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Luminescence age modeling of variably-bleached sediment: Model selection and input Elizabeth L. Chamberlaina,b,∗, Jakob Wallingac, Zhixiong Shend a
Department of Earth and Environmental Sciences, Tulane University, New Orleans, LA, USA Department of Earth and Environmental Sciences, Vanderbilt University, Nashville, TN, USA c Netherlands Centre for Luminescence Dating & Soil Geography and Landscape Group, Wageningen University, Wageningen, The Netherlands d Department of Marine Science, Coastal Carolina University, Conway, SC, USA b
A R T I C LE I N FO
A B S T R A C T
Keywords: Bleaching Luminescence dating Overdispersion Residual dose Quartz sand
Optically stimulated luminescence (OSL) dating of heterogeneously-bleached sediment by means of a minimum age model requires the input of a 'sigma_b' (σb) value describing the overdispersion of the single-aliquot De distribution expected for a well-bleached sample. We propose that σb and associated uncertainty can be accurately determined if a large dataset of De distributions is available and includes well-bleached samples. Our approach applies the bootstrapped Minimum Age Model (bootMAM) to a dataset of overdispersions in De distributions, to obtain quantitative estimates of σb. Corrections are made for constant-diameter aliquots of different grain sizes, based on the published dependency of overdispersion on the number of grains per aliquot. These adapted σb values are then input to bootMAM to obtain robust paleodoses for the samples. We test the sensitivity of paleodose to σb and we demonstrate that with correct σb, identical paleodoses are obtained using bootMAM and the Central Age Model on samples judged to be well-bleached. We conclude that for large datasets consisting of well- and heterogeneously-bleached samples, appropriate σb values can be obtained from the data, and that bootMAM can be applied to all samples within this dataset.
1. Introduction
sensitivity distribution of the grains (Duller, 2008) and the number of grains per aliquot (GPA), as these combined determine the number of grains contributing to the signal of an aliquot and thus the degree of within-aliquot signal-averaging (Cunningham et al., 2011). The proportion of luminescent quartz grains can vary by setting and has been reported to range from less than 1 to 5% (Duller, 2008; Harrison et al., 2008) to as high as 40% (Jacobs et al., 2008). In several studies, σb has been estimated based on the overdispersion obtained for analogues such as well-bleached aeolian samples (e.g., Jain et al., 2005; Cunningham et al., 2011). However, as pointed out by Thomsen et al. (2012), this approach only holds if such an analogue is available and indeed well-bleached, experienced similar dose rate heterogeneity as the sediments of interest, and has received a similar burial dose. Here we propose a quantitative approach to estimate σb, based on a combination of field data and statistical treatments of the dataset of interest itself. This effort is facilitated by a large (n = 42) and mainly archival luminescence dataset of quartz sand samples obtained from the Mississippi Delta, which contains abundant information regarding De scatter for this region and sediment-type. The results of our σb investigation are used to assess the degree of bleaching of the sediments, and ultimately, to comment on the selection of appropriate age
The degree of bleaching of sedimentary deposits is a primary consideration in optically stimulated luminescence (OSL) dating (e.g., Jain et al., 2004; Murray et al., 2012), especially in fluvial sediment where grains may not receive sufficient light exposure for complete zeroing of the OSL signal in all grains prior to burial (Wallinga, 2002). The identification of incomplete bleaching is an important step in age model selection (e.g., Galbraith et al., 1999; Arnold et al., 2009; Cunningham et al., 2015). When heterogeneous bleaching is suspected, a minimum age model (Galbraith et al., 1999) is often used to truncate the distribution of equivalent doses (Des) to identify the minimum burial dose that may be captured by well-bleached grains, i.e. grains of which the fast-component OSL signal was fully reset at the time of deposition and burial. This requires input to the model of a 'sigma_b' (σb) value describing the overdispersion of the single-aliquot De distribution expected for a well-bleached sample. The overdispersion of well-bleached sediment can vary by location and depositional environment, primarily because this value is sensitive to beta dose heterogeneity (e.g., Mayya et al., 2006). For multi-grain aliquots, the overdispersion also depends on the luminescence ∗
Corresponding author. Department of Earth and Environmental Sciences, Vanderbilt University, Nashville, TN, USA. E-mail address:
[email protected] (E.L. Chamberlain).
https://doi.org/10.1016/j.radmeas.2018.06.007 Received 25 November 2017; Received in revised form 30 May 2018; Accepted 2 June 2018 1350-4487/ © 2018 Elsevier Ltd. All rights reserved.
Please cite this article as: Chamberlain, E.L., Radiation Measurements (2018), https://doi.org/10.1016/j.radmeas.2018.06.007
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Fig. 1. Locations of samples from the modern Mississippi River and Lafourche subdelta deposits, of the Mississippi Delta, USA (inset). Original references are indicated by colored boxes that outline the samples.
analysis of Chamberlain et al. (2018) differed slightly from that applied in previous OSL dating studies of the Mississippi Delta (e.g., Shen et al., 2015). To avoid systematic biases associated with the use of archival data obtained from these two studies, we reanalyzed all data repurposed from Shen et al. (2015) identical to those of Chamberlain et al. (2018). Details of the approaches to extract Des used by this study and by previous work in the Mississippi Delta are presented in the Supplementary File (Table S3). Sediment from the modern river (21.9 m below the water surface) was obtained with a grab sampler in 2014, and prepared and measured in a similar fashion as the archival data, including use of the singlealiquot regenerative-dose (SAR) protocol (Murray and Wintle, 2003), subtraction of an early background interval (Cunningham and Wallinga, 2010), and standard aliquot acceptance criteria (e.g., Duller, 2003) detailed in the Supplementary File (Tables S2 and S3). The aliquot diameter of archival samples was previously described as 1–2 mm (Shen et al., 2015; Chamberlain et al., 2018). For the present study, we needed information on GPA. To estimate GPA for the different samples, we assumed that spheroid grains of a median diameter within the sample-specific selected grain-size range filled 75% of each aliquot area (assumed to be 2.7 mm2, based on 1.2 mm diameter).
models. For this archival dataset, no single-grain measurements were made, and hence we have no information on the single-grain sensitivity distribution. Availability of such data would have made our analysis easier, but an approach relying on availability of such data would be less widely applicable. 2. Sample selection and measurement This study repurposes OSL data from quartz sand (Supplementary File, Table S1) extracted from deposits of the Lafourche subdelta, Mississippi Delta, USA, measured by Shen et al. (2015, n = 23, EF, NV, and PV localities) and Chamberlain et al. (2018, n = 17, BC, CD, CV, DL, FC, GM, LR, RL, and SC localities). In addition, two grain-size fractions of a new sample obtained from the bed of the modern Mississippi River (BCU2 locality) were analyzed as part of an ongoing assessment of the luminescence characteristics of Mississippi Delta quartz (Fig. 1). The Lafourche subdelta deposits range in age from 1.6 - 0.6 ka (Törnqvist et al., 1996; Shen et al., 2015; Chamberlain et al., 2018) and thereby all have relatively low paleodoses. Modern river sediment is currently in transit and should have a zero OSL age and zero paleodose if well-bleached. The sampling, preparation, and measurement procedures for the archival data are presented in their primary publications. The data 2
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3. Quantifying σb
values for these three groups. Whether or not the dataset contains wellbleached samples is more difficult to assess; we propose that absence of a clear ‘leading edge’ (Lepper et al., 2000) in the distribution of overdispersion values may serve as a warning sign that this condition is possibly not met. From a theoretical perspective, a trend of increasing calculated σb with increasing grain size/decreasing GPA would be expected, as there is less averaging of signals during luminescence measurements of coarser sediment because there are fewer grains per constant-diameter aliquot (Duller, 2008). Moreover, the grain size and potassium concentration of the sampled sediments is of importance, as beta dose heterogeneity is greater for coarser sediment (e.g., Mayya et al., 2006) and lower K-concentrations (Guérin et al., 2015a). For our dataset, the sampled fluvial sediments were relatively homogeneous, but varied in median grain size. Although grain-size distributions were not available, the grain size used for luminescence dating provides a good proxy of the coarseness of the deposit, because the coarsest grain size possible was selected for each sample (Shen et al., 2015; Chamberlain et al., 2018). The mean bulk sediment potassium concentration of our samples is 1.75% with a standard deviation of 0.17%, generally showing a negative correlation with sample grain size, likely due to higher clay content of finer deposits (samplespecific values are provided in Shen et al., 2015; Chamberlain et al., 2018). Assuming that single-grain sensitivity distributions are independent of grain size, we conclude that greater overdispersion for well-bleached samples is to be expected for the larger grain sizes. This trend further enforces the grain-size trend expected due to reduced within-aliquot averaging effects for coarser grains with fewer GPA. The σb values calculated for the different grain-size classes (using the approach described above) tend to agree with the expected range (∼10–11%) within their uncertainties, but do not show the expected trend in calculated σb with grain size (Table 1, Supplementary File, Fig. S1). This likely indicates that not all grain-size classes contained enough samples to obtain accurate and precise estimates of σb. To overcome this challenge, we used the calculated σb for the 125–180 μm group (n = 14; σb = 10.6 ± 3.4%) as a benchmark because this class contained the most samples, and was expected to yield the most robust estimate of σb. From this benchmark, we modeled σb values for the other grain-size classes by applying procedures outlined in Cunningham et al. (2011). Cunningham et al. (2011) simulated overdispersion as a function of GPA, for three samples with varying single-grain OSL sensitivity distributions. This identified the reduction in overdispersion associated with the measurement of increasing grain numbers for three scenarios, and thereby produced correction factors that may be used to estimate the inherent De scatter for multiple-grain aliquots if the single-grain inherent De scatter is known. In absence of such information for our samples, we assumed a 20% overdispersion for well-bleached single grains (Duller, 2008; Arnold and Roberts, 2009) of Mississippi Delta sand. Much higher values have also been reported in literature (e.g., Jacobs et al., 2008), but these tend to be from highly heterogeneous and/or poorly-sorted deposits. Although it would be even better to have information on overdispersion for well-bleached samples at the singlegrain level, we note that such information is often not available, and that final results are not very sensitive to the assumed value (for example, results obtained assuming 25% at single-grain level are not statistically different). We observed that the assumed 20% single-grain overdispersion was diminished to a value of 10.6% in the 125–180 μm (46 GPA) class, yielding a factor of 0.53; this indicates that our samples show similar reduction in overdispersion as a function of GPA as samples RBM2 and TNE9503 from Cunningham et al. (2011). Therefore, correction factors for other GPA could be read from these two relevant graphs, and we adopted the average. We refer to values obtained through this approach as “adapted σb” (Table 1), and propose that these are the most valid estimates for input to a minimum age model. These adapted σb values range from 6.9 ± 2.2% (75–125 μm; 108 GPA) to 12.5 ± 4.0%
Mississippi Delta sediment is ideal for developing and testing new methods for quantifying overdispersion because quartz sand is suitable here for luminescence dating and there is a large archive of luminescence ages constrained by radiocarbon and relative chronologies (Shen et al., 2015; Chamberlain et al., 2018) to test the robustness of results. Shen et al. (2015) used a σb of 10% for their samples with quartz extracts of variable grain sizes (75–200 μm; corresponding to 48–108 GPA). This σb was judged to be characteristic of the overdispersion of Des for samples they qualified as well-bleached. Chamberlain et al. (2018) presented σb values for another subgroup of 75–125 μm grainsize samples (108 GPA, overdispersion = 11 ± 3%) and 125–180 μm grain-size samples (46 GPA, overdispersion = 11 ± 4%). These σb values were obtained through the following sequence of steps: 1) Determine the overdispersion of Des for each sample with the Central Age Model (CAM) (Galbraith et al., 1999). 2) Group overdispersion values and associated uncertainties obtained in Step 1 by grain-size class. 3) Apply the bootstrapped (Cunningham and Wallinga, 2012) Minimum Age Model (Galbraith et al., 1999) (bootMAM) to the overdispersion datasets for each grain-size class, assuming that each overdispersion dataset is not overdispersed, i.e., σb,OD = 0 ± 0. This latter step is particularly novel, and offers an objective and reproducible method to quantify overdispersion (including uncertainty) for the best-bleached sample(s) within each grain-size class. Such application of the bootMAM to the overdispersion dataset assumes that overdispersion distributions for well-bleached samples are log-normal distributed. As this condition is uncertain, we checked that similar results were obtained when applying the unlogged version of the minimum age model (bootMAMul). 4) The bootMAM output of Step 3 provides the σb input to bootMAM for age modeling of De datasets of all samples with the same grain-size class. Please note that while Cunningham and Wallinga (2012) used an unlogged version of the Minimum Age Model (MAM), we use a logged (standard) version for all calculations except the paleodose estimation of the modern river bedload sample. Our study builds on the σb estimation technique proposed by Chamberlain et al. (2018). Sand samples were grouped by grain-size class (75–125, 75–180, 90–180, 100–200, 125–180, or 180–250 μm). Values for overdispersion, quantified with CAM following a 4 standard deviation cleaning of the aliquots to remove the most anomalous outliers (see Chamberlain et al., 2018), were input to bootMAM to estimate σb for each grain-size class (Supplementary File, Table S1). We refer to these values as “calculated σb” (Table 1). For this approach to be effective and provide a robust σb for each group, it is a prerequisite that each group contains a sufficient number of samples to run the age models, and must also contain some samples that are completely bleached. While the former criteria is apparent, the latter criteria is something that may not be immediately known about a dataset. In our data, the 90–180 μm (n = 4), 100–200 μm (n = 2), and 180–250 μm (n = 1) groups did not have enough samples to allow for modeling σb with bootMAM, and so we do not present calculated σb
Table 1 Selection of σb values. The 125–180 μm class was used as benchmark (italic), and bold values derived from it were identified as the most valid estimation for input to the bootstrapped Minimum Age Model. Grain-size class (μm)
Samples (n)
Calculated average grains per disk (n)
Calculated σb (%)
Adapted σb (%)
75–125 75–180 90–180 100–200 125–180 180–250
11 10 4 2 14 1
108 66 59 48 46 23
11.0 ± 2.3 13.5 ± 3.2 – – 10.6 ± 3.4 –
6.9 ± 2.2 9.7 ± 3.1 10.1 ± 3.2 10.6 ± 3.4 10.6 ± 3.4 12.5 ± 4.0
3
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(De,CAM) and the paleodose obtained from the bootMAM (De,bootMAM) following a 3 standard deviation cleaning of De datasets (see Chamberlain et al., 2018), so that: Residual dose = De,CAM - De,bootMAM
(1)
This approach to quantify residual dose assumes that the minimum age model of choice has successfully estimated the burial dose (by isolating the Des of the well-bleached grains within the sample), an assumption that is supported by the stratigraphic correctness of sand ages for these samples demonstrated by Shen et al. (2015) and Chamberlain et al. (2018), by prior radiocarbon dating of underlying peat that provide an upper age limit of 1.6 ka for Lafourche deposits (Törnqvist et al., 1996), and by further stratigraphic assessment herein (see Results). Sand was classified as well-bleached if the residual dose minus 1σ uncertainty was equal to or less than zero. This means that some samples considered to be well-bleached may have possessed small residual doses.
5. Results Adapted σb values were generally lower than the calculated σb values for the grain-size classes (Table 1). The adapted σb values lay within the range of overdispersion quantified with CAM for individual samples within each grain-size class, with the exception of the 180–250 μm class for which there was only one sample (Fig. 3). To test whether the use of adapted σb values (which varied by grainsize class) may affect paleodoses, we also calculated De,bootMAM using a constant σb, value of 11 ± 3% (Chamberlain et al., 2018) for all sands regardless of grain size. We anticipated that this would cause the greatest offset in the 75–125 μm class, because this class had the greatest difference between the adapted (6.9 ± 2.2%) and constant (11 ± 3%) σb values. Surprisingly, there was little difference between the DebootMAM values estimated with these two approaches for all grainsize classes (Fig. 4). To explore further, the effects of σb on paleodose estimation via bootMAM were tested for five samples of 125–180 μm mouth bar sand representing various degrees of bleaching (Fig. 5). The tested samples and their residual doses included LR I-2 (3.18 ± 0.64 Gy), RL I-1 (1.56 ± 0.34 Gy), BC I-2 (0.75 ± 0.22 Gy), GM I-1 (0.24 ± 0.14 Gy), and CD I-2 (0.047 ± 0.080 Gy). Values of σb ranging from 0 to 100% were input to bootMAM at 5% intervals with a constant uncertainty of 3%. These σb values are referred to as “test σb”, and output paleodoses
Fig. 2. Steps used to obtain paleodoses by quantitatively establishing σb values for input to the bootstrapped Minimum Age Model (bootMAM) from the existing dataset. Products are presented in boxes and steps to obtain them are enumerated.
(180–250 μm; 23 GPA) (Table 1). Our technique to obtain the calculated (benchmark) and adapted σb values for paleodose estimation are summarized in Fig. 2. 4. Calculating residual dose Identifying incomplete bleaching is an important step in the selection of age models, and ultimately, toward the accurate estimation of burial dose. Modern sediments that are sufficiently reset in transit should yield zero Des, and so, any residual dose on these sediments can be easily identified as positive Des (e.g., Murray et al., 1995; Stokes et al., 2001). Estimating residual doses of sedimentary deposits without independent chronology is less straightforward (Murray et al., 2012). Such assessments have often relied on dose distributions obtained from measurements of small-diameter aliquots (e.g., Olley et al., 1998). However, those can be highly influenced by grain size (i.e., GPA) and require knowledge of the σb value (which is often poorly constrained). Additionally, De distributions act as a sort of pass/fail test for bleaching; high scatter can indicate bleaching heterogeneity but does not quantify exactly how this heterogeneity may affect the OSL age estimate of the sample. Other approaches to checking bleaching include analyzing the form of the optical decay curve (e.g., Singhvi and Lang, 1998; Bailey, 2000), comparing different luminescence signals measured for the same sample (e.g., Roberts et al., 1994; Murray et al., 2012), the use of independent chronology (e.g., Guibert et al., 2017) and, more recently, multiple-signal comparisons of polymineral sediment (Reimann et al., 2015; Chamberlain et al., 2017). Here we estimated the sample-average residual doses of quartz sand from the differences between a central De value determined by the CAM
Fig. 3. Values for overdispersion in the De distribution of each sample obtained with the Central Age Model (filled circles), values for calculated σb (open squares), and adapted σb (filled squares) of each grain-size class (see legend). The calculated σb for the 125–180 μm grain-size class was used as benchmark, to model adapted σb values for the other grain-size classes using the dependency of Cunningham et al. (2011). 4
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Fig. 6. Dependence of paleodose on σb input to the bootstrapped Minimum Age Model was tested using the Dose Overestimation Ratio (Equation (2)), for five samples with varying degrees of bleaching (See Fig. 5). Values for De,bootMAM obtained with σb = 10.6 ± 3.4% (dashed line) lie at the intersection of the dashed line and y = 1. Squares indicate values (overdispersion, De,CAM/ De,bootMAM) obtained from the Central Age Model.
Fig. 4. Comparison of Des obtained with the bootstrapped Minimum Age Model using constant σb values of 11 ± 3% for all samples and adapted σb values that varied with the number of grains per aliquot (i.e., grain size of the samples; see Table 1).
and allows for comparison across samples with different burial doses. The Dose Overestimation Ratio was plotted against test σb (Fig. 6). We found that the test paleodoses of the most heterogeneouslybleached samples (e.g., LR I-2, RL I-1) showed the greatest response to the σb input to bootMAM, while the test paleodoses of the better bleached samples (e.g., GM I-1, CD I-2) were less affected by varying σb input to bootMAM (Fig. 6). The test paleodose increased with the test σb up to the intersection of the test σb and overdispersion values obtained for a particular sample with CAM, and then plateaued (Fig. 6).
are referred to as “test paleodose”. The resulting De,bootMAM values were normalized by the paleodose of each sample, quantified with bootMAM using the benchmark σb value of 10.6 ± 3.4% for the 125–180 μm class and the adapted σb values for other grain-size classes. This produced a Dose Overestimation Ratio, defined as:
Dose Overestimation Ratio =
De, bootMAM [Test ] De, bootMAM [Benchmark or Adapted]
(2)
This ratio describes how responsive De,bootMAM is to forcing by σb,
Fig. 5. Radial plots showing the central De quantified with the Central Age Model (De,CAM) and the paleodose quantified with the bootstrapped Minimum Age Model (De,bootMAM) for samples with varying degrees of bleaching. The filled circles represent points that are consistent with the De,bootMAM paleodose within 2σ uncertainty. Residual doses (“RD”, in Gy) are given in parentheses. 5
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found to be internally consistent (Chamberlain et al., 2018). This demonstrated that CAM was indeed overestimating the age of some deposits, corroborating the presence of heterogeneous bleaching in some samples, and thus the use of a minimum age model.
Additional tests were performed on all samples that we judged as wellbleached; these showed little responsiveness in test paleodose to σb (Supplementary File, Fig. S2). These results were anticipated based on the construction of the model; the MAM extracts a central dose from a lognormal distribution that is included within the total distribution of the dataset and defined by σb. Previous research based on field and laboratory data has shown that overdispersion is dose-dependent, and thus may increase with sample age (Thomsen et al., 2012). This suggests that the use of a single σb value for a dataset with samples of different ages may not be valid (Murray et al., 2012). Given the relatively low natural dose and small age range of our samples (all doses obtained with bootMAM are less than 4 Gy), we expect this was not a major issue with our analyses. This is corroborated by our analysis of samples, which showed no trend in overdispersion with paleodose for samples that were judged to be wellbleached (Supplementary File, Fig. S3). We investigated the internal consistency (that is, the stratigraphic correctness of ages) of our data obtained with both age models. This was tested for four samples from a single borehole (PV I-4, PV I-5, PV I7 and PV I-8) with a maximum age constrained by radiocarbon dating of an underlying peat (Törnqvist et al., 1996; Shen et al., 2015). We found that bootMAM ages were stratigraphically correct, while CAM ages included an inversion within the OSL data and included one OSL age that exceeded the underlying radiocarbon age (Fig. 7). Furthermore, independent chronology previously obtained through radiocarbon dating of peats that underlie Lafourche subdelta deposits at other locations has established an upper age limit of ∼1.6 ka for the samples investigated herein (e.g., Törnqvist et al., 1996). We found that many CAM ages exceeded 1.6 ka (n = 8, considering the lowest age possible within the uncertainty), in some cases by more than 700 years. By contrast, bootMAM ages were all younger than 1.6 ka and were
6. Discussion 6.1. σb selection Our results confirm theoretical expectations that bootMAM will not overestimate paleodose compared to CAM, even with extra-ordinarily high σb input (Fig. 6). Our data also indicate that selecting too low σb may result in underestimation of paleodose, although the effect is smaller than 10% for our samples (Fig. 6). Small variations (on the order of a few percent) in σb did not majorly affect the paleodose of the samples tested in this study (Fig. 4). With our best-estimate σb, results obtained with bootMAM and CAM models were indistinguishable for samples that were apparently well-bleached. Based on these findings, we conclude that for large datasets consisting of well- and incompletely-bleached samples, appropriate σb values can be obtained from the data using the approach discussed in this paper (Fig. 2).
6.2. Age model selection Selection of an appropriate age model is regarded as an important component of accurate luminescence dating (e.g., Galbraith et al., 1999; Olley et al., 2004; Arnold et al., 2007; Arnold and Roberts, 2009). It has been previously suggested that the best-suited age model varies by sample based on such factors as the burial dose and degree of bleaching (Arnold and Roberts, 2009). As these conditions are often unknown, an age model decision process may be applied to guide selection toward the most likely model, however such an approach is selfadmittedly “rather convoluted” (Arnold and Roberts, 2009) and has been shown to yield aberrant results (Thomsen et al., 2016). Previously, the use of a minimum age model has been advocated only for samples in which poor bleaching is suspected based on criteria such as the width or skewness of the De distribution (Olley et al., 1999, 2004), while the CAM or an arithmetic mean (Guérin et al., 2017) is suggested for samples that are suspected to be better bleached or where wide De distributions may arise from non-bleaching factors such as dose heterogeneity (Galbraith et al., 1999; Olley et al., 2004). Recently further advances have been made in age models, for example, combining dose rate information and equivalent dose distributions or signals from different minerals (Guérin et al., 2015b; Jacobs and Roberts, 2015). However, the CAM and (bootstrapped) MAM models are most widely used in the luminescence dating community, and hence we concentrate on those here. We show that identical paleodoses are obtained through both a minimum and central age model for well-bleached young fluvial sand of the Mississippi Delta (Figs. 5–7). This indicates that with selection of an appropriate σb, bootMAM can safely be applied to both well- and heterogeneously-bleached deposits (see section 6.1; Fig. 5), while the application of CAM to heterogenously-bleached deposits would clearly provide erroneous results (Fig. 7). To the best of our knowledge, bootMAM is the only methods that considers uncertainty in the expected overdispersion of well-bleached samples, which is crucial to our approach and to producing ages with robust uncertainty estimates (Cunningham and Wallinga, 2012). We therefore conclude that bootMAM is the model of choice for all late-Holocene Mississippi Delta sand deposits. This finding significantly streamlines age model selection for this specific dataset, although we caution that further examination is needed to assess the appropriateness of bootMAM for well-bleached deposits in other settings with different luminescence characteristics, depositional ages, or dosing environments.
Fig. 7. OSL and radiocarbon ages for samples from the PV I borehole. Borehole data and radiocarbon ages are from Shen et al. (2015), and OSL ages were recalculated using our methods. OSL ages estimated with the bootstrapped Minimum Age Model (bootMAM) using adapted σb values are in black text, and OSL ages for the same samples estimated with the Central Age Model (CAM) are given in parentheses and blue text. Note that bootMAM ages are in correct stratigraphic order and agree with radiocarbon age constraints, while CAM ages show inconsistencies. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.) 6
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7. Conclusions
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• Appropriate σ •
b estimates for use in the bootstrapped Minimum Age Model (bootMAM) may be obtained from a large dataset of wellbleached and heterogeneously-bleached samples, through application of the bootMAM to a dataset of overdispersions in sample De distributions. At least for our dataset, the bootstrapped Minimum Age Model yields robust ages for both well-bleached and heterogeneouslybleached samples, provided that an appropriate σb is used.
Acknowledgements We thank Barbara Mauz and Susan Packman for laboratory support. This work benefited from conversations with Tony Reimann, Mayank Jain, and others at the LED 2017 conference, and was improved by the comments of two anonymous reviewers. Appendix A. Supplementary data Supplementary data related to this article can be found at http://dx. doi.org/10.1016/j.radmeas.2018.06.007. References Arnold, L.J., Bailey, R., Tucker, G., 2007. Statistical treatment of fluvial dose distributions from southern Colorado arroyo deposits. Quat. Geochronol. 2 (1), 162–167. Arnold, L.J., Roberts, R.G., 2009. Stochastic modelling of multi-grain equivalent dose (De) distributions: implications for OSL dating of sediment mixtures. Quat. Geochronol. 4 (3), 204–230. Arnold, L.J., Roberts, R.G., Galbraith, R.F., DeLong, S.B., 2009. A revised burial dose estimation procedure for optical dating of young and modern-age sediments. Quat. Geochronol. 4 (4), 306–325. Bailey, R.M., 2000. The interpretation of quartz optically stimulated luminescence equivalent dose versus time plots. Radiat. Meas. 32 (2), 129–140. Chamberlain, E.L., Törnqvist, T.E., Shen, Z., Mauz, B., Wallinga, J., 2018. Anatomy of Mississippi Delta growth and its implications for coastal restoration. Science Advances 4 (4), eaar4740. Chamberlain, E.L., Wallinga, J., Reimann, T., Goodbred, S.L., Steckler, M., Shen, Z., Sincavage, R., 2017. Luminescence dating of delta sediments: novel approaches explored for the Ganges-Brahmaputra-Meghna Delta. Quat. Geochronol. 41, 97–111. Cunningham, A.C., Wallinga, J., 2010. Selection of integration time intervals for quartz OSL decay curves. Quat. Geochronol. 5 (6), 657–666. Cunningham, A.C., Wallinga, J., 2012. Realizing the potential of fluvial archives using robust OSL chronologies. Quat. Geochronol. 12, 98–106. Cunningham, A.C., Wallinga, J., Hobo, N., Versendaal, A.J., Makaske, B., Middelkoop, H., 2015. Re-evaluating luminescence burial doses and bleaching of fluvial deposits using Bayesian computational statistics. Earth Surface Dynamics 3 (1), 55–65. Cunningham, A.C., Wallinga, J., Minderhoud, P.S.J., 2011. Expectations of scatter in equivalent-dose distributions when using multi-grain aliquots for Osl dating. Geochronometria 38 (4), 424–431. Duller, G.A.T., 2003. Distinguishing quartz and feldspar in single grain luminescence measurements. Radiat. Meas. 37 (2), 161–165. Duller, G.A.T., 2008. Single-grain optical dating of Quaternary sediments: why aliquot size matters in luminescence dating. Boreas 37 (4), 589–612. Galbraith, R.F., Roberts, R.G., Laslett, G.M., Yoshida, H., Olley, J.M., 1999. Optical dating of single and multiple grains of quartz from Jinmium rock shelter, northern Australia: Part I, experimental design and statistical models. Archaeometry 41 (2), 339–364. Guérin, G., Christophe, C., Philippe, A., Murray, A.S., Thomsen, K.J., Tribolo, C., Urbanova, P., Jain, M., Guibert, P., Mercier, N., 2017. Absorbed dose, equivalent dose, measured dose rates, and implications for OSL age estimates: introducing the Average Dose Model. Quat. Geochronol. 41, 163–173. Guérin, G., Jain, M., Thomsen, K.J., Murray, A.S., Mercier, N., 2015a. Modelling dose rate to single grains of quartz in well-sorted sand samples: the dispersion arising from the presence of potassium feldspars and implications for single grain OSL dating. Quat. Geochronol. 27, 52–65. Guérin, G., Frouin, M., Talamo, S., Aldeias, V., Bruxelles, L., Chiotti, L., Dibble, H.L., Goldberg, P., Hublin, J.-J., Jain, M., Lahaye, C., Madelaine, S., Maureille, B.,
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