Establishing a common standardised growth curve (SGC) can substantially reduce the instrumental time for equivalent-dose (De) measurements in optically stimulated luminescence (OSL) dating. Several studies have indicated that different samples have different dose–response curves (DRCs) and therefore that it is difficult to construct a common SGC, although an SGC has been proposed in some cases. In this study, our aims were to construct a regional SGC based on small aliquots of sedimentary quartz from more than 100 samples from different sedimentary environments in the Jilantai Basin in North China and to investigate the applicability of different methods of establishing an SGC for the area. The precision of the De values of aliquots which were obtained using the SGC was compared with those obtained using the single-aliquot regenerative (SAR) protocol. Our results indicate the following: (1) for establishing an SGC using the regenerative normalisation (Re-SGC) method, selecting a suitable re-normalisation dose that is close to double the characteristic saturation dose, 2D0, can reduce the inter-aliquot/inter-sample variation in the form of DRCs within a larger dose range. (2) A common regional SGC can be established for the Jilantai area using the Re-SGC and least-squares normalisation (LS-SGC) methods, which provides reliable dating results within the 200 Gy De range.
- Standardised growth curve (SGC)
- small aliquot
- Jilantai Basin
In optically stimulated luminescence (OSL) dating, the burial age of sediments can be estimated by dividing the equivalent dose (De) by the environmental dose rate (D). OSL dating plays a key role in providing chronological frameworks in Quaternary geology, environmental archaeology and studies of paleo-earthquakes and tectonic movements. The single-aliquot regenerative-dose (SAR) procedure for quartz is widely used in measuring the equivalent dose (De) of sediments (Banerjee
In order to reduce inter-aliquot/inter-sample variation in the form of DRCs, a variety of methods have been developed, including the following: 1) establishing a common growth curve based on the arithmetical average value of the sensitivity-corrected OSL signal (Lx/Tx) for different regenerative doses of six or more aliquots for each sample and then obtaining the De values of additional aliquots by projecting the test-dose-corrected OSL signal on the constructed common growth curve, namely the SAR-SGC method (Lai and Ou 2013). 2) Re-normalisation of the sensitivity-corrected natural signal (Ln/Tn) and regenerative-dose signal (Lx/Tx), respectively, with the OSL signals of a specific regenerative dose (Lr/Tr), which is called the regenerative normalisation or re-normalisation (Re-SGC) method (Li
The present study aims to investigate the applicability of the SGC method for the single-aliquot OSL dating of quartz and to establish a potential SGC of quartz fractions from sediments in different sedimentary environments (including lacustrine, fluvial and desert) in the Jilantai Basin in North China, using the three methods mentioned above. The De values obtained using different methods are validated based on a comparison with those obtained using the SAR protocol.
The Jilantai Basin is located on the western edge of the East Asian summer monsoon, in the arid–semi-arid transition zone, which is sensitive to climatic and environmental changes. The Yellow River flows through the south-eastern margin of the basin. Previous studies documented a series of ancient lake–shorelines distributed on the west bank of the Jilantai Salt Lake through remote sensing images and field investigations. It is believed that the area once contained the ‘Jilantai-Hetao’ megalake, which covered the entire Jilantai Basin and the adjacent Hetao Basin (Chen
More than 100 quartz samples were used in this study, including lacustrine sediments from 16 profiles, fluvial sediments from 6 profiles and desert sediments from 6 profiles (see Figs. S1–S4 in the supplementary material for details). The location of those profiles is shown in Fig. 1a.
Quartz fractions were extracted using conventional separation methods (Fan
The SGC was established using the sensitivity-corrected signal from a wide range of different regenerative doses using the three previously reported methods: SAR-SGC (Lai and Ou, 2013), Re-SGC (Li
However, in this study, in order to investigate whether the constructed SGC is widely applicable to samples from the study area, we classified all of the aliquots into two groups: the OSL signals of aliquots with De values widely distributed in samples of one group were used to establish the SGC, and the OSL signals of aliquots with De values within the range of 200 Gy in another group were used to validate the constructed SGC.
The SAR-SGC method is designed to obtain De values from large numbers of aliquots from a single sample, assuming that aliquots of the same sample have similar DRCs. The SGC is constructed by fitting the averaged sensitivity-corrected signals (Lx/Tx) of aliquots with regenerative doses in a single sample. An exponential plus linear function is usually used in curve fitting, and the De values are obtained from the intercept value on the regenerative-dose axis (x-axis) after projecting the sensitivity-corrected natural signal (Ln/Tn) to the SGC. The formula used is as follows:
Here, y is the intensity of the luminescence signal; x is the regenerative dose; a is the normalised OSL intensity at the saturation level for the exponential growth part; D0 is the characteristic dose where the slope of the growth curve (the exponential part) is equal to 1/
For the establishment of an SGC appropriate for samples from within a study profile, curve fitting was performed based on the DRCs of all samples from that profile, after excluding the DRC of the few outliers (<20 %) having dose–response curves which are markedly different from those of the majority of the aliquots for that sample.
Roberts and Duller (2004) suggested that inter-aliquot variation can be normalised using OSL signals of the test dose (Dt) in order to produce a ‘standardised luminescence signal’ ((Lx/Tx)* Dt). However, the similarity of the shape of a DRC of a test-dose-corrected signal [(Lx/Tx)*Dt] for different aliquots and grains depends critically on changes in the inter-aliquot and inter-grain sensitivity (
In order to further reduce the variation in the test-dose-corrected signals, Roberts and Duller (2004) and Li
The LS-SGC method involves a multiple iterative scaling and fitting process. The R package num OSL (version 2.5), written by Peng and Li (2017), implements the calculation of a series of iterative scaling and fitting processes required in the method. In this study, after extraction of the OSL signals of aliquots from Analyst (version 4.31), the subsequent iterative calculation was performed using part of the code in the R package num OSL (Peng and Li, 2017). The detailed steps are as follows:
Fitting the test-dose-corrected regenerative-dose OSL signals (Lx/Tx*De) using the GOK (general-order kinetic model) function. The choice of the fitting function for ‘starting curves’ is not crucial and does not affect the final results after iteration, which are only related to the number of iterations (Li
The test-dose-corrected regenerative-dose OSL signals of each aliquot are multiplied by a scaling factor, such that the sum of the squared residuals (the difference between the test-dose-corrected regenerative-dose OSL signal values, multiplied by the scaling factor and the fitted y value in step 1) is minimised. Note that the scaling factor could be different for different aliquots.
The normalised experimental data obtained for each aliquot in step 2 are then fitted again using one of the followings: single saturation exponential function (EXP), double saturation exponential function (DEXP), and single saturation exponential plus linear function (LEXP). (The function does not have to be the same as the initial fitting function in step 1.) The best fitting function is determined using a chi-square test.
Iteratively repeat steps 2 and 3, and the re-scaled data set in step 2 for each aliquot are then multiplied by a new scaling factor in order to minimise the least-squared residuals with the newly fitted DRC in step 3. The newly re-scaled data are then fitted again using the best-fit functions determined by chi-squared tests. For all growth curves, steps 2 and 3 are iteratively repeated until the change in all of the normalised data and the fitted SGC curve is < 1%. The best-fit curve is considered as the SGC.
The code is as follows:
#calculating the De obtained by SGC
res<-calSGCED(as_analyseBIN(data1), SGCpars=res_lsNORM$LMpars2[,1],model=”go k”,method=”gSGC”,origin=FALSE,avgDev=res_ lsNORM$avg.error2,errMethod=”sp”,SAR.Cycle= c(“N”,”R2”),outpdf=”DK12SGCED”,outfile=”DK1 2SGCED”)
The essence of the Re-SGC method is to take the signal of a specific regenerative dose as a reference point (hereafter called the re-normalisation dose), with which the DRCs of all samples are normalised in order to establish a common DRC suitable for samples from the same profile or even from different regions. In addition, via numerical simulations, the degree of reduction of the variation of the inter-aliquot/inter-sample ratio is observed to be slightly different when different regenerative doses were used for re-normalisation of the growth curves [Peng
In order to select a suitable re-normalisation dose for re-normalisation of the sensitivity-corrected natural signal (Ln/Tn) and regenerative-dose signal (Lx/Tx), we compared the impact on the relative standard deviation (RSD) and dispersion of the sensitivity-corrected OSL signals caused by different re-normalisation doses for representative sample LS-4 (Fig. 2) and from all of the samples in the area (Fig. 3). In detail, the comparison of the RSD and the dispersion of the re-normalisation of sensitivity-corrected OSL signals by re-normalisation doses of 73, 146, 220, 293, and 440 Gy for representative sample LS-4 indicates that the RSD (Fig. 2a) and the dispersion of the re-normalised signals of aliquots (Fig. 2b) were reduced, especially for doses within the regenerative-dose range of 73-300 Gy, when renormalised with doses of 146 and 220 Gy.
For all samples in the study area, the comparison made with re-normalisation using re-normalisation doses of 88 Gy, 147 Gy and 220 Gy (Fig. 3) shows that re-normalisation of sensitivity-corrected OSL signals of aliquots with a re-normalisation dose of 147 Gy yielded the smallest dispersion of the re-normalised OSL signals, which corresponds to a regenerative dose up to 250 Gy (Fig. 3b). As the characteristic saturation dose (D0) of quartz in most samples in this area is ~75 Gy, the comparison made in this study therefore shows that when using the Re-SGC method in quartz, re-normalisation of the sensitivity-corrected OSL signals (Lx/Tx) using an extra re-normalisation dose close to two times of the characteristic saturation dose (2D0) enables a value of De to be easily obtained, which has a smaller RSD of the re-normalisation OSL signals within the wide range of 0–200 Gy.
In this study, the SGC is established for each profile using the SAR-SGC, Re-SGC and LS-SGC methods. The results for representative profile LS and the other profiles are illustrated in Fig. 4 and supplementary Figs. S6–S14, respectively.
It is evident that the response of the sensitivity-corrected OSL signals (Lx/Tx) to the regenerative dose for samples from the profile is dispersed (Fig. 4a). Moreover, using the SAR-SGC method, the DRC would only be established for sensitivity-corrected OSL signals (Lx/Tx) of aliquots in a single sample after elimination of aliquots with substantial deviations. However, within the same profile, the DRCs established for different samples deviate substantially from each other (Fig. 4b), and it is difficult to determine a common growth curve that is suitable for samples from the same profile, with an acceptable degree of accuracy, using the SAR-SGC method.
Relative to the sensitivity-corrected OSL signal (Fig. 4a), based on the Re-SGC method, all of the sensitivity-corrected OSL signals (Lx/Tx) were re-normalised by dividing the OSL response (L147/T147) of the extra re-normalisation dose by 147 Gy, which is close to the 2D0 value. Therefore, the deviation of the re-normalised OSL signals among aliquots is reduced and a common SGC can be more reasonably established, especially within the dose range of 200 Gy, although the re-normalised signals are dispersed when De > 200 Gy (Fig. 4c).
When the LS-SGC method is used, the variation in the test-dose-corrected OSL signals (Lx/Tx*Dt) with the regenerative dose was fitted using a flexible function, and therefore, almost the same calibration level was reached among the regenerative doses for aliquots within the entire dose range. This does not alter the shape of the DRC of each aliquot, and it only minimises the difference between the DRCs of each aliquot. Almost the same dispersion range was obtained up to 300 Gy, and even up to 500 Gy, and therefore, a common DRC could be obtained for the samples from this profile (the red line in Fig. 4d).
In summary, a comparison based on samples from the same profile indicates the following. 1) The difference between sensitivity-corrected signals among samples was not substantially reduced using the SAR-SGC method, and therefore, it is difficult to establish a suitable SGC for the samples from a profile. 2) Using the Re-SGC method, differences in the sensitivity-corrected OSL signals among samples and aliquots can be effectively reduced when they are re-normalised with the OSL signal response to the extra re-normalisation dose, which is close to double the characteristic saturation dose (2D0). Therefore, an SGC suitable for samples from the same profile can be established with maximum De values up to 200 Gy. 3) Using the LS-SGC method, without considering any additional re-normalisation dose, the differences in the sensitivity-corrected signals among samples and aliquots from the same profile were uniformly reduced with a regenerative dose up to 300–500 Gy. Therefore, it is possible to establish an SGC suitable for samples from the entire area within a wide dose range using either the Re-SGC or LS-SGC method.
By using the Re-SGC and LS-SGC methods, the difference in the re-normalised OSL signals among samples and aliquots can be effectively reduced, and therefore, we tried to establish a potential SGC that is suitable for the quartz fraction of sediments from the entire Jilantai region (hereafter termed the regional SGC). Based on the OSL signals of the quartz fraction in samples from different profiles within the entire Jilantai Basin, the regional SGCs were established with the fitting results illustrated in Fig. 5 (red lines). The function of the regional SGC obtained using the Re-SGC method is given below:
and the function of the regional SGC obtained by the LS-SGC method using the GOK function is as follows:
In order to assess the quality of the SGCs, we calculated the ratios between the re-normalised Lx/Tx data (or LS-normalised Lx/Tx data) and the corresponding value on the SGC at the same dose and plotted them as a function of dose in Fig. 5c and d. Similarly, we plotted the ratios of De measured through normalised Lx/Tx data and that obtained from the SGC in a radial plot in Fig. 5e and f. There is no systematic dose dependency of the ratios for these two SGC methods, which is consistent with the observations on K-feldspar SGC (Li
Comparison of the re-normalised OSL signals, the fitting curves of samples from different profiles and the regional SGC (Fig. 5a and b) indicates the following. (1) Within the dose range of 0–200 Gy, the deviation in the shape of the fitting curves of samples from different profiles is less dispersed; therefore, a regional SGC can be established using either the Re-SGC or LS-SGC method. (2) Using the Re-SGC method, the regional SGC established from samples from different profiles shows deviations from the SGCs obtained from different profiles for regenerative doses > 200 Gy, which may be due to scattered re-normalised signals. (3) Relative to the re-normalised OSL signals obtained using the Re-SGC method, the re-normalised OSL signals obtained by the LS-SGC method are substantially less dispersed, and the regional SGC established from the LS-SGC method is almost overlapped by up to 300 Gy with DRCs obtained from most of the samples from a single profile. Deviations only occur when the regenerative dose is >300 Gy.
To validate the De values obtained through the regional SGC based on the Re-SGC and LS-SGC methods, a comparison was made with the De values obtained using the SAR protocol. For samples for which OSL signals were involved in establishing the SGC, we calculated the De values of 379 aliquots from the regional SGCs established using the Re-SGC and LS-SGC methods and made a comparison with the De values obtained using the SAR protocol. From the plots of De values obtained from the regional SGC using the Re-SGC method versus those obtained using the SAR protocol (Fig. 6a), it was found that 78% of the De values obtained from these two methods are consistent within a 20% error range of unity, and 53% were consistent within a 10% error range of unity. If the comparison is constrained within the range of De < 200 Gy, within which most of the De values are unsaturated, then 86% of the De values are consistent within a 20% error range of unity, and 63% are consistent within a 10% error range of unity. In a comparison of De values obtained from the regional SGC established using the LS-SGC method with those obtained from the SAR protocol (Fig. 6b), 56% of the De values are consistent within a 10% error range of unity and 81% are consistent within a 20% error range of unity. If the comparison is constrained within the range of De < 200 Gy, 84% of the De values are consistent within a 20% error range of unity, and 61% are consistent within a 10% error range of the unity. For De > 300 Gy, most of the data are scattered except for a small percentage which are distributed along the 1:1 line which is defined by the ratio of the De values obtained using the Re-SGC (or LS-RGC) method with those obtained from the SAR protocol. This indicates a large discrepancy in De values > 300 Gy between those obtained by using the regional SGCs established either using either the Re-SGC or LS-SGC method and those obtained using the SAR protocol (Fig. 6). This phenomenon may be the result of the saturation of the OSL signals. We also calculated the ratio of De values between those obtained from the SGCs and from the SAR protocol (Fig. 6c and d). From the De value ratios of Re-SGC to SAR, 95.8% of aliquots have ratios close to unity within the 2σ range (Fig. 6c). For the ratios of LS-SGC to SAR De values, 93.8% of ratios are close to unity within 2σ (Fig. 6d).
In order to further investigate whether the regional SGCs established using the Re-SGC and LS-SGC methods are widely applicable to samples from the study area, an additional comparison of De values (<200 Gy) was made on samples which were not involved in the establishment of the regional SGC. A total of 310 aliquots were used in the comparison. In general, the De values obtained using the regional SGC were consistent with those obtained using the SAR protocol within a 20% error range of unity (Fig. 7a and b). This situation is almost the same as that for the samples involved in the establishment of the regional SGCs (Fig. 6), which indicates that the two regional SGCs established from the limited sample set are also suitable for other samples from the Jilantai Basin. In detail, within the De range of 50–200 Gy, from the regional SGC established using the Re-SGC method, 69% of the aliquots yielded De values consistent with those obtained using the SAR protocol within a 10% error range of the unity, and 92% were consistent within the 20% error range of unity (Fig. 7a). From the regional SGC established using the LS-SGC method, 72% of the aliquots yielded De values consistent with those obtained using the SAR protocol within a 10% error range of unity, and 92% were consistent within the 20% error range of unity (Fig. 7b). However, for De <50 Gy, the number of aliquots with De values obtained using different methods consistent with those obtained using the SAR protocol within the 10% and 20% error ranges of unity was reduced significantly (Fig. 7c and d). In addition, the Re-SGC (or LS-SGC) and SAR De values are consistent, with more than 98% of the aliquots having ratios of SGC to SAR De clustered tightly within the 2σ range of unity (Fig. 7e and f).
In summary, irrespective of which regional SGC is established, within the 10% error range, more than 50% of aliquots have De values consistent with those obtained using the SAR protocol, and within the 20% error range, more than 80% of aliquots have De values consistent with those using the SAR protocol. Similarly, more than 95% of the aliquots had ratios of SGC to SAR De consistent with unity at 2σ. Within the range of De < 200 Gy, the comparison of the De values obtained using regional SGCs established using the Re-SGC and LS-SGC methods with those obtained using the SAR protocol indicates that the De values obtained using these two regional SGCs are consistent. Therefore, a valid SGC can be produced for the Jilantai area within the 200 Gy range.
Based on the OSL signals of small-aliquot quartz fractions of samples collected from different sedimentary environments in the Jilantai Basin, we have tried to establish a common SGC that is generally appropriate for samples from the area. Our main findings are as follows:
The inter-aliquot difference in sensitivity-corrected OSL signals can be effectively reduced using the Re-SGC and LS-SGC methods, and therefore, it is possible to establish a common SGC using these methods. However, the SAR-SGC method is not suitable for establishing a common SGC of quartz fractions, which is suitable for different samples from a profile or a region.
Using the Re-SGC method, selecting a re-normalisation dose that is close to double the characteristic saturation dose, 2D0, can reduce the variation in the shape of the DRCs among samples within a larger dose range. This is supported by a comparison in the RSD and dispersion of the renormalised OSL signals with different sizes of re-normalisation dose.
For De < 200 Gy, De obtained using the Re-SGC and LS-SGC methods is generally consistent with that obtained using the SAR protocol, which indicates that there is a common regional SGC in the Jilantai area. For the Jilantai area, the function of the regional SGC obtained by the Re-SGC method is
A summary of studied samples, including their locations, sedimentary types and grain size and measurement conditions in measuring OSL signals of quartz in this study.
|Profile/Core||Sample||Location||Sediment type||Grain size (μm)||Preheat/cut-heat (°C)||Test dose (s)||Number of aliquots||Data source|
|S32||S32-1 ||N39°44′01.0″,||Lacustrine ||90-125 ||160/160 ||30 ||8 ||(|
|S63||S63-2 ||N39°30′15.7″,||Lacustrine ||90-125 ||220/160 ||50 ||4 ||This work|
|WP130725||WP130725-1 ||N39°10′56.64″,||Fluvial ||90-125 ||160/160 ||50 ||14 ||(|
|WP130726-3||WP130726-3-1 ||N39°27′3.79″,||Fluvial ||90-125 ||240/160 ||50 ||9 ||This work|
The double SAR protocol applied in measuring OSL signals in this study.
|2||Preheat @160–260°C for 10 s|
|3||OSL @50°C for 40 s||Lx|
|4||OSL @125°C for 40 s|
|5||Test dose 20–100 s|
|7||OSL @50°C for 40 s|
|8||OSL @125°C for 40 s|
|9||Illumination @280°C for 100 s|