# Guide to TL Date Measurement

## 6. INTERPRETATION AND USES OF TL DATES

These guidance notes are intended to help clients understand the meaning of date information supplied by Quaternary TL Surveys. It is important to remember that the dated event is the initialisation of the TL. For flint, stone and ceramics, this event is the most recent heating or firing of the sample; for sedimentary depositions, it is the last exposure to daylight; while, for stalagmitic calcite, it is the formation of the crystals that is dated.

The interpretation to be placed on the date and its error limits is explained in section 6.1. The following sections describe the uncertainties which contribute most significantly to the size of the measurement error, and discuss the uses to which TL dates can be put. These applications fall into two classes. Firstly, when a number of dates refer to a single event, the dates may be combined to form a more precise age estimate. A brief account of averaging procedures is given. In the second case, the dates refer to a sequence of events, and the measurements need to be compared in order to establish the relative ages of the events. Because detailed knowledge of the date uncertainties is required in both cases, these procedures should only be carried out by the dating specialist.

### 6.1. TL Date Formats and Their Interpretation

TL dates are usually quoted in accordance with the format:

t ± e ka BP

Here, the unit of time (ka) represents 1,000 calendar years. The results of a TL date measurement are absolute dates which require no calibration or other adjustment. "BP" stands for "Before Present", which, when used in connection with TL data, means "Before the measurement date", and not "Before 1950". When a TL date refers to historical times or to late prehistory, it will be quoted in "years BC" or "years AD".

The values of t and e should be interpreted as follows. Figure 1(a) shows a typical probability distribution curve, in which the height of the curve gives the relative probability that the dated event occurred at the time represented along the horizontal axis. The curve shown in figure 1(a) is symmetric about a central date, and this is the most common form of probability distribution for TL dates. The value of t is the central date of the distribution, which is also the most probable date. The value, e, gives the error limits of the date measurement. Its significance is that there is a 68% probability that the true date lies between the age limits, t - e and t + e. From the symmetry of the curve, it is clear that the probability of the true age being older than t is equal to the probability of it being younger.

Figure 1. Curves describing distributions of probability vs date in the cases of symmetric (a) and asymmetric (b) date limits. Shaded areas represent the probability of the true date lying between the upper and lower date limits, while the total area under each curve corresponds to 100% probability. In both symmetric and asymmetric cases, the probability that the true age is less than the date, t, equals the likelihood of it being greater. Also, there is in both cases a 68% probability that the true date lies between the upper and lower date limits.

When dating sediments by TL, a correction is applied for the effects of signal decay. This results in a probability distribution curve that is no longer symmetric. Figure 1(b) shows an example of an asymmetric distribution. Dates of this type are quoted in the format:

t +e1 /-e2 ka BP

The significance of t, e1 and e2 is shown in figure 1(b). Note that in the asymmetric case, t is no longer the most probable date. However, it retains the property that there is an equal probability of the true date being older than t as there is of it being younger than t. As in the symmetric case, the probability that the true age lies between the date limits, t - e2 and t + e1, is 68%.

### 6.2. Evaluation of TL Date Uncertainty Limits

The TL date measurement in fact consists of two independent measurements. These are (i) an evaluation, by means of TL observations, of the palaeodose of the sample (i.e. the total radiation dose it received), and (ii) an assessment of the rate at which this dose accumulated. The uncertainty in the palaeodose measurement is readily evaluated from the reproducibility of repeated TL observations and calibrations. In most cases, the palaeodose measurement error lies between ±3% and ±7%, and is usually smaller than the uncertainty in the dose rate assessment. For the majority of TL measurements, therefore, the overall date limits depend mainly on the dose rate uncertainty, which in turn is dependent on site conditions.

Dose rate assessment is subject to a fundamental problem which affects all dating techniques. This problem involves the fact that, while the present day condition of the samples can be measured, changes that may have affected the way that the measured system has developed during its buried history can often not be evaluated. Therefore, an assumption is sometimes required which states that external factors have not significantly affected the expected development of the measured system. This can be referred to as the closed system assumption.

The uncertainty that this assumption represents can be expressed in two ways. Firstly, the date measurement may be accompanied by a proviso, either explicit or implicit, that the system has remained closed. Alternatively, the date limits may be enlarged to include an estimate of the possible effects that a failure of the closed system assumption could have upon the date measurement. Since the dating specialist is the person who is in the best position to make such an estimate, the second option is clearly preferable. Therefore, wherever it is practicable, TL date limits should take account of all sources of uncertainty that may be anticipated in a given situation. As the dating methodology advances, the number of these sources will tend to increase, and consequently, date error limits may also increase. In the longer term, however, as uncertainty factors become better understood, dating precision and reliability should improve.

In TL dating, what constitutes the system under consideration will depend on the particular circumstances of the case. The radiation dose received by the TL sample is made up of components from alpha, beta, gamma and cosmic rays. Alpha and beta rays are of short range, and therefore originate from radioactive elements within the TL sample itself. Gamma rays have a much larger range (approximately 30 cm) and consequently most of the gamma dose originates in the sediment surrounding the TL sample. Cosmic ray dose rates depend mainly on the overburden covering the sample, but are always a minor component of the total dose rate.

For samples which have received most of their dose internally, the system that needs to be considered approximates to the TL sample alone. In cases where the external gamma dose is dominant, the system includes the burial sediments up to 30 cm away from the TL sample. Failures of the closed system assumption can be caused by net movements of radioactive nuclides (in particular, radon gas) in or out of the system, by fluctuations in the water content of the sample or surrounding soil, or by recent decalcification of the sediments. Water and calcite affect the dose rate experienced by the TL sample by absorbing radiation energy that would otherwise reach the sample. Uncertainties in the past water content are greatest in sediments with high water retention, such as silts and clays. At the other extreme, flints which have received most of their dose internally will not have experienced significant dose rate fluctuations.

The uncertainty in the dose rate assessment therefore needs to include estimates of the ranges within which the average past radioactivity and water contents are likely to have lain. To some extent, it is preferable to overestimate the widths of these ranges rather than to underestimate them. In most cases of sediment dating, and some instances of flint or calcite dating, the range attached to the past water content estimate forms the major part of the dose rate uncertainty, and this in turn often dominates the date limits.

### 6.3. Uses of TL Dates

There are two main ways in which TL dates are used. In the first case, when a number of dates have been measured on samples which are known to be contemporaneous, they can be combined, or averaged, to obtain a more precise age determination. In the second case, when it is not known whether a number of events were contemporaneous, the date measurements are compared in order to detect differences in age.

### 6.3.1 The averaging of TL dates

The averaging of TL dates is not a simple procedure, and should only be undertaken by the laboratory that produced the date measurements. The averaging must take account of the error limits of the individual dates, so that the more precise measurements carry a greater weight in the final result. An average obtained in this way is called a weighted mean date. However, if the quoted overall date limits are used for this purpose an incorrect result is obtained. This is because some of the sources of uncertainty contributing to the overall error limits are common to all the dates, while some are specific to each individual date. The former class of uncertainties, which are referred to as systematic errors, include the external dose rate errors where all the TL samples have experienced the same environmental conditions. Errors that are specific to individual date measurements are called random errors. These are exemplified by the uncertainty in the palaeodose measurement.

The implications of the above are best illustrated with the aid of figure 2, which schematically shows two assemblages of flints, labelled A-D and E-H. It is assumed that these clusters are contemporaneous, but well separated (possibly at different sites) and in dissimilar burial environments. First, we consider the averaging of the flint dates for the group A-D. Because all these flints derive from the same burial environment, their external dose rate uncertainties count as systematic errors. The averaging procedure therefore begins by extracting from the overall date limits the contributions they receive from such sources. With only random errors remaining in the date limits, the weighted mean date is then computed. Finally, the systematic uncertainties are replaced as contributions to the date limits of the mean. This procedure results in a more precise estimate of the age of the flints A-D, but the size of the external dose rate uncertainty is not reduced.

Figure 2. Stratigraphic section, illustrating possible relationships between TL dating samples. Triangles A-D and E-H represent two assemblages of flints. It is assumed that these industries are known to be contemporaneous, but that the flint clusters are also well separated and derived from different stratigraphic contexts. Squares P-T represent a sequence of sediment TL samples collected for a study of deposition episodes and rates.

This procedure may be repeated for the second group of flints E-H. Because the clusters A-D and E-H are known to be coeval, it is then valid to combine the two mean dates to obtain even more precision. In the averaging of these results, the external dose rate uncertainties no longer count as systematic errors, because the burial environments are dissimilar and were independently measured. Random errors therefore form a much larger part of the date limits of the individual clusters. In consequence, when the two mean dates are combined, a significant improvement occurs in the final precision.

It follows from the above that, when selecting TL samples for dating a single event, they should be collected from as wide a range of burial environments as possible. If this is done, the final best estimate of the date will be more reliable than if all the samples were taken from the same location.

### 6.3.2 Comparing TL dates

Because TL dates are expressed in absolute units, and because their date limits represent overall uncertainties, they can be directly compared with the results of other dating techniques which are similarly expressed. The most common comparisons are those with calibrated radiocarbon dates and with uranium series dates for stalagmitic calcite. Because overall uncertainties need to be taken into account, such comparisons are not useful for detecting fine differences in age. However, in cases where the dated materials are known to be contemporaneous, they are valuable for testing whether date limits have been realistically assessed.

Relative dating is employed where the principal interest is in the differences in age that exist between contexts rather than their absolute dates. An example is the dating of a sequence of sediments in order to observe their rate of deposition or the presence of hiatuses in the record. Figure 2 shows schematically a set of sediment samples P-T collected for this purpose. When comparing the TL dates of these samples, only the random errors will be of significance. For instance, uncertainties in the past water contents of the sediments are not relevant if it can be assumed that all samples have experienced the same fluctuations in wetness. In many cases, date limits that include only the relevant random errors will be much smaller than the overall uncertainty which is normally quoted. This leads to an improvement in the ability to detect differences of age.

Queries and comments on TL dating procedures and the above literature are welcome.