The cosmogenic 21Ne production rate in quartz evaluated on a large set of existing 21Ne–10Be data

Earth and Planetary Science Letters 302 (2011) 163–171

Contents lists available at ScienceDirect

Earth and Planetary Science Letters j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e p s l

The cosmogenic 21 Ne–10Be data

21

Ne production rate in quartz evaluated on a large set of existing

F. Kober a,⁎, V. Alfimov b, S. Ivy-Ochs b,c, P.W. Kubik b, R. Wieler d a

Institute of Geology, ETH Zürich, 8092-Zürich, Switzerland Laboratory of Ion Beam Physics, ETH Zürich, 8093-Zürich, Switzerland Institute of Geography, University of Zürich, 8057-Zürich, Switzerland d Institute of Geochemistry and Petrology, ETH Zürich, 8092-Zürich, Switzerland b c

a r t i c l e

i n f o

Article history: Received 9 June 2010 Received in revised form 1 December 2010 Accepted 2 December 2010 Available online 28 December 2010 Editor: T.M. Harrison Keywords: cosmogenic nuclides production rate 21 Ne 10 Be erosion island

a b s t r a c t Based on a compilation of published combined 10Be and 21Ne cosmogenic nuclide data sets from quartz samples obtained at ETH Zürich we assess the 21Ne/10Be (P21/P10) production rate ratio with the goal to determine the 21 Ne production rate (P21) in quartz. A variety of sliding “erosion islands” in a 21Ne/10Be versus 10Be diagram were evaluated to find the one that fits the data best, which in turn yields the most probable P21 if the 10Be production rate is known. The approach minimizes the influence of samples with a complex exposure history. A best-fit value for P21/P10sp (sp — the 10Be fraction being produced by spallation, as opposed to production by muons) of 4.23± 0.17 is obtained for a 10Be half-life of 1.39 Ma. Adopting a P10sp value in quartz of 4.41 ± 0.52 at g−1 yr−1 this yields a P21 of 18.7± 2.3 at g−1 yr−1. It is possible that 2% of the 21Ne is produced by fast muons. © 2010 Elsevier B.V. All rights reserved.

1. Introduction Crucial in studies using terrestrial cosmogenic nuclides is a precise knowledge of the nuclide production rates (e.g., Gillespie and Bierman, 1995; Gosse and Phillips, 2001). For more than a decade a 21Ne production rate (P21) in quartz of 20.3 ±4.0 at g−1 yr−1 had been widely used. This value was derived from two granitic, glacially polished bedrock samples from the Sierra Nevada, California (Niedermann, 2000; Niedermann et al., 1994). The exposure age of these rocks was obtained by dating the retreat of the Sierra Nevada glaciers at 13 ky BP with 10Be and 26Al exposure ages calibrated against radiocarbon data (Clark et al., 1995; Nishiizumi et al., 1989). The short exposure age made an erosion rate correction unnecessary. New P21 determinations in quartz were made from rhyolitic rocks with 10Be-based exposure ages of b1 Ma also from the Californian Sierra Nevada by Amidon et al. (2009; P21 =17.7± 1.6 at g−1 yr−1) and Goethals et al. (2009; P21 20.1 ±0.8 at g−1 yr−1). The latter determinations involved a correction for erosion, based on independently known eruption ages of the tuffs. Furthermore, Balco and Shuster (2009a) recently determined a P21 of 18.3 ±0.5 at g−1 yr−1 based on a combined 10Be and 21Ne dataset from old (N10 Ma), slowly eroding landforms in Antarctica, with the erosion rate being independently constrained by the 26Al/10Be ratio.

⁎ Corresponding author. E-mail address: [email protected] (F. Kober). 0012-821X/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.epsl.2010.12.008

The still limited number of P21 determinations prompted us to evaluate the P21 production rate by a different approach. Cosmogenic neon concentrations in more than 450 quartz samples have been published (cut off end of 2009), and in about half of them also 10Be has been measured (Table 1 Appendix, lists only the samples used in this study). Geological reasoning suggests that a high enough number of these samples had acquired both their 10Be and 21Ne in a single exposure stage but over different exposure times. This would warrant the evaluation of the most probable mean production rate ratio P21/P10 based on these data, which would allow an estimation of a P21 via a known 10Be production rate (P10). While also other determinations of P21 are based on cross calibrations with P10, our approach is different from these studies as we do not rely on a single calibration site but on a large number of sites. About 70% of the combined 10Be and 21Ne data sets were obtained at the noble gas and AMS laboratories of ETH Zürich. To avoid complications due to possible interlaboratory bias we concentrate on these samples, but will also provide a P21 estimate including the remaining datasets. A P21 value can be obtained by determining the most likely value of the P21/P10 production rate ratio and adopting a P10 value for quartz. Relying on the 10Be production rate is justified because this nuclide can be analysed with high accuracy and may be less prone to analytical problems or non-cosmogenic contributions than 21Ne, especially in samples with relatively short exposure ages. P10 values have been determined with samples from a range of altitudes, latitudes and exposure ages (e.g., Balco et al., 2008, 2009; Putnam

164

F. Kober et al. / Earth and Planetary Science Letters 302 (2011) 163–171

et al., 2010; Stone, 2000). We adopt here a 10Be production rate P10sp of 4.41 ± 0.51 at g−1 yr−1, at sea level and high latitude (SLHL), scaled according to Desilets et al. (2006) (in Balco et al., 2008 and its online update). The fast and slow muogenic components are calculated according to Heisinger et al. (2002a,b). We will explain below how we consider the muogenic 10Be component individually for each sample. We will later compare our results with those that would be obtained with the scaling schemes of Lifton et al. (Li, 2005), Stone (St; 2000) and Dunai (Du, 2000). In the latter two scaling schemes, 10Be produced by fast muons is partially lumped with the spallation component. In this study we consider the spallation and muogenic components separately for all scaling schemes, which introduce minor inconsistencies for the St and Du scaling schemes. 1.1. The “steady state erosion-island” concept In general, for each terrestrial cosmogenic nuclide sample four parameters are relevant: production rate, erosion rate, exposure age and cosmogenic nuclide inheritance. Commonly, the local surface production rate is taken as a known value for both 21Ne and 10Be, while the inheritance is assumed to be zero. Then exposure age and erosion rate can in principle be determined from the measured 10Be and 21Ne concentrations, if the erosion rate is assumed to have been constant throughout the entire exposure. In such cases, all data points in so-called “steady state erosion-island” diagrams (such as Fig. 1A) will fall within an “erosion island”, bound by the lines representing zero erosion and infinite exposure, respectively (Klein et al., 1986; Lal, 1991; Nishiizumi et al., 1991). Data points resulting from continuous exposure under a given constant erosion rate follow a trajectory within the erosion island, starting at the initial production rate ratio and ending on the saturation line, with the end point depending on

the erosion rate. If we have a large ideal data set of samples with simple exposure histories and concurrently measured 21Ne and 10Be concentrations, the P21/P10 production rate ratio is given by the ordinate intercept of the zero erosion line of the erosion island encompassing the data points. Samples that suffered short burial episodes cannot be easily recognized, since their data points may still fall within the erosion island, data points of samples with a complex exposure history that includes longer episodes of pre-exposure or burial will plot above the erosion island (Fig. 1A). Finally, a data point in the “forbidden” area to the right and below the erosion island would indicate either an analytical problem or non-straightforward exposure scenarios. Here we use the 21Ne/10Be–10Be erosion-island concept to find a P21/P10 ratio that accommodates best the ensemble of the published paired Be–Ne data. Because the data set probably includes samples with complex exposure histories, a robust approach to fit an erosion island to the data should minimize the influence of samples which cannot a priori be rejected as complex. Our detailed approach is explained in Section 3. 2. Dataset About 70% (n = 95, as end of 2009) of the combined 21Ne/10Be data sets listed in Table 1 (Appendix) were obtained by the noble gas and AMS laboratories at ETH Zürich. To avoid potential interlaboratory bias we therefore primarily focus on these ETH data. In a second step, we will also consider the further data in Table 1 (Appendix), which were obtained at the noble-gas laboratories at GFZ-Potsdam (Germany), VU Amsterdam (The Netherlands), ANU (Canberra, Australia), Purdue University, West Lafayette (USA) and AMS facilities at the Lawrence Livermore National Laboratories (USA), and ANU.

Fig. 1. The “erosion island” concept and a sketch of the approach to obtain a mean 21Ne production rate via a 21Ne/10Be production rate ratio.1A) A schematic 21Ne/10Be “erosion island” diagram, with the optimal erosion island derived from the data according to the procedure outlined in the text, bounded by the zero erosion line (thick solid line) and the saturation line (black thick dashed line). The crossover of the two lines is the result of 10Be production by muons in addition to spallation production. Samples represented by circles fall within the “erosion island” and hence experienced a single exposure stage under different erosion rates. The thin black solid lines represent trajectories for specific erosion rates. Squares represent samples with a complex exposure history and triangles represent samples falling in the “forbidden” field. For a few samples typical error ellipses are shown. The additional grey solid and grey dashed erosion islands mark two examples of “sliding” erosion islands with either lower or higher 21Ne/10Be production ratio, respectively. The optimal resulting 21Ne/10Be ratio is marked as black dot on the ordinate. Grey bars, marked as 10Bex, indicate different 10Be cutoff values (e. g. samples with concentrations bx10Be at g− 1 of the saturation concentration at zero erosion being discarded, see text).1B) The “success” rate versus the 21Ne/10Be production rate ratio P21/P10 for “sliding” erosion islands. If only continuously exposed samples, samples with a complex history or samples plotting in the forbidden field, respectively, were considered, the success rate distributions would be represented by one of the three grey Gaussian curves. A combination of all samples would yield the black curves, either with all samples considered (10Beall) or only considering samples above a 10Be cutoff concentration of 10% (10Be0.1) and 20% (10Be0.2) of the 10 Be saturation concentration, respectively. The P21/P10 ratio corresponding to the maximum of the success rate distributions decreases slightly with increasing 10Be cutoff.1C) Plot schematically showing the P21/P10 ratio at the maximum of the success rate distributions obtained for the 10Be cutoff values given on the abscissa. The apparently “best” P21/P10 value will be too high as long as samples with very low 10Be concentrations are considered, because many of these samples had a complex exposure history, resulting in high 21Ne/10Be ratios. On the other hand with a very high 10Be cutoff, the few data points in the forbidden field will lead to too low “best” P21/P10 values. In between, however, a plateau may be expected, where the “best” P21/P10 ratio will hardly change with the 10Be cut-off value.

F. Kober et al. / Earth and Planetary Science Letters 302 (2011) 163–171

All datasets were subjected to the following selection criteria: 1.) Apart from atmospheric neon, no other non-cosmogenic neon contributions must be present. In a neon-three isotope diagram data points must therefore fall within uncertainties on the mixing line between atmospheric and cosmogenic Ne (Niedermann et al., 1993). Samples containing nucleogenic Ne (e.g., 21Ne produced from reactions such as 18O(n, α)21Ne) or trapped Ne from the terrestrial mantle with approximately solar isotopic composition were discarded. 2.) Samples were rejected if they were taken for purposes making them unsuitable for this evaluation. This included shielded samples, boulders with known zero exposure taken to test inheritance, or samples used for catchment-wide denudation rate determinations. Samples with insufficiently reported field description were also rejected. Note that we did not reject any sample based on the suspicion of a complex history, not even in clear-cut cases, i.e. even for data points clearly falling above or to the left of any possibly reasonable saturation line in Fig. 1A or 2. We will show below how our approach of fitting an erosion island to obtain a best fit for P21/P10 can also accommodate such data points. The dataset comprises samples from the northern and southern hemisphere, with focal points in Antarctica, northern Chile, the western US, Central Europe and Tibet, i.e. 47°N to 77°S (Table 1, Appendix). Elevation coverage below 2500 m is quite even (for the ETH only as well as the combined dataset), but samples from higher altitudes are more sparse (total elevation range: 124 to 5120 m). 25% of the samples have exposure ages below 50 ka and 75% have ages below 1 Ma. None of the samples from above 4000 m has an age above 200 ky. This is because many studies at these altitudes focus on glacially overprinted landscapes

Fig. 2. The simulated dataset based for all selected 10Be–21Ne data pairs from ETH. Scaling to sea level and high latitude (SLHL) has been done according to Desilets et al. (2006). Each measured data point is represented by 100 (color coded) simulated data points distributed by a Monte Carlo procedure around the measured point according to its uncertainties. For illustrative purposes two sets of erosion islands are shown. The first one has a 21Ne–10Be ratio of 3.95, which is the best value derived in this work (yielding a 21Ne production rate of 18.7 ± 2.3 at g−1 yr−1). Filled circles represent simulated data points falling within this first erosion island, open circles fall outside of this erosion island. The second set of erosion islands has been arbitrarily chosen and corresponds to 21Ne–10Be = 6.12 (yielding P21 = 27.0 at g−1 yr−1). A P21 value of 27 at g−1 yr−1, would obviously yield a poor fit to the data. The ensemble of slightly different saturation lines for each erosion island illustrates the fact that the muogenic production is a variable of altitude and therefore for each measured data point its specific altitude-dependent set of sliding erosion islands has been constructed.

165

of relatively young ages or with high erosion rates. In contrast, arid lowerosion environments conserving old landscapes are found predominantly at lower and mid altitudes, apart from Antarctica. If reported, individual density, thickness, and topographic shielding corrections were adopted, otherwise, a density of 2.7 g cm−3, a sample thickness of 2 cm and a shielding factor of 1 were assumed (Table 1, Appendix). These effects influence nuclide production by a few percent at best and have no significant consequences on our results. All samples have been renormalized from the original value published to the 10Be AMS standard by Nishiizumi et al. (2007). A 10Be half-life of 1.39 Ma was used in the calculations (Chmeleff et al., 2010; Korschinek et al., 2010). 3. Estimation of P21/P10 and P21 3.1. An optimal steady state erosion island The ETH-only data selected according to the criteria listed in the previous section are shown in Fig. 2 and are the basis for the following procedure and discussion. For each measured data pair [Bei ± ΔBei; Nei ± ΔNei] (SLHL) a set of 100 synthetic data points was created by a Monte Carlo method, yielding a Gaussian distribution around Bei and Nei with standard deviations ΔBei and ΔNei (Fig. 2). Note that a larger set of synthetic data points is insensitive to our results. The synthetic data points derived from each measured data point are therefore distributed within an “error ellipse” centered around the respective analysis point. These synthetic data sets are color-coded for each individual measurement in Fig. 2. Next, as shown schematically in Fig. 1A, hypothetical erosion islands were calculated by varying P21 between 10 and 30 at g−1 yr−1 (equivalent to a P21/P10 range of ~2.2 to 6.6 for a P10 value of ~4.5 at g−1 yr−1), in steps of 0.1 at g−1 yr−1. Several percent of the cosmogenic 10Be in surface rocks is not produced by spallation by high energy secondary neutrons but by nuclear reactions induced by either fast or slow secondary cosmic ray muons (Heisinger et al., 2002a,b; Lal, 1991). Because the relative muogenic contribution depends on altitude, for each data point its specific altitude-dependent set of erosion islands has been constructed (see below and Fig. 2). On the other hand, we assume for the following analysis that 21Ne is entirely produced by spallation reactions; although later we will consider the possibility of a minor muon-induced production of this nuclide as recently suggested by Balco and Shuster (2009a,b) and Goethals et al. (2009). For each sliding erosion island (i.e., for each assumed P21/P10 ratio) the number of “successes” was now counted, i.e. the number of synthetic data points falling inside of each erosion island (cf. Fig. 1B). If all samples had experienced simple exposure histories, had negligible analytical uncertainties, and were spread over the range of possible 10Be concentrations, a unique erosion island would then encompass all data points. The y-axis intercept of its zero erosion line would yield the most probable P21/P10 production rate ratio and hence the most probable P21. The solid grey line in Fig. 1B schematically shows the resulting distribution of the number of successes for the sliding erosion islands and the corresponding P21/P10 values. Analytical errors in the otherwise ideal data set will result in a broadening of the success rate distribution. A further broadening will occur if part of the samples suffered a complex exposure or some data points fall into the forbidden region (the dashed and dotted distributions in Fig. 1B illustrate extreme cases where only data points in the complex or forbidden fields exist, respectively). The black curve in Fig. 1B labelled 10Beall represents the distribution resulting if all samples in a set are considered. This distribution has considerably more pronounced tails than the one for the ideal data set, in particular on the high P21/P10 side due to the complex samples. Due to the influence of the complex samples, also the maximum of the distribution, i.e. the “most likely” P21/P10 value, would become higher. However, because complex irradiations manifest themselves mainly at low 10Be concentrations, i.e. for samples with a relatively short last irradiation stage or under high erosion rates, considering only samples

166

F. Kober et al. / Earth and Planetary Science Letters 302 (2011) 163–171

above a certain 10Be concentration threshold will reduce the influence of the complex samples and thus also the maximum of the P21/P10 distribution will shift towards lower values. This is schematically shown by the two curves labelled 10Bex1 and 10Bex2 in Fig. 1B. For these two examples, the grey areas in Fig. 1A indicate the samples not considered, as their 10Be concentrations are below ×1% and ×2% of the saturation concentration, respectively. Fig. 1C shows an idealized expected influence of the 10Be cut-off on the resulting inferred P21/P10 values. Because of the strong influence of samples with complex histories, the apparently “best” P21/P10 values will be too high as long as also the samples with very low 10Be concentrations are considered. On the other end, when only samples with very high 10Be concentrations would be considered, the few data points in the forbidden field (or encompassing within their error bars the forbidden field), will lead to too low “best” P21/P10 values. In between, however, the “best” P21/P10 ratio is relatively insensitive to the 10Be cutoff. Such a plateau would then represent a optimal choice for the P21/P10 ratio best fitting our data, i.e. best, eliminating the influence of samples represented by data points in the complex or forbidden fields. A 10Be cutoff concentration in the range of the value corresponding to the cross-over of the saturation and zero-erosion lines (a result of 10Be production by muons in addition to spallation production) may be expected to efficiently eliminate samples with a complex exposure, because at the cross-over the area within the erosion island is minimal and hence the resulting “best” P21/P10 value varies least with the cutoff value. We will show in the next section that our actual data set conforms to this expectation. Therefore our approach indeed yields meaningful P21/P10 and hence P21 values without a priori discriminating against samples with a suspected complex exposure history or with data points suspected to fall in the forbidden field. Therefore we decide to make a minimal adjustment to the data, by removing data with low 10Be concentrations and whose low 21Ne concentrations often are associated with analytical complications. The natural choice for the cut-off is then the cross-over of the “erosion island” plot, where the resulting P21 is the least sensitive to the selection of the cut-off value. One can also consider that to the left of the cross-over, the synthetic data set for each measurements hardly fits into the “erosion island”, so the largest part of each synthetic data set is actually outside of any possible “erosion island”, while to the right of the cross over, a relatively large part of any synthetic data set can fit into some “erosion islands”. Furthermore, by choosing the crossover, the modeling is much less sensitive to assumptions regarding muogenic production for 21Ne and the preferable inclusion of longer-exposed samples benefits much more from the time averaging effect of the cosmic ray flux.

(corresponding to 11% of the saturation concentration for samples experiencing zero erosion) most of the synthetic points plot inside or close to the best-fit erosion island, many points with 10Be b 1 * 106 at g−1 clearly fall above this erosion island, into the complex field of exposure. Fig. 3 is the equivalent of Fig. 1B for our real data set, showing the success rate distributions of the synthetic data points as a function of P21/P10. On the right ordinate, the corresponding P21 values are indicated. Shown are the distributions for the entire ETH data set as well as for subsets with various 10Be cutoff values (i.e. successively considering only samples with a 10Be concentration higher than 10% or 20%, 30% of the 10Be saturation concentration). The maximum number of successes decreases with increasing 10Be cutoff, due to the progressively lower number of samples considered. Remarkably, all curves have their maximum in a narrow P21 interval between 16.5 and 18.5 at g−1 yr−1, and with increasing 10Be cutoff values the position of the maximum of each distribution is shifted only slightly towards lower P21 values. This is shown again in Fig. 4, displaying on the abscissa the lowest accepted 10Be concentrations and on the ordinate the P21 value corresponding to the maximum of the respective success rate distribution. If one would accept all ETH-samples, the “most probable” P21 value would become 19.2 at g−1 yr−1. With increasing 10Be cutoff, i.e. by eliminating mainly samples with complex exposure, the “most probable” P21 slightly decreases, but – as expected from the schematic Fig. 1C – reaches a plateau at 10Be cutoff values between about ~1 * 106 and ~2.5* 106 10Be at g−1. The position of the best-fit erosion island in this range depends only marginally on the 10Be cut-off value. The 10Be concentrations corresponding to the positions of the crossover of saturation and zero erosion lines in Fig. 2 are near 1.5 * 106 10Be at g−1. The crossover concentrations, which we proposed above to be a good choice for the 10Be cut-off, therefore fall within the range of 10Be concentrations covered by the plateau in Fig. 4. A further increase of the 10 Be cutoff concentration results in a further decrease of the most probable P21 value, because the few (synthetic) data points falling in the forbidden field get more weight. However, even if all samples with 10Be below 4 * 106 10Be at g−1 are excluded, the corresponding “most probable” P21 value of 17.5 at g−1 yr−1 would still only be ~7% below the plateau value in Fig. 4. The existence of a plateau in Fig. 4 indicates the robustness of this approach and we adopt the plateau between 10Be cutoff values of 1–2.5 * 106 at g−1 10Be in order to derived P21/P10 from the ETH data set. Accordingly, we obtain a most probable mean P21/P10sp ratio of 4.23 ± 0.17. This is our recommended production

4. Results 4.1. Most probable P21/P10 and P21 derived from the ETH data set Fig. 2 shows the synthetic data points, all scaled to SLHL with a Desilets et al. (2006) scaling. Also shown are two erosion islands. The one labelled “18.67 atoms/g yr” yields the best fit to the data, as is explained in the following, the second one is explained in the figure caption. The ensemble of slightly different saturation lines for each erosion island is the result of the fact that actually for each measured data point its altitude-specific erosion island is being considered. The P21/P10sp production rate ratio corresponding to the best-fit erosion island is 4.23 ± 0.17 (uncertainty derived from the fitting procedure as explained below). With our preferred P10sp value of 4.41 ± 0.52 at g−1 yr−1 (Desilets et al., 2006 scaling, as in Balco et al., 2008 and update) this yields a P21 value of 18.7 ±2.3 at g−1 yr−1 in quartz (the stated error includes the uncertainty of P10sp). Note that these values are calculated under an assumption that the entire production of 21Ne is by spallation reactions. Synthetic points inside the adopted erosion island are shown as filled symbols, other data points as open symbols. While for 10Be concentrations higher than 1 * 106 at g−1

Fig. 3. Success rate distributions. Shown is the percentage of simulated data points from the ETH dataset inside a sliding erosion island against P21/P10 that defines the respective erosion island (left ordinate). The different curves represent success rate distributions for the entire data set and for 10Be concentration cut-off values at N1 106 at g−1, N 2 106 at g−1, and so on (see text). Also shown are the Gaussian fits to the various success curves. The P21/P10 value corresponding to the maximum of each Gaussian fit decreases slightly with increasing 10Be cut-off values, but remains nearly constant for cut-off values between about 1–3 106 at g−1 (see also Fig. 4). The right ordinate gives P21 according to the adopted P10sp of x at g−1 yr−1.

F. Kober et al. / Earth and Planetary Science Letters 302 (2011) 163–171

Fig. 4. The P21/P10 ratio corresponding to the maximum of the Gaussian fits to the success rate curves shown in Fig. 3 versus the 10Be cutoff values for the different success rate curves. The P21/P10 plateau value of 4.23 observed between 10Be cutoff values of 1–2.5 106 at g−1 is taken as the most probable P21/P10 ratio derived in this work. This corresponds to a best P21 value of 18.7 at g−1 yr−1 derived from the ETH data set (see text).

167

production systematics by muons for 26Al and 21Ne are expected to be similar (Heisinger et al., 2002a,b). If altitudinal and latitudinal dependence of production rates is scaled by other schemes than that proposed by Desilets and Zreda (2003), Desilets et al. (2006) and used here, the P21/P10sp is: 4.01± 0.17 (St); 4.25 ± 0.19 (Du) and 4.39± 0.20 (Li). The resulting P21 would be 18.0± 1.7 (St), 18.8 ± 2.4 (Du) and 21.4 ± 2.3 (Li) at g−1 yr−1, respectively, relying on the P10sp values given by Balco et al. (2008, and update). The P21/P10 values based on St and Du scaling do actually not reflect the pure spallation-produced component of 10Be, because in these two scaling schemes, 10Be produced by fast muons is partially lumped with the spallation component. However, the resulting small inconsistency in the calculation of P21 is well within uncertainties. The observation that somewhat higher values result with a Lifton-scaling has been discussed elsewhere (Balco et al., 2008; Lifton et al., 2005). Our P21 value matches best with the recently derived P21sp of Balco and Shuster (2009a,b) of 18.3± 1.6 at g−1 yr−1. Likewise, our preferred values overlap with those of St and Du within uncertainties. Note further that a P21 value of 18.6 (=De, 18.5 St, 18.8 Du, 21.6 Li) at g−1 yr−1 results with our approach, if we include in addition to the ETH data all other published 21Ne–10Be data sets which fulfill the criteria outlined in Section 2. We prefer here the P21 value of 18 at g−1 yr−1 derived from our own data alone, as this avoids all potential problems that may arise from interlaboratory comparisons.

5. Conclusions rate ratio, adopted to construct the best fit erosion island shown in Fig. 2. As uncertainty of our P21/P10sp value we have chosen the standard error of the mean by taking the standard deviation of a Gaussian fit to the adopted success-rate distribution which is divided by the square root of the number of measured data points falling into the most probable erosion island and having a 10Be concentration of ≥1 * 106 10Be at g−1. In order to eliminate the influence of samples with complex histories on this error estimate, the Gaussian fit was obtained iteratively, assuming that that we do not have non-Gaussian tails within one standard deviation around the peak (Fig. 3). After a first fit to all data, subsequent fits only considered the data within one standard deviation of the preceding fit. After 3 iterations the standard deviation remained constant. The most probable values obtained here for P21/P10sp of 4.23 ± 0.17 and the 21Ne production rate P21 of 18.7± 2.3 at g−1 yr−1 are in good agreement with published values, which fall in the range of 3.63–4.31 (P21/P10) and (17.7–20.1 at g−1 yr−1) (P21) (Amidon et al., 2009; 2009; Balco and Shuster, 2009a; Goethals et al., Niedermann, 2000). Note that our preferred P21 “ETH-only” value does not take into account any of the samples used in the other production rate determinations, none of which were measured at ETH. Furthermore, as pointed out above, our value is based on a large number of sample sites, in contrast to the earlier studies which concentrated on single or a few sites. Nevertheless, the good agreement among different studies based on different approaches and different sample sites is satisfying and indicates that the 21Ne production rate in quartz is now known with a considerably lower uncertainty than yet a few years ago. For 21Ne, production by secondary cosmic ray muons has usually been considered negligible (cf Niedermann, 2000). However, recently, Balco and Shuster (2009a,b), Fernandez-Mosquera et al. (2010) and Goethals et al. (2009) suggested that production by muons accounts for a small fraction of ~ 2–4% of the total cosmogenic 21Ne produced at a rock surface. We expect from nuclear systematics that only fast muons are able to produce 21Ne while contributions from negative muon capture should be negligible. We estimate that the fast muon production channel does not account for more than 2% of the total 21 Ne production at the rock surface similar to 26Al. This is because

We show here that a large data set of combined cosmogenic 21Ne and Be concentrations in quartz is suitable to constrain the P21/P10 production ratio. The resulting value is based on numerous sample sites from variable geomorphic settings, complementing other studies which relied on single calibration sites. The approach chosen here is robust even in the presence of samples with complex exposure histories. The P21/P10 derived for samples measured at ETH Zürich, Switzerland is P21/P10sp of 4.23±0.17. With this value, and adopting the recent P10sp in quartz of 4.41±0.52 at g−1 yr−1 reported by Balco et al. (2008, and update) for a Desilets et al. (2006) scaling, a 10Be half-life of 1.39 Ma and the aforementioned P21/P10sp, we derive a P21 of 18.7±2.3 at g−1 yr−1 for the datasets obtained at ETH Zürich. This number is in good agreement with other recent estimates. The P21 value proposed here is proportional to the adopted 10Be production rate and can thus easily be modified should the preferred 10Be production rate value change. However, care has to be taken in the selection of the data going into the analysis. In principle, the 21Ne production rate can also be determined via 26Al instead of 10Be, because 26Al and 21Ne have occasionally been measured in the same samples (Balco and Shuster, 2009b; Goethals et al., 2009; Kober et al., 2007, 2009). However, the available data base is much smaller than for 10Be–21Ne data pairs, and P26 calibration are by far less well constraint compared to P10 (Balco et al., 2008) and additionally the production rate of 26Al is less well constrained than that of P10. The new determinations of the 21Ne-production rate in quartz require modifications of production rates determined for other minerals which were normalized to P21 in coexisting quartz (e.g., Kober et al., 2005; Schäfer et al., 1999). Hence the reported 3He and 21Ne production rate estimates for pyroxenes, olivines and Fe–Ti-oxides (and the elemental production rates determined from these data) need to be lowered by about 10–15%. 10

Acknowledgements We acknowledge the productive discussions with G. Balco. We are grateful for the support provided by H. Baur in the noble gas laboratory and to the ETH AMS-group. The comments by W.H. Amidon and an anonymous reviewer are appreciated.

168

F. Kober et al. / Earth and Planetary Science Letters 302 (2011) 163–171

Appendix A

Appendix Table 1 Compilation of all data used for the analysis of the most probable P21. Note that studies/samples that have not gone into the analysis and failed the selection criteria have been not listed. Citation/Source

Locality

Sample ID

Latitude Longitude Elevation Thickness Density Shielding 21Ne (°) (°) (m) (cm) (g cm−3) (at g−1)

Fujioka et al. (2005)

Australia

Oberholzer et al. (2003) Schäfer et al. (1999) Ivy-Ochs et al. (1995)

Antarctica

G115 G199 G499 B2

−28.6 −27.2 −27.2 −74.33

136 136 136 163.5

Antarctica

320

−77

Bruno et al. (1997) Bruno (1995) Ivy-Ochs et al. (1995)

Antarctica

322 323 325 326 309 TMK93-17B

Schäfer et al. (2008)

Tibet

Ivy-Ochs et al. (2006) Schäfer et al. (2002)

Switzerland

Hetzel et al. (2004)

Tibet

Strasky et al. (2009)

Antarctcia

Di Nicola et al. (2009)

Antarctica

Graf et al. (2007)

Switzerland

Kober et al. (2007)

Chile

21

Ne err (at g−1)

10

Bec (at g−1)

10 Be err (at g−1)

250 220 250 980

2.00 2.00 2.00 2.00

2.70 2.70 2.70 2.70

1 1 1 1

8.40E + 07 8.45E + 07 1.07E + 08 2.00E + 07

3.50E + 06 3.90E + 06 9.80E + 06 2.00E + 06

9.59E + 06 6.63E + 06 8.29E + 06 4.87E + 06

4.70E + 05 3.10E + 05 3.10E + 05 2.60E + 05

162

2140

2.00

2.70

1

1.43E + 09

3.05E + 07 7.04E + 07

3.66E + 06

−77 −77 −77 −77 −77 −77

162 162 162 162 162 162

2140 2060 2060 2060 2750 1820

2.00 2.00 2.00 2.00 2.00 5.00

2.70 2.70 2.70 2.70 2.70 2.70

1 1 1 1 1 1

6.78E + 08 6.81E + 08 5.40E + 08 7.06E + 08 5.36E + 08 2.47E + 08

2.73E + 07 1.25E + 07 2.15E + 07 2.46E + 07 7.12E + 06 6.08E + 06

6.74E + 07 6.20E + 07 5.18E + 07 6.54E + 07 7.10E + 07 3.92E + 07

3.50E + 06 4.22E + 06 2.69E + 06 3.66E + 06 5.04E + 06 3.84E + 06

TMK93-7 TMK93-8 TMK93-9 TMK93-5 TMss93-13A TMss93-18 TMss93-19A TMss93-19B Ny1 Ny2 Ny3B Ny4 Ny5 Ny6 Ny7 Ny8 Ny15 Ny16 Ny17 MON

−77 −77 −77 −77 −77 −77 −77 −77 28.13 28.13 28.13 28.15 28.15 28.15 28.15 28.15 28.13 28.13 28.15 47.22

162 162 162 162 162 162 162 162 85.97 85.97 85.97 85.97 85.97 85.97 85.97 85.97 85.98 85.98 85.98 7.3

1820 1840 1840 1820 2080 2170 2100 2100 3902 3902 3902 3840 3885 3941 3976 3905 3890 3893 3891 1200

5.00 2.50 5.00 3.50 7.00 7.00 3.00 2.00 3 3 4.5 2.5 3 3.5 5.5 3.2 3 2.5 1.5 2

2.70 2.70 2.70 2.70 2.70 2.70 2.70 2.70 2.7 2.7 2.7 2.7 2.7 2.7 2.7 2.7 2.7 2.7 2.7 2.7

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1.66E + 08 1.20E + 08 1.08E + 08 2.26E + 08 4.31E + 08 1.81E + 08 2.90E + 08 3.32E + 08 1.06E + 07 1.19E + 07 2.50E + 07 2.50E + 07 3.22E + 07 5.00E + 07 1.71E + 07 3.12E + 07 2.39E + 07 3.24E + 07 3.69E + 07 7.66E + 06

4.50E + 06 1.67E + 07 3.32E + 06 1.36E + 07 4.38E + 06 1.17E + 07 1.19E + 07 5.82E + 06 1.11E + 06 1.04E + 06 2.42E + 06 2.42E + 06 2.45E + 06 7.34E + 06 1.88E + 06 1.38E + 06 1.92E + 06 3.81E + 06 3.36E + 06 1.31E + 06

2.87E + 07 2.13E + 07 1.59E + 07 4.19E + 07 5.57E + 07 3.37E + 07 3.76E + 07 4.61E + 07 2.74E + 06 2.51E + 06 5.36E + 06 3.29E + 06 7.97E + 06 1.50E + 07 2.81E + 06 7.71E + 06 5.55E + 06 9.63E + 06 6.28E + 06 1.44E + 06

1.72E + 06 1.24E + 06 1.24E + 06 2.51E + 06 3.62E + 06 3.47E + 06 2.67E + 06 2.54E + 06 1.10E + 05 1.28E + 05 1.66E + 05 1.68E + 05 2.79E + 05 5.54E + 05 2.05E + 05 3.32E + 05 2.33E + 05 6.64E + 05 1.88E + 05 6.30E + 04

Tan2 Tan4 Tan5 Tan7 00C21 00C24 00C23 RH06/03 RHP10 RHS3 ABL1 K3 ABB1 ABB2 ABB3 ABB4 ABB8 BROW1 BROW7 BROW8 MON-04-01 MON-04-02 MON-04-03 MON-04-04 CN1c CN5 CN8b CN16 CN19 CN23 CN26 CN36 CN104A CN111F CN112

32.5 32.5 32.5 32.5 39.78 39.75 39.75 −75.68 −75.68 −75.68 −74.33 −74.33 −74.33 −74.33 −74.33 −74.33 −74.33 −74.6 −74.6 −74.6 47.22 47.22 47.22 47.22 −18.47 −18.7 −18.42 −18.35 −18.7 −18.38 −20.3 −19.55 −18.3 −18.4 −18.1

91.83 91.83 91.83 91.83 99.38 99.43 99.43 159.22 159.22 159.22 163.85 163.5 163.92 163.92 163.92 163.92 163.92 164.08 164.08 164.08 7.3 7.3 7.3 7.3 −69.9 −69.6 −69.85 −69.6 −69.7 −69.7 −68.92 −70.1 −69.7 −69.82 −69.7

5015 4925 4925 5120 1395 1380 1375 1438 1435 1589 1022 1090 596 596 608 520 430 470 674 660 1200 1260 1050 1060 1930 3260 1670 3270 2730 3280 4205 1150 3235 3435 3920

2 2 2 2 2 2 2 2.8 2 4.5 3.00 2.00 2.00 4.00 4.50 4.50 1.50 4.50 4.50 4.50 2 2 2 2 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00

2.7 2.7 2.7 2.7 2.7 2.7 2.7 2.65 2.65 2.65 2.65 2.70 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.38 2.38 2.38 2.38 2.38 2.38 2.38 2.70 2.38 2.38 2.38

1 1 1 1 1 1 1 0.98 1 0.96 0.96 1 0.98 0.97 0.87 0.87 0.98 0.94 0.96 0.96 0.99 1 0.97 0.93 1 1 1 1 1 1 1 1 1 1 1

8.10E + 07 3.80E + 07 7.10E + 07 3.13E + 07 1.04E + 07 9.00E + 06 8.20E + 06 1.12E + 07 2.52E + 07 7.28E + 07 1.50E + 08 1.67E + 08 1.57E + 07 9.60E + 06 9.00E + 06 1.16E + 07 2.52E + 07 1.95E + 07 1.24E + 07 6.90E + 06 6.34E + 06 5.64E + 06 3.64E + 06 5.87E + 06 7.96E + 07 2.00E + 08 4.66E + 07 1.44E + 08 3.20E + 08 2.26E + 08 7.86E + 07 4.32E + 07 1.13E + 08 1.34E + 08 2.61E + 07

6.80E + 06 3.50E + 06 5.58E + 06 2.41E + 06 2.00E + 06 1.50E + 06 1.60E + 06 9.10E + 05 7.60E + 05 1.64E + 06 5.80E + 06 1.00E + 07 2.00E + 06 1.30E + 06 1.30E + 06 9.00E + 05 1.30E + 06 1.50E + 06 1.00E + 06 7.00E + 05 1.22E + 06 1.78E + 06 9.40E + 05 1.12E + 06 2.78E + 06 6.21E + 06 2.16E + 06 7.58E + 06 5.28E + 06 4.16E + 06 2.35E + 06 4.41E + 06 2.75E + 06 5.12E + 06 9.09E + 05

1.64E + 07 9.03E + 06 1.61E + 07 7.71E + 06 3.44E + 06 2.75E + 06 2.56E + 06 2.39E + 06 5.15E + 06 1.49E + 07 2.04E + 07 2.26E + 07 1.58E + 06 1.45E + 06 1.59E + 06 1.29E + 06 1.40E + 06 3.15E + 06 1.56E + 06 1.46E + 06 1.35E + 06 1.09E + 06 7.30E + 05 1.23E + 06 1.33E + 07 3.08E + 07 7.33E + 06 1.85E + 07 3.46E + 07 3.71E + 07 1.89E + 07 5.39E + 06 2.20E + 07 2.73E + 07 6.75E + 06

2.47E + 05 1.37E + 05 3.58E + 05 1.83E + 05 4.00E + 05 3.00E + 05 3.10E + 05 7.00E + 04 1.50E + 05 4.50E + 05 1.90E + 06 1.22E + 06 1.20E + 05 1.40E + 05 1.20E + 05 1.00E + 05 9.00E + 04 2.10E + 05 1.20E + 05 1.40E + 05 4.00E + 04 1.10E + 05 5.00E + 04 6.00E + 04 2.67E + 05 9.60E + 05 2.86E + 05 6.29E + 05 8.67E + 05 5.56E + 05 5.67E + 05 2.46E + 05 6.67E + 05 9.32E + 05 3.11E + 05

F. Kober et al. / Earth and Planetary Science Letters 302 (2011) 163–171

169

Appendix Table 1 (continued) Citation/Source

Locality

Sample ID

Latitude Longitude Elevation Thickness Density Shielding 21Ne (°) (°) (m) (cm) (g cm−3) (at g−1)

Kober et al. (2007)

Chile

Dühnforth (2007) Kober (2004)

USA

CN113 CN201 CN203 CN301 CN302 CN305 CN309 CN310 90303-2

−18.17 −18.37 −19.2 −18.73 −18.73 −18.18 −18.23 −18.35 35.98

−69.5 −69.83 −70.25 −69.68 −69.68 −69.68 −69.15 −39.6 −116.83

4560 3440 500 2185 2590 3670 4510 3220 124

4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 5.00

2.38 2.38 2.70 2.38 2.38 2.38 2.38 2.38 2.70

1 1 1 1 1 1 1 1 1

4.31E + 06 5.44E + 05 2.84E + 08 8.07E + 06 2.43E + 08 7.07E + 06 8.63E + 07 1.41E + 06 9.30E + 07 1.29E + 06 4.63E + 07 1.56E + 06 9.35E + 06 4.77E + 05 1.92E + 07 4.76E + 05 1.206E + 07 1.150E + 06

35.96 35.97 −71.58 −71.67 −71.42 −71.67 −26.33 −26.83 −76.75 −76.75 37.46 37.43 37.43 37.41 37.41 37.41 37.42 37.42 37.45 37.45 37.44 37.44 37.42 37.42 37.42 37.42 37.42 37.43 −77 −77 −77 −77 36.03 36.03 −74.72 −74.72 −73.69 −74 −74.4 −74.4 −75.04 −74.19 −74.19 −74.19 −74.99 −75.01 −74 −73.75 −73.75 −74.73 −74.73 −74.4 −77.64 −77.64 −77.86 −77.88 −77.89 −77.89 −77.88 −77.51 −77.51 37.42

−116.86 −116.85 159.75 160.33 159.58 160.33 −69.98 −69.74 160 160 −118.49 −118.43 −118.42 −118.46 −118.47 −118.46 −118.46 −118.46 −118.49 −118.4 −118.4 −118.49 −118.43 −118.43 −118.43 −118.43 −118.43 −118.43 162 162 162 162 −117.8 −117.8 163.7 163.7 162.64 163 163.64 163.64 162.57 163.74 163.74 163.74 162.39 162.38 163 162.77 162.77 162.64 162.64 163.61 160.94 160.94 160.93 160.82 160.77 160.81 160.92 161 161 −118.67

349 308 2850 2850 2726 1850 2295 1950 1760 1705 1507 1366 1361 1387 1368 1376 1395 1394 1502 1411 1406 1496 1365 1365 1365 1369 1369 1366 415 610 2090 710 1333 1333 298 298 2726 910 915 937 888 1622 1615 1614 810 558 1979 2640 2640 420 420 1000 1721 1671 1289 1455 1681 1628 1690 1463 1463 3556

5.00 5.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 3.50 5.00 2.00 2.00 4.00 2.80 2.00 3.80 4.50 5.00 4.50 2.50 2.00 7.00 9.50 2.00 2.00 5.00 7 7 1.5 5 3 2.5 4 1 1.5 2

2.70 2.70 2.65 2.65 2.65 2.65 2.70 2.70 2.70 2.70 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 2.70 2.70 2.70 2.70 2.70 2.70 2.70 2.70 2.70 2.70 2.70 2.70 2.70 2.70 2.70 2.70 2.70 2.70 2.70 2.70 2.70 2.70 2.70 2.70 2.20 2.20 2.20 2.20 2.20 2.20 2.20 2.20 2.20 2.70

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0.930 0.918 0.983 0.946 0.950 0.976 0.963 0.976 0.952 0.959 0.959 0.979 0.891 0.924 0.943 0.983 0.959 0.959 0.98 1 0.99 0.99 0.98 1 1 1 1 0.731

38.87

−120.18

2452

2

2.70

0.928

190303-1 10303-1 van der Wateren Antarctica DW91013 et al. (1999) DW91014 DW91016 DW90108 Nishiizumi et al. Chile 21 (2005) 74 Tschudi et al. Antarctica 227 (2003) AL9711c Goethals et al. Sierra Nevada, USA 05BT1 (2009) 05BT10 05BT11 05BT15 05BT16 05BT17 05BT18 05BT19 05BT2 05BT20 05BT21 05BT3 05BT4 05BT5 05BT6 05BT7 05BT8 05BT9 Ivy-Ochs et al. Antarctica 6a (unpubl.) 9 220 237 Amidon et al. SW-US CO-5 (2009) CO-6 Strasky (2008) Antarctica ANL1 Di Nicola (2008) ANL2 ARC1 BELL1 BR1 BR2 CR1 EMI1 EMI3 EMI5 GER1 GERL8 LH1 POL2 POL3 971210-01 971210-02 971210-10 Balco and Shuster Antarctica 05-EG-118-BR (2009a,b) 05-EG-119-BR 04-AV-001-BR 04-AV-005-BR 04-AV-006-BR 04-AV-010-BR 04-AV-018-BR 05-WO-137-BR 05-WO-140-BR Niedermann Sierra Nevada, US W86-8 et al. (1994) Nishiizumi W86-12 et al. (1989)

10

Bec (at g−1)

10 Be err (at g−1)

1.19E + 06 4.16E + 07 5.93E + 06 1.47E + 07 1.66E + 07 1.08E + 07 2.13E + 06 4.66E + 06 2.73E + 06

5.60E + 04 1.25E + 06 1.82E + 05 4.46E + 05 5.04E + 05 3.94E + 05 1.14E + 05 1.82E + 05 2.73E + 05

2.072E + 07 1.149E + 06 4.44E + 06 1.923E + 07 1.519E + 06 4.07E + 06 1.46E + 09 3.00E + 07 1.22E + 08 2.27E + 09 4.00E + 07 1.30E + 08 2.15E + 09 4.00E + 07 1.14E + 08 6.78E + 08 1.10E + 07 2.47E + 07 5.94E + 08 3.00E + 07 3.09E + 07 4.56E + 08 2.30E + 07 3.38E + 07 9.60E + 07 3.60E + 06 1.61E + 07 1.71E + 08 4.00E + 06 2.65E + 07 2.14E + 07 1.10E + 06 5.02E + 06 2.38E + 07 1.30E + 06 4.90E + 06 2.18E + 07 1.20E + 06 4.46E + 06 1.70E + 07 9.30E + 05 3.40E + 06 1.23E + 07 8.40E + 05 2.68E + 06 1.04E + 07 8.40E + 05 2.75E + 06 1.75E + 07 9.50E + 05 3.78E + 06 1.80E + 07 1.20E + 06 4.12E + 06 2.31E + 07 1.20E + 06 4.56E + 06 2.17E + 07 1.40E + 06 4.57E + 06 1.70E + 07 9.30E + 05 4.63E + 06 2.27E + 07 1.10E + 06 4.71E + 06 1.83E + 07 1.10E + 06 3.98E + 06 2.17E + 07 1.20E + 06 4.98E + 06 1.93E + 07 1.20E + 06 4.40E + 06 2.48E + 07 1.30E + 06 4.49E + 06 1.72E + 07 1.20E + 06 4.03E + 06 2.29E + 07 1.30E + 06 4.66E + 06 5.59E + 07 3.07E + 06 4.13E + 06 5.11E + 07 3.12E + 06 2.54E + 06 7.52E + 08 2.48E + 07 6.62E + 07 1.37E + 07 2.67E + 06 1.72E + 06 2.27E + 06 1.10E + 05 6.37E + 05 4.44E + 06 1.50E + 05 1.20E + 06 5.53E + 06 6.80E + 05 5.00E + 05 3.51E + 06 3.99E + 05 4.00E + 05 8.28E + 08 3.20E + 07 1.09E + 08 8.60E + 07 3.63E + 06 1.09E + 07 9.00E + 06 1.10E + 06 2.20E + 06 1.70E + 07 2.21E + 06 4.10E + 06 1.03E + 08 3.05E + 06 1.61E + 07 4.07E + 06 5.48E + 05 1.20E + 06 6.56E + 07 2.04E + 06 1.33E + 07 8.44E + 07 2.91E + 06 1.64E + 07 5.53E + 07 2.00E + 06 6.80E + 06 2.05E + 07 2.03E + 06 2.60E + 06 1.04E + 07 8.97E + 05 2.44E + 05 8.50E + 08 2.59E + 07 9.16E + 07 9.56E + 08 2.37E + 07 9.00E + 07 7.56E + 07 3.13E + 06 1.00E + 05 6.13E + 06 1.19E + 06 6.00E + 05 3.16E + 06 3.58E + 05 8.00E + 05 1.34E + 08 3.20E + 06 2.06E + 07 7.83E + 07 2.40E + 06 1.27E + 07 3.81E + 07 1.90E + 06 5.75E + 06 1.76E + 08 3.50E + 06 2.08E + 07 9.36E + 07 6.30E + 06 1.62E + 07 9.50E + 07 1.70E + 06 1.54E + 07 1.68E + 08 2.80E + 06 2.50E + 07 3.64E + 08 1.80E + 07 2.95E + 07 2.99E + 08 4.90E + 06 2.80E + 07 2.05E + 06 3.70E + 05 5.73E + 05

4.44E + 05 4.07E + 05 1.20E + 07 3.30E + 06 9.10E + 06 9.00E + 05 3.80E + 05 6.80E + 05 1.10E + 06 1.40E + 06 1.51E + 05 2.36E + 05 2.83E + 05 1.85E + 05 9.46E + 04 1.05E + 05 1.17E + 05 1.24E + 05 1.38E + 05 1.37E + 05 2.84E + 05 1.42E + 05 2.69E + 05 1.50E + 05 1.32E + 05 2.89E + 05 2.06E + 05 2.25E + 05 2.56E + 05 2.29E + 05 4.70E + 06 1.41E + 05 1.50E + 04 1.90E + 04 0.00E + 00 0.00E + 00 6.50E + 06 6.58E + 05 1.00E + 05 2.00E + 05 1.00E + 06 1.00E + 05 8.00E + 05 1.00E + 06 4.00E + 05 2.00E + 05 6.06E + 04 6.40E + 06 5.40E + 06 0.00E + 00 1.00E + 05 1.00E + 05 2.00E + 05 2.00E + 05 2.10E + 05 5.70E + 05 3.40E + 05 6.10E + 05 4.00E + 05 8.60E + 05 6.90E + 05 7.30E + 04

1.78E + 06

21

Ne err (at g−1)

4.70E + 05 3.86E + 05

1.05E + 05

170

F. Kober et al. / Earth and Planetary Science Letters 302 (2011) 163–171

Appendix The calculation of the erosion island outlines The local erosion island is confined between the zero-erosion line and steady state line. These lines can be parametrically defined as the following: t

N10 ðtÞ = P10;SLHL;sp ∫ Ssp ðtÞe

−λt

t

0

dt + P10;SLHL;μ ∫ Sμ ðtÞe

t

t

0

−λt

dt

N21 ðtÞ = P21;SLHL;sp ∫ Ssp ðtÞdt + P21;SLHL;μ ∫ Sμ ðtÞdt 0

∞

0

N10 ðÞ = P10;SLHL;sp ∫ Ssp ðtÞe 0

∞

N21 ðÞ = P21;SLHL;sp ∫ Ssp 0

ρ Þt Λsp dt

−ðλ + 

ρ t − ðtÞe Λsp dt

 ∞

+ P10;SLHL;μ ∫ Sμ ðtÞe 0

∞

+ P21;SLHL;μ ∫ Sμ 0



ρ t Λμ

− λ + 

dt

ρ − t ðtÞe Λμ dt

Pxx,SLHL,sp are production rates by fast neutron spallation at sea level high latitude (SLHL), and Sxx(t) are time-dependent scaling factors that relate SLHL production rates to the local production rates. In the case of muons, we consider that the temporal variation of their scaling factors to be negligible due to the overall small fraction of muogenic production. This step simplifies the second part of the presented equations: Pxx,SLHL,μ * Sμ = Pxx,loc,μ, where Pxx,loc,μ. is the local production by slow muon capture and fast muogenic processes. The SLHL production rates P10,SLHL,sp, the scaling factors Ssp(t) and the local muogenic production rates Pxx,loc,μ are based on the code of Balco et al. (2008). References Amidon, W.H., Rood, D.H., Farley, K.A., 2009. Cosmogenic He-3 and Ne-21 production rates calibrated against Be-10 in minerals from the Coso volcanic field. Earth Planet. Sci. Lett. 280, 194–204. Balco, G., Shuster, D.L., 2009a. Production rate of cosmogenic Ne-21 in quartz estimated from Be-10, Al-26, and Ne-21 concentrations in slowly eroding Antarctic bedrock surfaces. Earth Planet. Sci. Lett. 281, 48–58. Balco, G., Shuster, D.L., 2009b. Al-26−Be-10−Ne-21 burial dating. Earth Planet. Sci. Lett. 286, 570–575. Balco, G., Stone, J.O., Lifton, N.A., Dunal, T.J., 2008. A complete and easily accessible means of calculating surface exposure ages or erosion rates from Be-10 and Al-26 measurements. Quat. Geochronol. 3, 174–195. Balco, G., Briner, J., Finkel, R.C., Rayburn, J.A., Ridge, J.C., Schaefer, J.M., 2009. Regional beryllium-10 production rate calibration for late-glacial northeastern North America. Quat. Geochronol. 4, 93–107. Bruno, L.A., 1995. Datierung von Moränen und glazial überprägten Oberflächen in der Antarktis mit in situ produzierten kosmogenen Edelgasen [PhD Diss. No. 11256 thesis]. Zürich, ETH Zürich. Bruno, L.A., Baur, H., Graf, T., Schlüchter, C., Signer, P., Wieler, R., 1997. Dating of Sirius Group tillites in the Antarctic Dry Valleys with cosmogenic 3He and 21Ne. Earth Planet. Sci. Lett. 147, 37–54. Chmeleff, J., von Blanckenburg, F., Kossert, K., Jakob, D., 2010. Determination of the 10Be half-life by multicollector ICP-MS and liquid scintillation counting. Nucl. Instrum. Methods Phys. Res. B 268, 192–199. Clark, D.H., Bierman, P.R., Larsen, P., 1995. Improving in-situ cosmogenic chronometers. Quat. Res. 44, 367–377. Desilets, D., Zreda, M., 2003. Spatial and temporal distribution of secondary cosmic-ray nucleon intensities and application to in situ cosmogenic data. Earth Planet. Sci. Lett. 206, 21–42. Desilets, D., Zreda, M., Pradu, T., 2006. Extended scaling factors for in situ cosmogenic nuclides. New measurements at low latitude. Earth Planet. Sci. Lett. 246, 265–276. Di Nicola, L., 2008. Multiple cosmogenic nuclide dating of Late Cenozoic rock surfaces and glacial drifts in the Terra Nova Bay region (Antarctica). PhD Thesis, Università dell'Aquila, Italy 116. Di Nicola, L., Strasky, S., Schluchter, C., Salvatore, M.C., Akcar, N., Kubik, P.W., Christl, M., Kasper, H.U., Wieler, R., Baroni, C., 2009. Multiple cosmogenic nuclides document complex Pleistocene exposure history of glacial drifts in Terra Nova Bay (northern Victoria Land, Antarctica). Quat. Res. 71, 83–92. Dühnforth, M., 2007. Sediment flux and deposition on arid-region fans, eastern California, USA [PhD, No. 17020 thesis]. Zurich, ETH. Dunai, T.J., 2000. Scaling factors for production rates of in situ produced cosmogenic nuclides. A critical re-evaluation. Earth Planet. Sci. Lett. 176, 157–169. Fernandez-Mosquera, D., Hahm, D., Marti, K., 2010. Calculated rates of cosmic ray muonproduced Ne in subsurface quartz. Geophys. Res. Lett. 37, L15403 doi:10.1029/ 2010GL044106 Fujioka, T., Chappell, J., Honda, M., Yatsevich, I., Fifield, L.K., Fabel, D., 2005. Global cooling initiated stony deserts in central Australia 2–4 Ma, dated by cosmogenic 21Ne–10Be. Geology 33, 993–996. Gillespie, A.R., Bierman, P.R., 1995. Precision of terrestrial exposure ages and erosion rates estimated from analysis of cosmogenic produced in situ. J. Geophys. Res. 100, 24637–24649.

.

Goethals, M.M., Hetzel, R., Niedermann, S., Wittmann, H., Fenton, C.R., Kubik, P.W., Christl, M., v.B., F., 2009. An improved experimental determination of cosmogenic 10Be/21Ne and 26Al/21Ne production ratios in quartz. Earth Planet. Sci. Lett. doi:10.1016/j. epsl.2009.04.027. Gosse, J.C., Phillips, F.M., 2001. Terrestrial in situ cosmogenic nuclides. Theory and application. Quat. Sci. Rev. 20, 1475–1560. Graf, A.A., Strasky, S., Ivy-Ochs, S., Akcar, N., Kubik, P.W., Burkhard, M., Schluchter, C., 2007. First results of cosmogenic dated pre-last glaciation erratics from the Montoz area, Jura Mountains, Switzerland. Quat. Int. 164–165, 43–52. Heisinger, B., Lal, D., Jull, A.J., Kubik, P.W., Ivy-Ochs, S., Neumaier, S., Knie, K., Lazarev, V., Nolte, E., 2002a. Production of selected cosmogenic radionuclides by muons. 1. Fast Muons. Earth Planet. Sci. Lett. 200, 345–355. Heisinger, B., Lal, D., Jull, A.J., Kubik, P.W., Ivy-Ochs, S., Knie, K., Nolte, E., 2002b. Production of selected cosmogenic radionuclides by muons. 2. Capture of negative muons. Earth Planet. Sci. Lett. 200, 357–369. Hetzel, R., Tao, M.X., Niedermann, S., Strecker, M.R., Ivy-Ochs, S., Kubik, P.W., Gao, B., 2004. Implications of the fault scaling law for the growth of topography. Mountain ranges in the broken foreland of north-east Tibet. Terra Nova 16, 157–162. Ivy-Ochs, S., Schlüchter, C., Kubik, P.W., Dittrich-Hannen, B., Beer, J., 1995. Minimum 10Be exposure ages of early Pliocene for the Table Mountain plateau and the Sirius Group at Mount Fleming, Dry Valley, Antarctica. Geology 23, 1007–1010. Ivy-Ochs, S., Kerschner, H., Reuther, A., Maisch, M., Sailer, R., Schaefer, J., Kubik, P.W., Synal, H.A., Schlüchter, C., 2006. The timing fof glacier advances in the northern Alps based on surface exposure dating with cosmogenic 10Be, 26Al, 36Cl and 21Ne. In: Siame, L.L., Bourles, D.L., Brown, E.T. (Eds.), In Situ-Produced Cosmogenic Nuclides and Quantification of Geological Processes: Boulder, GSA Special Paper, vol. 415, pp. 43–60. Klein, J., Giegengack, R., Middleton, R., Sharma, P., Underwood, J., Weeks, R.A., 1986. Revealing histories of exposure using in situ produced 26Al and 10Be in Libyan desert glass. Radiocarbon 28, 547–555. Kober, F., 2004. Quantitative analysis of the topographic evolution of the Andes of northern Chile using cosmogenic nuclides [ETH PhD, No. 15858 thesis]. Zurich, ETH. Kober, F., Ivy-Ochs, S., Leya, I., Wieler, R., Baur, H., Magna, T., 2005. In situ cosmogenic 10 Be and 21Ne in sanidine and in situ cosmogenic 3He in Fe–Ti-oxide minerals. Earth Planet. Sci. Lett. 236, 404–418. Kober, F., Ivy-Ochs, S., Schlunegger, F., Baur, H., Kubik, P.W., Wieler, R., 2007. Denudation rates and a topography-driven rainfall threshold in northern Chile. Multiple cosmogenic nuclide data and sediment budgets. Geomorphology 83, 97–120. Kober, F., Ivy-Ochs, S., Zeilinger, G., Schlunegger, F., Kubik, P.W., Baur, H., Wieler, R., 2009. Complex multiple cosmogenic nuclide concentration and histories in the arid Rio Lluta catchment, northern Chile. Earth Surf. Proc. Landf. 34, 398–412. Korschinek, G., Bergmaier, A., Faestermann, T., Gerstmann, U.C., Knie, K., Rugel, G., Wallner, A., Dillmann, I., Dollinger, G., von Gostomski, C.L., Kossert, K., Maiti, M., Poutivtsev, M., Remmert, A., 2010. A new value for the half-life of Be-10 by heavy-ion elastic recoil detection and liquid scintillation counting. Nucl. Instrum. Methods Phys. Res. B 268, 187–191. Lal, D., 1991. Cosmic ray labeling of erosion surfaces. In-situ nuclide production rates and erosion models. Earth Planet. Sci. Lett. 104, 424–439. Lifton, N.A., Bieber, J.W., Clem, J.M., Duldig, M.L., Evenson, P., Humble, J.E., Pyle, R., 2005. Addressing solar modulation and long-term uncertainties in scaling secondary cosmic rays for in situ cosmogenic nuclide applications. Earth Planet. Sci. Lett. 239, 140–161. Niedermann, S., 2000. The 21Ne production rate in quartz revisited. Earth Planet. Sci. Lett. 183, 361–364. Niedermann, S., Graf, T., Marti, K., 1993. Mass spectrometric identification of cosmicray-produced neon in terrestrial rocks with multiple neon components. Earth Planet. Sci. Lett. 118, 65–73. Niedermann, S., Graf, T., Kim, J.S., Kohl, K., Nishiizumi, K., 1994. Cosmic-ray-produced 21 Ne in terrestrial quartz. the neon inventory of Sierra Nevada quartz separates. Earth Planet. Sci. Lett. 125, 341–355. Nishiizumi, K., Winterer, E.L., Kohl, J.R., Klein, J., Middleton, R., Lal, D., Arnold, J.R., 1989. Cosmic ray production rates of 10Be and 26Al in quartz from glacially polished rocks. J. Geophys. Res. 94, 17907–17915. Nishiizumi, K., Kohl, C.P., Shoemaker, E.M., Arnold, J.R., Klein, J., Fink, D., Middleton, H., 1991. In situ 10Be–26Al exposure ages at Meteor Crater, Arizona. Geochim. Cosmochim. Acta 55, 2401–2708. Nishiizumi, K., Caffee, M., Finkel, R.C., Brimhall, G., Mote, T., 2005. Remnants of a fossil alluvial fan landscape of Miocene age in the Atacama Desert of northern Chile using cosmogenic nuclide exposure age dating. Earth Planet. Sci. Lett. 237, 499–507. Nishiizumi, K., Imamura, M., Caffee, M.W., Southon, J.R., Finkel, R.C., McAninch, J., 2007. Absolute calibration of Be-10 AMS standards. Nucl. Instrum. Methods Phys. Res. B 258, 403–413. Oberholzer, P., Baroni, C., Schäfer, J.M., Orombelli, J., Ivy-Ochs, S., Kubik, P.W., Baur, H., Wieler, R., 2003. Limited Pliocene/Pleistocene glaciation in Deep Freeze Range, northern Victoria Land, derived from in-situ cosmogenic nuclides. Ant. Sci. 15, 493–502. Putnam, A.E., Schaefer, J.M., Barrell, D.J.A., Vandergoes, M., Denton, G.H., Kaplan, M.R., Finkel, R., Schwartz, R., Goehring, B.M., Kelley, S.E., 2010. In situ cosmogenic 10Be production-rate calibration from the Southern Alps, New Zealand. Quat. Geochronol. 5, 392–409. Schäfer, J.M., Ivy-Ochs, S., Wieler, R., Leya, I., Baur, H., Denton, G.H., Schlüchter, C., 1999. Cosmogenic noble gas studies in the oldest landscape on earth. surface exposure ages of the Dry Valleys, Antarctica. Earth Planet. Sci. Lett. 167, 215–226.

F. Kober et al. / Earth and Planetary Science Letters 302 (2011) 163–171 Schäfer, J.M., Tschudi, S., Zhao, Z., Wu, X., Ivy-Ochs, S., Wieler, R., Baur, H., Kubik, P.W., Schlüchter, C., 2002. The limited influence of glaciations in Tibet on global climate over the past 170,000 yr. Earth Planet. Sci. Lett. 194, 287–297. Schäfer, J.M., Oberholzer, P., Zhao, Z., Ivy-Ochs, S., Wieler, R., Baur, H., Kubik, P.W., Schlüchter, C., 2008. Cosmogenic beryllium-10 and neon-21 dating of late Pleistocene glaciations in Nyalam, monsoonal Himalayas. Quat. Sci. Rev. 27, 295–311. Stone, J., 2000. Air pressure and cosmogenic isotope production. J. Geophys. Res. 105, 23753–23759. Strasky, S., 2008. Glacial response to global climate changes: Cosmogenic nuclide chronologies from high and low latitudes. [ETH PhD, No. 17569 thesis]. p. 181.

171

Strasky, S., Di Nicola, L., Baroni, C., Salvatore, M.C., Baur, H., Kubik, P.W., Schluchter, C., Wieler, R., 2009. Surface exposure ages imply multiple low-amplitude Pleistocene variations in East Antarctic Ice Sheet, Ricker Hills, Victoria Land. Ant. Sci. 21, 59–69. Tschudi, S., Schafer, J.M., Borns, H.W., Ivy-Ochs, S., Kubik, P.W., Schluchter, C., 2003. Surface exposure dating of Sirius Formation at Allan Hills nunatak, Antarctica. New evidence for long-term ice-sheet stability. Eclo. Geol. Helv. 96, 109–114. van der Wateren, F.M., Dunai, T.J., van Balen, R.T., Klas, W., Verbers, A.L.L.M., Passchier, S., Herpers, U., 1999. Contrasting Neogene denudation histories of different structural regions in the Transantarctic Mountains rift flank constrained by cosmogenic isotope measurements. Glob. Planet. Change 23, 145–172.