Employing Minimum age model (MAM) and Finite mixture modeling (FMM) for OSL age determination of two important samples from Ira Trench of North Tehran Fault

The commonly observed scatter in D_e distributions of sedimentary samples can be attributed to different sources, referred to by Thomsen et al. (2005) as ‘extrinsic’ and ‘intrinsic’ sources of uncertainty. The former sources include: post depositional mixing of grains from adjacent sedimentary layers (e.g. Roberts et al., 1998 and 1999; Bateman et al., 2003, 2007a; Feathers et al., 2006; Jacobs et al., 2006; David et al., 2007) and dosing, poor or heterogeneous bleaching of grains prior to burial (e.g. Olley et al., 2004; Bøtter-Jensen et al., 2000; Duller and Murray, 2000; Duller et al., 2000; Murray and Olley, 2002; Olley et al., 1999, 2004), and dosing, particularly at the micro-scale in the beta-radiation field such as beta-dose heterogeneity in the natural burial environment (e.g. Olley et al., 1997; Murray and Roberts, 1997; Nathan et al., 2003; Mayya et al., 2006; Jacobs et al., 2008a, 2008b).

‘Intrinsic’ sources of inconsistency include differences in the OSL signals response from different grains to identical treatments (e.g., Bailey, 2002, 2004) or differing grain-to-grain responses to fixed SAR conditions (e.g. Jacobs et al., 2003); statistical uncertainty due to photon counting and instrument uncertainties and luminescence measurements and then their combination to determine D_e (e.g. Thomsen et al., 2005; Duller, 2007), such as thermal transfer and photo-transferred recuperation (i.e. transfer of charge from thermally shallow but optically insensitive traps to the deeper trap responsible for the OSL signal, as a result of laboratory heating, optical stimulation, or a combination of the two) (e.g. Aitken and Smith, 1988; Stokes, 1992; Banerjee, 2000). Internal variability leads to the observation of different ‘grain behavioural types’, seen in luminescence properties such as brightness and dose response characteristics (e.g. Murray and Roberts, 1997; Roberts et al., 1999; Yoshida et al., 2000; Jacobs et al., 2003, 2006, 2008b; Stone and Bailey, 2012).

However, an essential assumption of the method is that the luminescence signal from a grain can be reset, or zeroed, by exposure to sufficient daylight. This is a process commonly termed ‘bleaching’ and occurs in many processes of erosion, transportation or deposition, particularly those that occur sub-aerially. Where all the grains in the sample were exposed to sunlight for sufficient time at deposition to remove any trapped charge, then the sample is fully bleached and all grains would have a D_e of zero at deposition, and after some period of burial all the aliquots would give the same value of D_e (e.g., aeolian sediments). Where the luminescence signal from some of the grains were not zeroed, grains would have different D_e values at the time of deposition; this is termed incomplete or partially bleaching (e.g., alluvial and colluvial sediments) (Duller, 2007).

Sediment mixing by post depositional processes is a dominant source of D_e variability across a range of sedimentary environments even in quartz-dominated, well-bleached, aeolian, dryland sediments (e.g. Arnold and Roberts, 2009 and references therein). Recognition of sediment mixing in the field is often difficult because the absence of depositional bedding structure is not neces-sarily indicative of sediment mixing, whilst the presence of sedimentary structure does not necessarily prevent post-depositional disturbance (Bateman et al., 2007a).

The appearance of D_e distributions can be affected by the kind of post-depositional processes. The dominant younger (or older) grains intrusion increases positive (negative) skewness. It can increase symmetrically the overall spread of D_e values, or create discrete dose populations (including zero-age grains) and multi-modal D_e distributions. Arnold and Roberts (2009) reported some of the important issues associated with the analysis of mixed D_e distributions, using simulated D_e data sets produced with a simple stochastic model.

However, partial bleaching and post-depositional mixing of young/old samples cannot be overcome through optimisation of experimental apparatus and measurement conditions and needs to be addressed via careful statistical analysis of D_e distributions and use of appropriate statistical age models.

Several statistical age models have been suggested to obtain estimates from the burial dose associated with only the most fully bleached (and undisturbed) grains in each sample (e.g., Olley et al., 2004; Bailey and Arnold, 2006; Arnold and Roberts, 2009); or of the post-depositionally mixed sediments (e.g. Roberts et al., 2000; Spencer et al., 2003; Sivia et al., 2004).

The most statistically suitable of these are the mini-mum age model (MAM) of Galbraith and Laslett (1993) for OSL dating of samples that not all the grains have been fully bleached.

The finite mixture model (FMM) of Galbraith and Green (1990) has been used in a number of recent OSL studies of mixed sediments (e.g. Roberts et al., 2000, 2001; Jacobs et al., 2006, 2008b; David et al., 2007; Bateman et al., 2007b).

In this study Mark Bateman spreadsheet was used to calculate the FMM and the program for MAM calculation was provided by Sebastien Huot.

Quartz was extracted and cleaned under low-intensity red light at the Sheffield Centre for International Dryland research luminescence laboratory. Carbonates and organ-ics were removed with HCL and H₂O₂. A 45 minutes HF treatment was followed after heavy minerals separation (S.G. 2.7 gcm^-3). IR stimulation revealed no feldspar contamination. Standard medium single-aliquot dating of the 90–250 μm quartz fractions of samples IRA1, IRA4, IRA5 and IRA8, was performed using standard protocols as outlined in Fattahi et al. (2006).

To test if there were problems from the thermal trans-fer of charge into the OSL trap as a result of preheating, natural aliquots of sample IRA4 were stimulated at room temperature without any prior preheating and OSL was measured for 100 s. After more than 4 h delay the OSL was measured again. No significant OSL signal was ob-served for the second measurement. Then, SAR was applied to measure the D_e at different preheat tempera-tures (expected to be zero in ideal scenario). All subsequently measured apparent values of D_e were less than 0.4 Gy for preheat temperatures from 170°C to 300°C. This is small compared with typical natural D_e and suggests that the samples do not suffer from significant thermal transfer.

Dose recovery preheat tests (as per Murray and Wintle, 2000, 2003) were carried out and showed that overall effects of sensitivity changes had been properly corrected for and known laboratory doses were recovered by the SAR protocol. The mean ratios of measured to given doses for IRSL were statistically consistent with unity.

Some aliquots were rejected as they were dim or the recycling values were not within 10% of unity. Some aliquots produced a reasonable OSL signal of which some passed the SAR criteria. These aliquots were chosen for D_e determination. The CAM provided average ages close to large aliquots for all four samples. The ages of IRA4 and IRA8 were overestimated as compared to the stratigraphy.

The single-aliquot D_e distributions and the relative profile likelihood graphs are shown in Figs. 3 and 4. A common feature of the D_e values of these samples is the widespread distribution of equivalent doses. The spread of single aliquot D_e values are because of ‘experimental’ and ‘natural’ variations. Experimental errors are reducible but natural variation is inherent. When more than 5% of D_e values lie outside ±2σ of the central value, the dose distribution is termed over dispersed. Over-dispersion (OD) is a quantitative estimate of the amount of spread in the D_e data set after allowance has been made for measurement uncertainties (Galbraith et al., 1999; Roberts et al., 2000; Galbraith et al., 2005; Galbraith and Roberts, 2012). Many studies have reported up to 20% over-dispersion among De estimates for single aliquots and individual grains that are known or thought to have been well bleached (e.g., Roberts et al., 2000; Olley et al., 2004; Thomsen et al., 2005; Jacobs et al., 2006; Galbraith and Roberts, 2012).

The D_e of IRA1 and IRA5 is not as widely spread as IRA4 and IRA8. Their OD (30% and 25% for IRA1 and IRA5, respectively) is low compared to IRA4 (92%) and IRA8 (57%).

But what are the sources of the wide spread D_e of medium aliquot measured samples? A medium aliquot is still an average of many grains and may hide the wide spread of D_e’s of single grains inside medium aliquots. An OD value of ~6% was obtained for the dose recovery data sets for sample IRA4, so high over-dispersion cannot be due to inherent differences. Therefore, other sources, such as grain-to-grain variations of bleaching and bioturbation may contribute to D_e scatter for IRA4 and IRA8 samples, with high over-dispersion values (92% and 57%).

Various statistical methods have been developed to isolate grains which represent a true burial dose. For well bleached samples one of the mean calculation methods such as central age model is commonly used. If there are samples that contain a mixture of grains with different bleaching histories, the minimum age model is suitable to determine the minimum age provided by fully bleached grains. The finite mixture model enables one to estimate the number of dose components within a dose distribution and the corresponding D_e for each component. The lowest component is the youngest cluster of D_es.

In order to consider among different statistical approaches which age model is more suitable for our sam-ples, the age model decision process by Arnold et al. (2007) and Bateman et al. (2007a) was used. Specific De distribution characteristics (e.g., over-dispersion, skew-ness) were taken to identify the appropriate statistical approach.

These age model decision processes suggested the use of CAM for IRA1 and IRA5, and MAM and FMM for IRA4 and IRA8 samples.

The suggestion of age models is consistent with reality. IRA4 and IRA8 samples most likely include grains from different sources and time scales. They are from the environment that the sediments are fluvial, or colluvial. Therefore, grains are likely to be incompletely bleached. MAM is a suitable model to be employed to provide the ages of these samples.

FMM can separate different clusters of Des and suggest an average for each cluster. IRA4 and IRA8 are sampled at the bottom of the units 29 and 23, respective-ly. Therefore, it is probable that these samples include post-depositional grain through bioturbation from the layer below. For example the age of underlying unit (unit 17) of sample IRA4 was 85.4 ± 12.1ka, and transfor-mation of grains from this unit to sample IRA4 obviously increase the average age of IRA4. This can be the reason that IRA4 has overestimated the age of unit 29. In this circumstance the age of youngest cluster of FMM can provide the true age of aimed unit.

Therefore, on the basis of the D_e scatter, age model decision process and stratigraphy, it has been concluded that, MAM (13.1 ± 4.3 and 3.5 ± 0.3 ka) and the first component of FMM (21.5 ± 2.2 and 6.1 ± 0.6 ka) may give a better indication of the deposition age, rather than CAM (35 ± 6.1 and 58.1 ± 6.5ka) for IRA8 and IRA4 samples, respectively. If we combine the age provided by first component of FMM and the age provided by MAM OSL, it will give us 8.8–23.7 and 3.2–6.7 ka for units 23 and 29, respectively. These ages are more consistent with stratigraphy.

At the multi-grain scale of analysis, however, any heterogeneity in D_e that individual grains have, may still be masked, as individual D_e estimates are obtained from aliquots containing several tens, hundreds of grains. The presence of intrusive grains may therefore become ‘covered’ in the final D_e estimates of individual aliquots that contain a variety of both younger/older intrusive grains and in situ grains. By averaging, as the number of grains that are measured (i.e. the number of grains on each aliquot) increases, the variation in D_e will decrease (Olley et al., 1999; Wallinga, 2002).

Therefore, due to dim signals of the limited measured aliquots, the best way to find the accurate age for these units is to collect more and bigger samples and try to find shine grains and date them using single grains or very small aliquots.