstitutNational des Sciences de l'Univers for the analyt-ical work at the Ecole Normale Superieure deLyon. NSF supplemented EAR-9526536, and en-abled this collaboration between the University ofArizona and Lyon.[AH]
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