For permission to copy, contact editing@geosociety.org© 2011 Geological Society of America

Hydrodynamic fractionation of zircon age populations

Rebecca L. Lawrence1, Rónadh Cox1,†, Russell W. Mapes2,§, and Drew S. Coleman2

1Geosciences Department, Williams College, Williamstown, Massachusetts 01267, USA2Department of Geological Sciences, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, USA

295

GSA Bulletin; January/February 2011; v. 123; no. 1/2; p. 295–305; doi: 10.1130/B30151.1; 7 fi gures; 3 tables; Data Repository item 2010138.

†E-mail: rcox@williams.edu§Current address: ExxonMobil Corporation, Houston, Texas 77210, USA

ABSTRACT

Zircons in transport in the modern Ama-zon River range from coarse silt to medium sand. Older grains are smaller on average: Mesozoic and Cenozoic grains have aver-age equivalent spherical diameter (ESD) 122 ± 42 µm (lower fi ne sand), whereas grains >2000 Ma have average ESD 67 ± 14 µm (up-per coarse silt). As a full Wentworth size class separates the two values, zircons in these age populations are hydraulically distinct.

Host sand size is correlated with average size of co-transported zircons, implying hydrodynamic fractionation. Zircon size is positively correlated with percent medium sand, and inversely correlated with percent very fi ne sand (p <0.0001 in both cases). In samples with >50% medium sand, average zircon size is 100 µm, compared with 80 µm in samples with >50% very fi ne sand. We infer from these data that zircon deposition is not size-blind, and that zircons track with hydraulically comparable sand grains. As different aged grains tend to have different characteristic sizes, this indicates the pos-sibility of hydrodynamic fractionation of age populations.

Five samples representing different hydro-dynamic microenvironments of a single dune present signifi cantly different detrital zircon age spectra, apparently the result of hydrau-lic processes. Peak mismatch (age peaks fail-ing to overlap at 2σ level) is the most com-mon disparity; but age populations present in some samples are missing from other samples. The lack of correspondence among the samples appears to exceed that attribut-able to random sampling. We conclude that hydrodynamic fractionation of zircons and zircon-age populations does occur. Zircon size should therefore be taken into consider-ation in detrital zircon provenance analysis.

populations are likely, therefore, to have differ-ent (and unpredictable) size characteristics.

Detrital zircon geochronology often does reveal size differences among zircon popula-tions. For example, Sager-Kinsman and Parrish (1993) used detrital zircon age data to differ-entiate metasedimentary sequences from two tectonostratigraphic terranes, but the distinct age differences between the two sequences also correlate with sediment grain size: the fi nest zir-con grains (pre-analytical weights) yielded the youngest ages. Data in Chen et al. (1995) like-wise show a correlation between grain size and zircon age. Miller and Saleeby (1995) sorted zir-cons into size fractions that yielded signifi cantly different age characteristics on multigrain anal-ysis. Gehrels et al. (1996) found a population of detrital zircons from the Alexander terrane in southeast Alaska present only in smaller size fractions from one formation, and which were signifi cantly older than any other zircons found (1.0–1.3 Ga versus 400–500 Ma). Stewart et al. (2001) analyzed grains >100 µm (sieve retention size), except for one sample in which all grains were ~80 µm. The latter sample had a unique, single peak age. In grain-size data from image analysis of dated zircons presented by Sircombe et al. (2001), there is a weak but statistically sig-nifi cant correlation between age and grain-size parameters (younger grains tend to be longer or have greater values for width × length). In Kock et al. (2007), Proterozoic grains are all <200 µm long, whereas Phanerozoic grains range up to 380 µm. Clearly, zircon age populations com-monly have different characteristic size ranges.

Age populations with different sizes can—and will—be sorted differently. Heavy minerals are substantially smaller than co-transported, hydraulically equivalent quartz sand grains (Ru-bey, 1933; Rittenhouse, 1943), and are system-atically concentrated in the fi ner size fractions of the host sand (Garzanti et al., 2008). The heavy minerals tend to nestle deep among the host grains at deposition, hindering re- entrainment

INTRODUCTION

Large–data set detrital zircon geochronology has changed the way we investigate paleogeog-raphy, permitting us to examine source- sediment connections and to reconstruct the distribu-tion of crystalline terranes on regional and continental scales (Rainbird et al., 1992; Sir-combe, 1999; Rainbird et al., 2001; Gehrels et al., 2003; Miller et al., 2006). Although robust statistics are provided by the tens to hundreds of zircons analyzed per sample, the number of samples used to characterize each location, stratigraphic interval, or rock unit is often very small: commonly just one sample per compari-son group. This approach assumes that zircons measured from a single sample are fully repre-sentative of provenance for the unit, location, or interval, and presupposes that hydrodynamic fractionation does not occur during transport and deposition of the detrital zircon grains, so that differences among detrital zircon age populations refl ect provenance differences only. Error analysis in detrital zircon provenance studies focuses on reporting analytical errors (e.g., Morton et al., 2009b; Neumann et al., 2009; Perry et al., 2009) or considers statistical problems in interpretation (Sircombe, 2000a; Sircombe, 2000b); but the work presented here indicates that hydrodynamic fractionation can be a source of variability in zircon age popula-tions, and hence a source of error in comparative provenance analysis.

The fact underpinning this analysis is that zircons grow to different sizes in different ig-neous and metamorphic environments (e.g., Rubatto et al., 2001; Corfu et al., 2003): one pluton, volcano, or gneiss may contain zircons that are larger or smaller than another, or may contain multiple generations of zircons grown at different rates under different conditions, with consequently different shapes and sizes. Zircons also abrade in transport, and so decrease in size with sedimentary cycling. Different zircon age

Lawrence et al.

296 Geological Society of America Bulletin, January/February 2011

and transport (Slingerland, 1977; Reid and Frostick, 1985). The extent of fractionation will depend on many factors in the depositional environment—including host sediment grain size, the degree of sorting, the fl ow regime, and bed morphology, all of which vary from time to time and from place to place—but in general, the smaller the heavy mineral, the more marked the effect (Komar and Wang, 1984). Komar et al. (1989) demonstrated that selective sorting can skew results from factor analysis by intro-ducing new factors and producing random irreg-ularities in the spatial patterns; and Garzanti et al. (2008) showed that settling-rate equivalence is the dominant cause of size-dependent com-positional variability in siliciclastic sediments. These principles, although articulated to explain fractionation among different heavy minerals, also imply that there should be differential sort-ing within single-mineral (e.g., zircon) popula-tions as a function of grain size.

Zircons dated for provenance analysis gen-erally range in size from coarse silt (>30 µm) to medium sand (<500 µm). Applying the 0.58 phi-unit size shift predicted from the Stokes’-law–derived, settling-equivalence formula—a minimum estimate, as empirically derived size shifts are up to twice this value (Garzanti et al., 2008)—the size range of analyzed zircon corre-sponds hydrologically to quartz sand sizes in the range 50 to 750 µm (coarse silt to coarse sand). With such a wide range in grain size, differen-tial sorting is bound to occur; and if there are size differences among age populations, then the population age spectrum will be skewed in consequence. Much of the differential sorting is likely to be local: examples include segregation up the stoss sides of dunes because of variations in fl ow velocity and bed shear stress over the bedform; or the mass concentrations that com-monly line the surfaces of scour pits (Slinger-land and Smith, 1986). Sampling merely lag or heavy-mineral accumulations, for instance, means that smaller zircons fractionated out of the lag are missed. A single sample may not therefore cover a suffi cient range of hydrody-namic microenvironments to fully retrieve the range of zircon sizes (hence possibly age popu-lations) in local transport.

The problem of incomplete sampling becomes more critical as the amount of analyzed sediment decreases: the smaller the depositional volume over which the sample integrates, the greater the possibility that local, small-scale fractionation processes may affect the range of zircon grain sizes captured. As analytical techniques have im-proved, sample size has decreased; so although much work is based on samples weighing several kilograms (e.g., Ansdell et al., 1992; Rainbird et al., 1992; Chen et al., 1995; Gehrels et al., 2003;

65˚W

10˚S

75˚W

0 1000 500

km

0˚

55˚W

Sample location

Amazon River and/or tributary

Amazon drainage basin

1

2

9 14

15

8763

1018

1917

D

2

Figure 1. Map of the Amazon basin, showing locations of the 14 sample sites. Sample num-bers correspond to those in Mapes (2009). Location D is the site for DUNE samples A–E.

Kalsbeek et al., 2008), the rock mass represented by a couple of hundred zircons is now commonly a kilogram or less (e.g., Knudsen, 2001; De-Graaff-Surpless et al., 2002; Cawood et al., 2003; Hartmann et al., 2006; Morton et al., 2009b). Single samples—especially small ones—may therefore provide an inaccurate view of the detri-tal zircon populations present.

In this contribution we examine the relation-ship between zircon grain size and age along the length of the Amazon River basin. We show fi rst that different age populations have different characteristic sizes. We then present zircon data from fi ve samples representing different mi-croenvironments of a river bedform, and show that there are statistically signifi cant differences among age populations recorded in different samples from a single location.

SAMPLING AND ANALYSIS

We sampled sand in active transport at 14 locations along the Amazon River (Fig. 1). The regional data set and sampling strategy are de-scribed in Mapes (2009). At one location we collected fi ve separate samples (DUNE A–E), to examine age populations in the hydrodynamic subenvironments of a single bedform.

The bedform sample location DUNE (2.4086°S, 54.6232°W) was 10 km northeast of

Santarém (Fig. 1), on the outer edge of a mid-channel island built from scroll-bar deposits. Annual water-level fl uctuations in this area are 5.4 m (Novo et al., 2006); so at high water, the sample site is inundated, several hundred me-ters offshore of the island. Low-amplitude du-noid bedforms (sensu Leeder, 1999) at the site (Fig. 2) had been in recent alluvial transport, and became emergent as water levels fell at the onset of the dry season. Active wind ripples formed a thin aeolian layer on the bedform sur-faces, beneath which lay fl at-laminated and low-angle, cross-bedded sand. The bedforms were ≈1.25 m high with wavelength ≈20 m, formed by sand migration on the submerged portion of the scroll-bar island system. We trenched one dunoid, close to the water’s edge (hence most recently emergent), at fi ve places along a tran-sect normal to the bedform crest (Fig. 2). The samples were collected from beneath the wind-rippled layer, within the alluvial deposits. A gal-lon bag (few kg) of sand was collected at each site. Samples were quantitatively split, and a 400 g aliquot was brought to the UNC Chapel Hill for analysis.

Grain-size distribution of the bulk sand was measured following methods of Folk (1965). We used stacked U.S. standard sieves at quarter-phi intervals, ranging from 4 ϕ (63 μm, lower bound-ary for fi ne sand) to −0.75 ϕ (1.68 mm, very

Hydrodynamic fractionation of zircon age populations

Geological Society of America Bulletin, January/February 2011 297

coarse sand). Sizes less than 4 ϕ (coarse silt and fi ner) were collected in the basal pan. Samples were shaken for 5–7 min, and the sieve stack was allowed to sit briefl y to permit settling of fi nes be-fore being opened. Size distribution and sorting parameters were calculated using GRADISTAT (Blott and Pye, 2001). Detailed methods are re-ported in Lawrence (2007); sand size data are in GSA Data Repository Appendix DR1A1.

Zircons were separated and prepared at the University of North Carolina at Chapel Hill. To maximize zircon retrieval and to avoid pref-erential loss of small zircons, we bypassed the hydraulic extraction step; and in recognition of the bias that can be introduced by magnetic separation (Sircombe and Stern, 2002), we ran the samples only once, at 0.5 A, to remove the most paramagnetic minerals while avoiding sep-arating out any of the zircons. We used standard heavy-liquid separation techniques (see Law-rence [2007] for full sample preparation details). Zircons were fi nally mounted in epoxy, and the mount was polished to reveal the grain interiors.

Zircon grain length and width (X and Z) were measured directly from the polished mounts via light microscope, immediately prior to laser ablation. We approximated the third axis (Y) as equivalent to the measured Z axis. We converted the XYZ dimensions to equivalent spherical di-ameter (ESD; also known as nominal diameter; Garzanti et al., 2008) to permit hydrodynamic comparisons among the zircons and between zircons and quartz sand (Komar and Reimers, 1978; Garzanti et al., 2008).

Uranium-lead (U-Pb) dating was carried out by laser ablation–multicollector–inductively

AAABBB

CCC DDD E

*****

* ** **

AB

C D E

**

* * *

A DB

E

C

Figure 2. Sample site DUNE, at 2.4086°S, 54.6232°W, which had been recently exposed by dropping water levels. Locations of the fi ve samples (DUNE A–E) are indicated on the photograph.

coupled plasma mass spectrometry (LA-MC-ICPMS) at the University of Texas at Austin and the University of Florida, Gainesville (Lawrence, 2007; Mapes, 2009). The full U-Pb data set for the dune samples (DUNE A to E) is in Appendix DR1B (see footnote 1); data for the rest of the Amazon River samples are in Mapes (2009). In our analysis, we used the 207Pb/206Pb age for zircons older than 1.0 Ga and the 206Pb/238U age for younger grains, be-cause at 1.0 Ga the 206Pb/238U measurement error (which increases with age) becomes ap-proximately equal to the 207Pb/206Pb measure-ment error (which is larger for younger grains; see Lawrence [2007] for error analysis). If the U/Pb ratios changed suddenly during analysis (suggestive of structural complexity within the zircon grain), the data were split, and two ages were calculated for the grain. Only con-cordant ages were used for analysis, so mixed core-rim ages are not a source of complexity in the data set. We did not correct for common Pb. The common-Pb correction is problem-atic in LA-MC-ICPMS, both because of the very minor amounts of 204Pb present in zircon and because of the isobaric interference from 204Hg; and we were unable to measure 202Hg (required to quantify the 204Hg interference) because the ion counters were static. The uncorrected 206Pb/204Pb ratios for most of our measured grains were high, suggesting that common Pb was not signifi cant; but in any case, common-Pb problems would manifest as discordance; and our analysis was restricted to concordant data.

The average number of grains analyzed per river sample was 163 (Mapes, 2009), and for the DUNE location, 110 grains were dated for each of the fi ve samples (Appendix DR1B [see footnote 1]). The data were fi ltered to remove discordant grains, with concordance defi ned as:

Concordance =238U 206Pbage

207Pb 206Pbage

×100.

But because 207Pb/206Pb ages are unreliable for young grains, using the 207Pb/206Pb ages to defi ne concordance resulted in the preferential elimina-tion of young grains. So a separate calculation, using the 207Pb/235U age and based on results of Chang et al. (2006) and Tiepolo (2003), was used for grains younger than 300 Ma:

Concordance (grains < 300 Ma) =

238U 206Pbage

235U 207Pbage

×100.

Our cutoff values for inclusion of data in subse-quent analysis was concordance = 100 ± 10%, and the yield of acceptable grain ages ranged from 50 to 188 per sample. The smallest num-ber of concordant grains in a single sample was 50 (in sample A, Table 1). This corresponds to a 2% chance of missing populations comprising 12% of the total population, and a 20% chance of missing age populations that are 8% of the total. For N = 71 (as for sample B, Table 1), the probability of missing a 10% age component is <2% (using statistics of Vermeesch, 2004).

To calculate numbers and proportions of age components in each sample, we used mixture modeling (Sambridge and Compston, 1994), implemented by means of the program MIX (version 21.1.97, by K. Gallagher and M. Sambridge). Iterative application of the mixture-modeling algorithm, each time in-crementing the number of age components, generates the optimum number of age compo-nents to satisfy the frequency distribution of

1GSA Data Repository item 2010138, Appen-dixes A and B, is available at http://www.geosociety.org/pubs/ft2010.htm or by request to editing@ geosociety.org.

Lawrence et al.

298 Geological Society of America Bulletin, January/February 2011

the data. Three conditions characterize the op-timum number of components. First, the misfi t of the solution (the negative log of the like-lihood function) is stabilized: as the number of age components increases toward the opti-mum, the misfi t value decreases; but beyond the optimum, further increase in the number of components produces little or no reduction in the misfi t value (Sambridge and Compston, 1994). Second, the χ2 statistic is minimized: χ2

decreases with increasing component number until the optimum number is reached, at which point it levels off. Note that χ2 is not used as a measure of statistical reliability but as an indicator value. Third, the ages and propor-tions produced by MIX visually match the frequency distribution of the detrital zircon data (Sambridge and Compston, 1994). For the data presented here, the optimum number of age components (Table 1), as determined by χ2 and misfi t values, matches the number of peaks in the independently generated age probability curves (which were plotted using AGEDISPLAY, Sircombe, 2004).

RESULTS AND DISCUSSION

Zircon Grain Size and Age are Correlated

Zircon grains measured from the Ama-zon River system span a full order of magni-tude in grain size (Fig. 3), from medium silt size (near 30 µm ESD) to medium sand (near 300 µm ESD). The data also show that zircon grain size and age are not independent: the aver-age grain size of older grain populations is less than that of younger age components, and only a few age classes include large grains (Fig. 3). There are two average-size maxima, in the Mesozoic–Cenozoic and late Middle Protero-zoic (Grenvillian: ≈1.1 Ga) age populations,

TABLE 1. DETRITAL ZIRCON AGE POPULATIONS FOR THE FIVE DUNE SAMPLES

A B C D EAge (Ma)

± (Ma)* N Percent

Age (Ma)

± (Ma) N Percent

Age (Ma)

± (Ma) N Percent

Age (Ma)

± (Ma) N Percent

Age (Ma)

± (Ma) N Percent

<200 – 0 0 <200 – 2 3 <200 – 1 1 <200 – 4 6 <200 – 3 5210 22 3 6 218 10 8 11 265 17 4 6 247 9 13 20 221 9 9 16332 30 5 10 306 22 3 4 481 32 6 9 548 23 11 17 528 22 10 17550 38 9 18 490 38 3 4 657 34 11 16 1005 33 13 20 810 52 5 9976 42 9 18 675 32 12 17 1088 27 18 26 1233 35 10 16 1150 52 13 221170 24 8 16 1006 22 17 24 1453 22 15 22 1448 51 5 8 1395 43 4 71491 22 13 26 1197 20 9 13 1710 30 4 6 1686 35 5 8 1844 36 11 191758 50 2 4 1458 33 4 6 1995 41 8 12 >2000 – 3 5 >2000 – 3 51954 42 1 2 1754 18 9 13 >2000 – 2 3>2000 – 0 0 >2000 – 4 6

Note: Populations were calculated by mixture modeling, using methods of Sambridge and Compston (1994) as implemented in the program MIX (written by K. Gallagher and M. Sambridge). The data sets are large enough to give statistically reliable information about the constituent populations: using Dodson’s (1988) test for statistical adequacy, the exclusion probability is less than 1% for age groups comprising 10% of each zircon population. The mixture modeling results are best-fi t age ranges that represent a probability density derived from the detrital grain suites: i.e., they are related to but not the same as the absolute age ranges of source-rock suites (Sircombe, 2000b). *95% confi dence on the population mean age, given by 2σ standard deviation on the estimated age after 60 iterations of the model.

Log y = 4.71 - 0.0003 xP = 0.0001

N = 897

100

90

80

70

60

50

40

30

200

300

Equ

ival

ent s

pher

ical

dia

met

er (

µm)

0 500 1000 1500 2000 2500 3000

Age (Ma) (100% ± 10% concordant)

Medium sand

Very fine sand

Fine sand

Coarse silt

Figure 3. Zircon size as a function of age for grains from 14 locations along the Amazon River. The number of grains represented is 897, all with ages 100 ± 10% concordant. Equiv-alent spherical diameter (ESD) is the cube root of the product of the three grain axis lengths (Garzanti et al., 2008). Raw grain-length data show the same trend, but because length-width ratios vary by a factor of 6 (Lawrence, 2007), ESD is a more robust measure of detri-tal grain size. The trend is signifi cant at the 99% level (see P statistic on fi gure), and is robust at that level, even if the six small grains >2400 Ma are removed. Although the uncertainly in age determinations is not incorporated into the linear regression analysis, the scale of that uncertainty (a few percent of the age; Appendix DR1B [see footnote 1]) is small relative to the scale of the X axis. Plotting the data with their age error bars does not change the trend. The Wentworth size-class boundaries for silt and sand are shown to emphasize that a sub-stantial fraction of the age distribution is concentrated in the fi ne grain sizes.

Hydrodynamic fractionation of zircon age populations

Geological Society of America Bulletin, January/February 2011 299

and an average-size minimum for grains >2 Ga. Mesozoic and Cenozoic grains, for example, have average ESD 122 μm (with standard error 42 μm); whereas grains older than 2000 Ma have average ESD about half that: 67 μm (±14 μm). The average size of the younger grains is near the lower bound for fi ne sand, and that of the older grains is about the upper limit for coarse silt: i.e., a full Wentworth size class separates the two average values, meaning that zircons in these age populations are hydrodynamically different from one another.

Host Sand Grain Size is a Predictor of Average Zircon Grain Size

To evaluate whether the different size grades of zircon are fractionated during transport, we compared detrital zircon sizes with the grain-size distributions of their host sands, and found statis-tically signifi cant relationships (Fig. 4). The aver-age grain sizes of the sand sample and the zircons it contains show a correlation that is signifi cant at the 95% level (P = 0.05), but with a very low correlation coeffi cient (R2 = 0.2; Fig. 4A), so not

very persuasive. Likewise, there is a noisy, albeit statistically signifi cant correlation between the amount of coarse sand in the host deposit and the average size of the zircons yielded (Fig. 4B). These data suggest a relationship but are not in themselves convincing. The fi ner sand grades, however, return more compelling correlations: the size of zircons is positively correlated with the percentage of medium sand and inversely corre-lated with the amount of very fi ne sand (Figs. 4C and 4D). The correlations are signifi cant above the 99% level, suggesting that larger zircons

Coarse sand in host deposit (%)

Med

ian

zirc

on E

SD

(µm

)

100

90

80

70

60100 200 300 400

log y = 2.766 + log 0.33 xR2 = 0.2

P = 0.0593

Median grain size of host sand (µm)

160

100

90

80

70

600.01 0.1 1 10

log y = 4.576 + 0.04 log xR2 = 0.2

P = 0.0424

160

100

90

80

70

600.1 1 10

log y = 4.431 + 0.07 log xR2 = 0.5

P = 0.0013

160

100

90

80

70

601 10

log y = 4.822 - 0.15 log xR2 = 0.5P = 0.0016

160

Med

ian

zirc

on E

SD

(µm

)

A

DC

B

Very fine sand in host deposit (%)Medium sand in host deposit (%)

AB

CDE

AB

C D E

A

C

B

D E

AB

C D E

Figure 4. There are statistically signifi cant relationships between median size (equivalent spherical diameter [ESD]) of zircon grains (measured individually prior to U-Pb analysis) and the grain-size distribution of the host sand (derived by sieving and weighing bulk sand samples; Appendix DR1A [see footnote 1]). All trends are signifi cant above the 95% level, and those in Fig-ures 4C and 4D are signifi cant at the 99% level. Error bars show 2× standard error on the zircon size averages. The total number of zircon grains represented in these plots is 2669 (average 148 zircons per sample). Because age is not a variable, we include all zircons, not just ones with concordant ages. Black dots represent the fi ve DUNE samples; white dots are samples from 13 other locations throughout the Amazon River mainstem drainage system (see Fig. 1). DUNE samples B and C contained no coarse sand, but their median ESD values are shown at the far left of Figure 4B for comparison purposes.

Lawrence et al.

300 Geological Society of America Bulletin, January/February 2011

are tracking with the larger grains, and smaller zircons are tracking with the fi ner grained sand. The zircon sizes are not correlated with any mea-sures of sorting, skewness, or kurtosis (Lawrence, 2007): it is the proportion of hydraulically com-parable sand grains in co-transport that appears to provide the primary control.

These results make sense when considered in terms of the hydraulic equivalence of the zircons, comparing their grain sizes to those of co-transported quartz grains by applying a hydraulic size shift. Stokes’ law predicts that minerals of different density have the same set-tling velocity (i.e., will be deposited together) when the difference between their diameters, measured in ϕ (phi size units; Krumbein, 1936, 1938) is half the difference between the log

2

values of their submerged densities. The size shift for zircon relative to hydraulically equiva-lent quartz grains, based on Stokes’ equation, is −0.57 ϕ (Garzanti et al., 2008). Using an em-pirically calibrated formula that accounts also for the effects of drag coeffi cient and Reynolds’ number (Cheng, 1997), the zircon size shift is given as −0.6 to −0.9 ϕ, which compares well with values measured in natural mixed-grain populations (Garzanti et al., 2009). Applying the full range of size shift values, zircons of ESD 150 μm (2.75 ϕ) (the highest average size represented in Fig. 4) are hydraulically equiva-lent to quartz of size 2.15–1.85 ϕ, i.e., lower medium to upper fi ne sand; whereas zircons

with ESD 60–80 μm (4–3.6 ϕ) are equivalent to quartz grains 3.4–2.7 ϕ, i.e., lower fi ne to very fi ne sand. So samples with a higher proportion of medium-grained sand tend to have zircons with average sizes hydraulically equivalent to medium-grained sand (Fig. 4), and samples with abundant very fi ne sand are more likely to have zircons with average size hydraulically equiva-lent to very fi ne sand. Zircons of different sizes, as predicted by settling equivalence theory (Garzanti et al., 2008, 2009), are tracking with hydrodynamically similar host-sand grains.

Sands from a Single Dune Show Zircon Age-Population Variations

We examined sands from a single bedform (Fig. 2), to look at local variability in grain size and zircon age populations. There is a range of sand sizes within the bedform (Fig. 5), although considerably less than the grain-size variation seen in the rest of the Amazon River sample set (Fig. 4). The DUNE samples are dominated by fi ne-grained, well-sorted sand. Three of the samples (A, D, and E) are very fi ne skewed, and two (B and C) are fi ne skewed. Two are lep-tokurtic (A and E), and the other three (B, C, and D) are very leptokurtic (using methods of Folk and Ward, 1957; see Lawrence, 2007, for data). These values are consistent with river bedload transport (Singh et al., 2007), and the subtle differences among samples refl ect small-scale

A

D

B

E

C

20

40

60

80

100

0

Sand grain size (mm)0.30.10.080.06 0.2

Cum

ulat

ive

% c

oars

er b

y w

eigh

t

Very fine Fine

A DB

E

C

Figure 5. Grain-size distributions for dune sands (A–E) from sample site DUNE (shown in Fig. 2). Dune geometry and relative location of samples (not to scale) shown in inset.

Figure 6. Probability density diagrams for the fi ve dune samples (DUNE A–E). The probability axes in all graphs are at the same scale but are calibrated to facilitate compar-ison of pre-Cenozoic populations; therefore, the very tall Cenozoic peaks (an artifact of the very high precision on young U-Pb ages) are cut off. The shading by sample matches that in Figure 7. Histograms show the num-ber of grains in 100-Ma bins, but the prob-ability density function was estimated using 1-Ma time increments (Sircombe, 2004). All data are 100 ± 10% concordant. Pie diagrams show percentages of grains in fi ve broad age categories (ages in Ma, increasing clockwise), to quantify the variation among the samples (for comparison with data in Andersen, 2005, fi g. 10; see text for details).

hydrodynamic differences across the bedform (Kleinhans, 2004; Komar, 2007). Sample A, which came from the dune trough, contained a few isolated pebbles, up to small gravel in size; and sample E, taken from the base of the stoss slope (in the trough of the upstream bedform), had a small amount (less than 1%) of coarse sand grains. The largest grains in the other four samples were in the medium sand class. The very-fi ne skewness of the trough samples, for instance (Fig. 5), is consistent with a contribu-tion from suspension sedimentation within the dune-lee separation eddy. Likewise, the coars-est grains are also found in the trough samples (Fig. 4B), refl ecting lag accumulation at the base of the foreset slope.

Mixture Modeling Indicates Age-Population Differences among the Samples

So are the different hydrodynamics also re-fl ected in zircon age populations? The fi ve DUNE samples do show differences among their age populations (Fig. 6), which we quanti-fi ed and tested for statistical signifi cance using mixture modeling (Sambridge and Compston, 1994; Table 1). The 2σ ranges on the calculated population ages for the different samples are compared in Figure 7. There is substantial dis-similarity between the samples in spite of their derivation from the same locality and the same bedform. Several age populations are identifi ed in some samples but not others. For example, the mid–600s Ma population occurs only in sam-ples B and C (12 and 11 grains, respectively); the ≈1100 Ma population is in C (18 grains); the 1170–1240 Ma population is only in A, B, and D (8, 9, and 10 grains); and the 1840 Ma popula-tion is only in E (11 grains). These populations make up 13%–26% of the samples in which

Hydrodynamic fractionation of zircon age populations

Geological Society of America Bulletin, January/February 2011 301

EN = 58

1 2 3 4 5 6 7

0

Fre

quen

cy

Age (Ma)

0.0

0.5

1.0

Probability (e

-3)

DN = 64

1

3

5

7

9

11

Fre

quen

cy

0.0

0.5

1.0

Probability (e

-3)

CN = 69

1 2 3 4 5 6 7 8

Fre

quen

cy

BN = 71

1

3

5

7

9

11

0.0

0.5

1.0 P

robability (e-3)

Fre

quen

cy

0.0

0.5

1.0

Probability (e

-3)

Fre

quen

cy

1 2 3 4 5 6 7 8 A

N = 50

0.0

0.5

1.0

Probability (e

-3)

<400

E

D

C

B

A700-1299

400-699 1300-1599

>1600

300020001000

Lawrence et al.

302 Geological Society of America Bulletin, January/February 2011

they occur; so by the criteria of Vermeesch (2004), the probability of missing those popu-lations in our other samples (each comprising 50–75 grains with 5–10 subpopulations) is less than 5%. This suggests that the absence of those populations from the other samples is real.

Further examination of the age clusters shows that pairs of samples can differ substantially from one another. In the mid-Phanerozoic cluster, for example, the Permo-Carboniferous popula-tion (306 ± 22 Ma) of sample B does not over-lap with the Permo-Triassic population (221 ± 9 Ma) in sample D. In the Middle Proterozoic cluster, the 1388 ± 44 Ma age peak of sample E does not overlap with the 1491 ± 22 Ma peak in sample A. The multiplicity of the mismatched age populations, the statistical signifi cance of the separation between population mean ages (Sambridge and Compston, 1994; Sircombe, 2000a), and the low probability that popula-tions making up one-sixth to one-fourth of some samples would be absent from others (based on statistics of Vermeesch, 2004), all imply real dif-ferences among the fi ve samples.

Could it be Due to Random Sampling?But—statistical signifi cance of the interpopu-

lation variation aside—the question remains

whether the overall differences among the sam-ples are greater than those possible from random sampling of a heterogeneous background popu-lation. Andersen (2005) demonstrated the large variations in age populations that can result from random sampling; so we used his work as our comparison base. From a pool of data com-prising all published ages from a single geo-logic province (southwestern Baltica), Andersen (2005) generated ten synthetic data sets of 100 ages each. He quantifi ed the variation by isolat-ing three age brackets, each of 300 to 400 Ma duration, and examining their relative propor-tions among the ten samples. The youngest bracket, which constituted 8% of the parent data set, made up 4% to 15% of the synthetic subsets (i.e., a range of 11% in proportion outcome); the middle group, which comprised 37% of the par-ent sample, yielded 29% to 43% in the subsets (a range of 14%); and the oldest age bracket, 40% in the parent data, made up 36% to 47% (11% range) in the synthetic subsets. In sum, for age brackets making up 8% to 40% of a par-ent population, variations of 11% to 14% were found in the relative proportions of age brackets in random subsamples (Andersen, 2005).

We applied Andersen’s (2005) method to our data, to quantify the variation among our fi ve

samples and evaluate whether it was greater or less than that which Andersen had obtained by random sampling. We subdivided our age data into fi ve brackets and plotted their proportions on pie charts (Fig. 6), using breaks in the age group-ings (Fig. 7) at 400, 700, 1300, and 1600 Ma as the boundaries. We found substantially greater differences among population proportions in our fi ve samples (Table 2) than did Andersen (2005) among his ten. The proportional differences amoung our samples range from 7% to 20%, and three of our values exceeded the highest value obtained by Andersen (2005). Although our N per sample was lower than Andersen’s (we had 50–71 concordant ages per sample; Andersen’s subsets were 79–89 grains each), we also had only half the number of random-sample events (fi ve dune samples analyzed versus Andersen’s ten synthetic samples). That we fi nd a greater range of variation within our smaller set of sam-ples, strongly suggests that the variation among our DUNE samples is greater than could be ex-pected from random sampling.

It is important to point out that our compara-tive analysis with the Andersen (2005) data is qualitative and not statistical. But we argue that, in combination with the statistically signifi cant results of the mixture-modeling tests, it presents a compelling case that there is more variation among the zircon age populations in the differ-ent dune hydrodynamic environments than can be accounted for by sampling alone.

Kolmogorov-Smirnov Analysis Indicates the Samples are Quite Different from One Another

As a fi nal measure of the degree of dissimilar-ity among samples, we applied the Kolmogorov-Smirnoff (K-S) statistic, a nonparametric test that compares unbinned data from pairs of sam-ples (Guynn, 2006). Based on similarity between the cumulative distribution functions of any two data sets, the test returns a probability (P value) that the two samples were drawn from the same parent distribution, ranging from P = 0 for no correspondence to P = 1 for complete identity. In detrital zircon analysis, a P value of 0.05 (i.e., 95% statistical likelihood of nonequivalence) is the criterion for confi dent interpretation that samples have different provenance (Berry et al., 2001; DeGraaff-Surpless et al., 2003).

We know the DUNE samples come from the same overall parent population: all fi ve samples are from a single bedform. So we fully expect the P statistic to exceed 0.05 in every compari-son (Table 3). We fi nd it noteworthy, however, that in spite of the close spatial relationship of these samples, many of the P values are low. The comparison of samples D and C, for example, returns a P value of 0.11 (89% probability that they represent different parent distributions).

0

5

10

15

20

Num

ber

of g

rain

s

0 500 1000 1500 2000

Age (Ma)

A

EDCB

Figure 7. Age populations from the fi ve DUNE samples (A–E), derived by mixture modeling. Ages <200 Ma and >2000 Ma in these samples are represented by very small numbers of grains (N < 1–2 per population); so, in this fi gure we compare only the populations between 200 and 2000 Ma. The Y axis shows the number of grains in each population, and the bars represent 95% (2σ) confi dence intervals about the calculated detrital-grain population ages (see Table 1).

Hydrodynamic fractionation of zircon age populations

Geological Society of America Bulletin, January/February 2011 303

Similarly, B and C return a 64% probability that they are different. Sample D shows the most consistent difference from other distributions, with a 68% average probability that its parent population is different from those of all the other samples. We take this, together with the mixture modeling and comparison to random-sampling differences, to indicate that the differences among the DUNE samples are real. As there is no question of provenance differences, the source of the variation must be hydrodynamic fractionation among the various microenviron-ments of the bedform.

Our statistics do not permit us to address quantitatively the grain-size characteristics of the various age populations within individual DUNE samples. Although the age populations are statistically distinct (Table 1), adding size as an additional variable means that comparisons between populations are not signifi cant. Future work will hopefully quantify the grain size-age relationships at the individual sample level. The combination of observations, however—clear size-age relationships across the range of zircon

grain sizes (Fig. 2), correlation between sand grain size and co-transported zircon grain size, and signifi cant differences in age populations among samples from varying hydrodynamic settings within a single location—points to a de-trital zircon age fractionation problem.

CONCLUSIONS

The Amazon River data set shows that zircon size and age are not independent of one another, with a factor-of-two variation in the average grain size of different age classes (Fig. 3). The data presented here do not make any prediction about general relationships between age and grain size, nor about the presence or absence of trends in detrital zircon populations from other locations; but—given the variation in crystalli-zation histories of source rocks, and the range of recycling experiences of detrital grains—zircon age populations of different provenance are likely to present an assortment of character-istic sizes. Each age population will include a range—possibly a very wide range—of zircon

TABLE 2. COMPARISON OF INTERSAMPLE AGE-BRACKET VARIATION AMONG DUNE SAMPLES, USING THE APPROACH OF ANDERSEN (2005)

Age bracket(Ma) Grains in A Grains in B Grains in C Grains in D Grains in E

Count Count Count Count Count0–399 8 13 5 17 12400–699 9 15 17 11 10700–1299 17 26 18 23 181300–1599 13 4 15 5 4>1600 3 13 14 8 14

Total 50 71 69 64 58

Percent Percent Percent Percent Percent Range0–399 16 18 7 27 21 20400–799 18 21 25 17 17 7800–1199 34 37 26 36 31 111200–1599 26 6 22 8 7 20>1600 6 18 20 13 24 18

Note: Count values represent raw data for numbers of grains in each age bracket. Percent values are the grains in that age bracket as a fraction of total dated grains in the sample. The Range column shows the variance among the samples as the difference between the maximum and minimum percent values. In his random-sampling experiments using synthetic data sets compiled from published Baltica geochronology, Andersen (2005) found range variation among different samples of no more than 14%. Three of our comparisons exceed that value.

TABLE 3. KOLMOGOROV-SMIRNOV TEST FOR DEGREE OF DIFFERENCE BETWEEN DUNE SAMPLES

DUNE Sample A B C D EA 0.68 0.74 0.31 0.47B 0.68 0.36 0.36 0.67C 0.74 0.36 0.11 0.64D 0.31 0.36 0.11 0.51E 0.47 0.67 0.64 0.51

Averages 0.55 0.52 0.46 0.32 0.57 Note: The table is a matrix of probabilities (P values). A P value greater than 0.05 indicates 95% probability

that the corresponding pair of samples was drawn from the same parent population. All samples have P values greater than 0.05, as expected in the case of samples from the same locality. Given that all samples are from a single dune, however, the P values are small, with statistical confi dence that they share a single parent population as low as 11%.

sizes; but the shape of the distribution, and its average size, are likely to vary.

This being the case, age populations will be subject to differential transport and hy-draulic fractionation. The route followed by each individual grain depends on a number of factors—including its shape, interaction with its neighbors in transport, and the chaotic nature of turbulence within the fl ow—but is governed largely by the grain’s mass. Larger zircons will respond differently than smaller zircons. If age and size are related, then this translates to sort-ing pressure in the age spectrum. Age popula-tions with a higher proportion of larger zircons will therefore accumulate a different set of transport paths than age populations dominated by smaller zircons, with the result that some age populations may be fractionated into different depositional settings.

Depending on the size characteristics of the age population, the fractionation may be mild, or it may be severe. An age population with a wide range of grain sizes would not be much affected by these processes, but one with a restricted range of zircon grain sizes might be strongly fractionated into specifi c host-sand size fractions. Identifi cation of such an age population would therefore depend on (possibly serendipitous) sampling of the appropriate sand; and its absence from other samples, rather than representing provenance information, might simply refl ect the stochastic effects of sample selection (in terms of the grain-size characteristics of the host sand).

Simply using larger sample sizes is unlikely to solve the problem. A multi-kg sample might encompass the local range of microenviron-ments in a small-scale bedform but not in larger scale features. In big river systems, for example, individual dunes may be meters high and tens of meters in wavelength. A single sample, however large, would still be restricted to the trough or the slip face or the lee slope of such a feature. Multiple samples, therefore, may be necessary to fully characterize zircon populations in lo-cal transport. Likewise, limiting sample col-lection to a restricted grain-size class will not resolve the issue. The fi ve samples from a single bedform examined in this study all classify as fi ne-grained sand; but their grain-size distribu-tions vary, and so do their zircon age popula-tions. Sieving samples and using a restricted size fraction from each sample (e.g., Morton et al. [2009a], who analyzed only the 62–125 µm fraction) is one approach, but although this does standardize the grain-size range, it may also eliminate or marginalize age populations that are represented in coarser or fi ner zircons. Ana-lytical procedures are also important.

There are a number of ways to avoid the prob-lem of size bias in the geochronologic data set.

Lawrence et al.

304 Geological Society of America Bulletin, January/February 2011

One approach is to sample the least fraction-ated deposits. Poorly sorted sands will provide the best cross section of zircon populations in local transport, and may therefore be the best single-sample candidates; but the problem with this is that many settings will not provide poorly sorted deposits. Alternatively, therefore, one could take a number of samples from differ-ent hydrodynamic subenvironments, analyzing them separately, and then construct a compos-ite probability-density result for the collective zircon data set. This approach maximizes in-formation retrieval for the location and permits intersample comparison. But it does, however, require multiple sets of n ≈100 zircons to be an-alyzed, as each analyzed sample must contribute a statistically signifi cant population to the com-posite result.

An alternative option is therefore to “de- fractionate” the sediment by constructing a com-posite sample to represent each sample locality, consisting of equal proportions of sand (or sand-stone) from a range of subenvironments. In a fl u-vial environment, this might include, for example, sand from the crest, mid-stoss, lee, and trough of a dune; fi ne sand from the reworking zone at the water’s edge; coarse silt from the higher parts of a point bar; and anything else in the coarse silt to medium sand range that looks different or inter-esting. The composite sample would be fabricated by mixing equal portions of the subsamples. This crude-sounding approach maximizes the grain-size window through which to look at the detrital zircon population; and Garzanti et al. (2009) have shown that wider windows provide the most pre-cise estimates of heavy- mineral, grain-size distri-butions. The advantage of a composite sample is that analysis of a single set of ≈100 zircons pro-vides statistical signifi cance in provenance analy-sis for that location.

Whatever sampling and analysis approach is taken, we consider it most important that the size of the dated zircons should be reported. Measurement of the long and short axes of each grain prior to analysis permits easy evaluation of whether there are any size-age relationships in the data. Recording—and reporting—the size of zircon grains analyzed is the simplest way to evaluate hydrodynamic effects on zircon age populations.

ACKNOWLEDGMENTS

This paper is dedicated to the memory of Dr. Todd Housh (1962–2009), who assisted with all aspects of data acquisition and reduction at the University of Texas at Austin. We are grateful to William R. Dick-inson and Keith Sircombe for their searching and constructive reviews of the manuscript, by which it was greatly improved. Keith also helped with age-distribution interpretations. We thank Afonso Nogui-era (Universidade Federal do Pará) and his colleagues

in Brazil for assistance with sample collection and logistics, and Kerry Gallagher for providing us with the mixture-modeling program, MIX. This research was supported by Petroleum Research Fund grants 1756.01-AC8 (Cox) and 41756-AC8 (Coleman), Martin research funds from the University of North Carolina at Chapel Hill (Mapes), and the Sperry Fam-ily Fund of Williams College (Lawrence).

REFERENCES CITED

Andersen, T., 2005, Detrital zircons as tracers of sedimen-tary provenance: Limiting conditions from statistics and numerical simulation: Chemical Geology, v. 216, p. 249–270, doi: 10.1016/j.chemgeo.2004.11.013.

Ansdell, K.M., Kyser, T.K., Stauffer, M.R., and Edwards, G., 1992, Age and source of detrital zircons from the Missi Formation: A Proterozoic molasse deposit, Trans-Hudson Orogen, Canada: Canadian Journal of Earth Sciences, v. 29, p. 2583–2594, doi: 10.1139/e92-205.

Berry, R.F., Jenner, G.A., Meffre, S., and Tubrett, M.N., 2001, A North American provenance for Neoprotero-zoic to Cambrian sandstones in Tasmania?: Earth and Planetary Science Letters, v. 192, p. 207–222, doi: 10.1016/S0012-821X(01)00436-8.

Blott, S.J., and Pye, K., 2001, GRADISTAT: A grain size distribution and statistics package for the analysis of unconsolidated sediments: Earth Surface Processes and Landforms, v. 26, p. 1237–1248, doi: 10.1002/esp.261.

Cawood, P.A., Nemchin, A.A., Smith, M., and Loewy, S., 2003, Source of the Dalradian Supergroup constrained by U-Pb dating of detrital zircon and implications for the East Laurentian margin: Journal of the Geo-logical Society of London, v. 160, p. 231–246, doi: 10.1144/0016-764902-039.

Chang, Z., Vervoort, J.D., McClelland, W.C., and Knaack, C., 2006, U-Pb dating of zircon by LA-ICP-MS: Geochemistry Geophysics Geosystems, v. 7, doi: 10.1029/2005GC001100.

Chen, Y.-D., Lin, S., and van Staal, C.R., 1995, Detrital zircon geochronology of a conglomerate in the north-eastern Cape Breton Highlands: Implications for the relationships between terranes in Cape Breton Island, the Canadian Appalachians: Canadian Journal of Earth Sciences, v. 32, p. 216–223.

Cheng, N.-S., 1997, Simplifi ed settling velocity for-mula for sediment particle: Journal of Hydrau-lic Engineering, v. 123, p. 149–152, doi: 10.1061/(ASCE)0733-9429(1997)123:2(149).

Corfu, F., Hanchar, J.M., Hoskin, P.W.O., and Kinny, P., 2003, Atlas of zircon textures, in Hanchar, J.M., and Hoskin, P.W.O., eds., Zircon: Reviews in Mineralogy and Geochemistry: Mineralogical Society of America, v. 53, p. 469–500.

DeGraaff-Surpless, K., Graham, S.A., Wooden, J.L., and McWilliams, M.O., 2002, Detrital zircon provenance analysis of the Great Valley Group, California: Evolu-tion of an arc-forearc system: Geological Society of America Bulletin, v. 114, p. 1564–1580, doi: 10.1130/0016-7606(2002)114<1564:DZPAOT>2.0.CO;2.

DeGraaff-Surpless, K., Mahony, J.B., Wooden, J.L., and McWilliams, M.O., 2003, Lithofacies control in de-trital zircon provenance studies: Insights from the Cretaceous Methow basin, southern Canadian Cordil-lera: Geological Society of America Bulletin, v. 115, p. 899–915, doi: 10.1130/B25267.1.

Folk, R.L., 1965, Petrology of Sedimentary Rocks: Austin, Hemphill’s, 159 p.

Folk, R.L., and Ward, W.C., 1957, Brazos River bar: A study in the signifi cance of grain size parameters: Journal of Sedimentary Petrology, v. 27, p. 3–26.

Garzanti, E., Andò, S., and Vezzoli, G., 2008, Settling equivalence of detrital minerals and grain-size depen-dence of sediment composition: Earth and Planetary Science Letters, v. 273, p. 138–151, doi: 10.1016/j.epsl.2008.06.020.

Garzanti, E., Andò, S., and Vezzoli, G., 2009, Grain-size dependence of sediment composition and environ-mental bias in provenance studies: Earth and Planetary

Science Letters, v. 277, p. 422–432, doi: 10.1016/j.epsl.2008.11.007.

Gehrels, G.E., Butler, R.F., and Bazard, D.R., 1996, Detrital zircon geochronology of the Alexander terrane, southeastern Alaska: Geological Soci-ety of America Bulletin, v. 108, p. 722–734, doi: 10.1130/0016-7606(1996)108<0722:DZGOTA>2.3.CO;2.

Gehrels, G.E., Yin, A., and Wang, X.F., 2003, Detrital-zircon geochronology of the northeastern Tibetan plateau: Geo-logical Society of America Bulletin, v. 115, p. 881–896, doi: 10.1130/0016-7606(2003)115<0881:DGOTNT>2.0.CO;2.

Guynn, J., 2006, Comparison of detrital zircon age distribu-tions using the K-S test: Arizona LaserChron Center, University of Arizona.

Hartmann, L.A., Endo, I., Suita, M.T.F., Santos, J.O.S., Frantz, J.C., Carneiro, M.A., McNaughton, N.J., and Barley, M.E., 2006, Provenance and age delimita-tion of Quadrilátero Ferrífero sandstones based on zircon U-Pb isotopes: Journal of South American Earth Sciences, v. 20, p. 273–285, doi: 10.1016/j.jsames.2005.07.015.

Kalsbeek, F., Frei, D., and Affaton, P., 2008, Constraints on provenance, stratigraphic correlation and struc-tural context of the Volta basin, Ghana, from detrital zircon geochronology: An Amazonian connection?: Sedimentary Geology, v. 212, p. 86–95, doi: 10.1016/j.sedgeo.2008.10.005.

Kleinhans, M.G., 2004, Sorting in grain fl ows at the lee side of dunes: Earth-Science Reviews, v. 65, p. 75–102, doi: 10.1016/S0012-8252(03)00081-3.

Knudsen, T.L., 2001, Contrasting provenance of Trias-sic/Jurassic sediments in North Sea Rift: A single zircon (SIMS), Sm-Nd and trace element study: Chemical Geology, v. 171, p. 273–293, doi: 10.1016/S0009-2541(00)00253-9.

Kock, S., Martini, R., Reischmann, T., and Stampfl i, G.M., 2007, Detrital zircon and micropalaeontological ages as new constraints for the lowermost tectonic unit (Talea Ori unit) of Crete, Greece: Palaeogeography, Palaeoclimatology, Palaeoecology, v. 243, p. 307–321, doi: 10.1016/j.palaeo.2006.08.006.

Komar, P.D., 2007, The entrainment, transport and sorting of heavy minerals by waves and currents, in Mange, M.A., and Wright, D.T., eds., Heavy Minerals in Use: Amsterdam, Elsevier, p. 3–48.

Komar, P.D., and Reimers, C.E., 1978, Grain shape ef-fects on settling rates: The Journal of Geology, v. 86, p. 193–209.

Komar, P.D., and Wang, C., 1984, Processes of selec-tive grain transport and the formation of placers on beaches: The Journal of Geology, v. 92, p. 637–655, doi: 10.1086/628903.

Komar, P.D., Clemens, K.E., Li, Z., and Shih, S.-M., 1989, The effects of selective sorting on factor analyses of heavy-mineral assemblages: Journal of Sedimentary Petrology, v. 59, p. 590–596.

Krumbein, W.C., 1936, Application of logarithmic moments to size frequency distributions of sediments: Journal of Sedimentary Petrology, v. 6, p. 35–47.

Krumbein, W.C., 1938, Size frequency distributions of sedi-ments and the normal phi curve: Journal of Sedimen-tary Petrology, v. 8, p. 84–90.

Lawrence, R.L., 2007, Testing for hydrodynamic fraction-ation of zircon populations in a sedimentary microen-vironment [B.S. thesis]: Williams College, 84 p., http://library.williams.edu/theses/pdf.php?id=67.

Leeder, M., 1999, Sedimentology and Sedimentary Basins: From Turbulence to Tectonics: Oxford, Blackwell Sci-ence, 592 p.

Mapes, R.W., 2009, Past and present provenance of the Am-azon River drainage basin [Ph.D. thesis]: University of North Carolina.

Miller, E.L., Toro, J., Gehrels, G., Amato, J.M., Prokopiev, A., Tuchkova, M.I., Akinin, V.V., Dumitru, T.A., Moore, T.E., and Cecile, M.P., 2006, New insights into Arctic paleogeography and tectonics from U-Pb detri-tal zircon geochronology: Tectonics, v. 25, TC3013, doi: 10.1029/2005tc001830.

Miller, M.M., and Saleeby, J.B., 1995, U-Pb geochronol-ogy of detrital zircon from Upper Jurassic synorogenic turbidites, Galice Formation, and related rocks, western

Hydrodynamic fractionation of zircon age populations

Geological Society of America Bulletin, January/February 2011 305

Klamath Mountains: Correlation and Klamath Moun-tains provenance: Journal of Geophysical Research, B, Solid Earth and Planets, v. 100, p. 18,045–18,058, doi: 10.1029/95JB00761.

Morton, A.C., Hallsworth, C., Strogen, D., Whitham, A., and Fanning, M., 2009a, Evolution of provenance in the NE Atlantic rift: The Early-Middle Jurassic suc-cession in the Heidrun Field, Halten Terrace, offshore Mid-Norway: Marine and Petroleum Geology, v. 26, p. 1100–1117, doi: 10.1016/j.marpetgeo.2008.07.006.

Morton, A.C., Hitchen, K., Fanning, C.M., Yaxley, G., John-son, H., and Ritchie, J.D., 2009b, Detrital zircon age constraints on the provenance of sandstones on Hat-ton Bank and Edoras Bank, NE Atlantic: Journal of the Geological Society of London, v. 166, p. 137–146, doi: 10.1144/0016-76492007-179.

Neumann, N.L., Southgate, P.N., and Gibson, G.M., 2009, Defi ning unconformities in Proterozoic sedimen-tary basins using detrital geochronology and basin analysis—An example from the Mount Isa Inlier, Aus-tralia: Precambrian Research, v. 168, p. 149–166, doi: 10.1016/j.precamres.2008.09.012.

Novo, E.M.L., Barbosa, C.C.F., Melack, J.M., de Frei-tas, R.M., Titonelli, F., and Shimabukuro, Y., 2006, Comparing MODIS and ETM+ image data for inland water studies: Spatial resolution constraints: Revista Brasileira de Cartografi a, v. 58, p. 109–118.

Perry, S.E., Garver, J.I., and Ridgway, K.D., 2009, Transport of the Yakutat terrane, southern Alaska: Evidence from sediment petrology and detrital zircon fi ssion-track and U/Pb double dating: The Journal of Geology, v. 117, p. 156–173, doi: 10.1086/596302.

Rainbird, R.H., Heaman, L.M., and Young, G.M., 1992, Sampling Laurentia: Detrital zircon geo-chronology offers evidence for an extensive Neo-proterozoic river system originating from the Grenville Orogen: Geology, v. 20, p. 351–354, doi: 10.1130/0091-7613(1992)020<0351:SLDZGO>2.3.CO;2.

Rainbird, R.H., Hamilton, M.A., and Young, G.M., 2001, Detrital zircon geochronology and provenance of the Torridonian, NW Scotland: Journal of the Geological Society of London, v. 158, p. 15–27.

Reid, I., and Frostick, L.E., 1985, Role of settling, entrain-ment and dispersive equivalence and of interstice trap-ping in placer formation: Journal of the Geological

Society of London, v. 142, p. 739–746, doi: 10.1144/gsjgs.142.5.0739.

Rittenhouse, G., 1943, Transportation and deposition of heavy minerals: Geological Society of America Bul-letin, v. 54, p. 1725–1780.

Rubatto, D., Williams, I.S., and Buick, I.S., 2001, Zircon and monazite response to prograde metamorphism in the Reynolds Range, central Australia: Contributions to Mineralogy and Petrology, v. 140, p. 458–468, doi: 10.1007/PL00007673.

Rubey, W.W., 1933, The size-distribution of heavy minerals within a water-lain sandstone: Journal of Sedimentary Petrology, v. 3, p. 3–29.

Sager-Kinsman, E.A., and Parrish, R.R., 1993, Geochronol-ogy of detrital zircons from the Elzevir and Frontenac terranes, Central Metasedimentary Belt, Grenville Province, Ontario: Canadian Journal of Earth Sciences, v. 30, p. 465–473, doi: 10.1139/e93-034.

Sambridge, M.S., and Compston, W., 1994, Mixture modeling of multi-component data sets with ap-plication to ion-probe zircon ages: Earth and Plan-etary Science Letters, v. 128, p. 373–390, doi: 10.1016/0012-821X(94)90157-0.

Singh, M., Singh, I.B., and Müller, G., 2007, Sediment characteristics and transportation dynamics of the Ganga River: Geomorphology, v. 86, p. 144–175, doi: 10.1016/j.geomorph.2006.08.011.

Sircombe, K.N., 1999, Tracing provenance through the iso-tope ages of littoral and sedimentary detrital zircon, eastern Australia, in Bahlburg, H., and Floyd, P.A., eds., Advanced Techniques in Provenance Analysis of Sedimentary Rocks: Amsterdam, Netherlands, Sedi-mentary Geology, v. 124, nos. 1–4, Elsevier, p. 47–67.

Sircombe, K.N., 2000a, Quantitative comparison of large sets of geochronological data using multivariate analy-sis: A provenance study example from Australia: Geo-chimica et Cosmochimica Acta, v. 64, p. 1593–1616, doi: 10.1016/S0016-7037(99)00388-9.

Sircombe, K.N., 2000b, The usefulness and limitations of binned frequency histograms and probability density distributions for displaying absolute age data: Geologi-cal Survey of Canada, Current Research 2000-F2, Ra-diogenic Age and Isotope Studies Report 13.

Sircombe, K.N., 2004, AGEDISPLAY: An EXCEL workbook to evaluate and display univariate geochronological data using binned frequency

histograms and probability density distributions: Com-puters and Geosciences, v. 30, p. 21–31, doi: 10.1016/j.cageo.2003.09.006.

Sircombe, K.N., and Stern, R.A., 2002, An investigation of artifi cial biasing in detrital zircon U-Pb geochronology due to magnetic separation in sample preparation: Geo-chimica et Cosmochimica Acta, v. 66, p. 2379–2397, doi: 10.1016/S0016-7037(02)00839-6.

Sircombe, K.N., Bleeker, W., and Stern, R.A., 2001, Detri-tal zircon geochronology and grain-size analysis of a approximately 2800 Ma Mesoarchean proto-cratonic cover succession, Slave Province, Canada: Earth and Planetary Science Letters, v. 189, p. 207–220, doi: 10.1016/S0012-821X(01)00363-6.

Slingerland, R.L., 1977, The effect of entrainment on the hydraulic equivalence relationships of light and heavy minerals in sands: Journal of Sedimentary Petrology, v. 47, p. 753–770.

Slingerland, R.L., and Smith, N.D., 1986, Occurrence and formation of water-laid placers: Annual Review of Earth and Planetary Sciences, v. 14, p. 113–147, doi: 10.1146/annurev.ea.14.050186.000553.

Stewart, J.H., Gehrels, G.E., Barth, A.P., Link, P.K., and Wrucke, C.T., 2001, Detrital zircon provenance of Mesoproterozoic to Cambrian arenites in the western United States and northwestern Mexico: Geological Society of America Bulletin, v. 113, p. 1343–1356, doi: 10.1130/0016-7606(2001)113<1343:DZPOMT>2.0.CO;2.

Tiepolo, M., 2003, In situ Pb geochronology of zircon with laser ablation-inductively coupled plasma-sector fi eld mass spectrometry: Chemical Geology, v. 199, p. 159–177, doi: 10.1016/s0009-2541(03)00083-4.

Vermeesch, P., 2004, How many grains are needed for a prov-enance study?: Earth and Planetary Science Letters, v. 224, p. 441–451, doi: 10.1016/j.epsl.2004.05.037.

MANUSCRIPT RECEIVED 11 AUGUST 2009REVISED MANUSCRIPT RECEIVED 18 DECEMBER 2009MANUSCRIPT ACCEPTED 19 JANUARY 2010

Printed in the USA