The Open University Uranium-Series Laboratory U-series systematics

A disadvantage of many authigenic precipitates suchs as lake marls is that they contain significant amounts of ‘inherited’ ²³⁰Th from allogenic material. This can include detrital material such as carbonate or clay from the drainage area, or wind-blown dust (loess) or volcanic ash. It is a safe assumption that the allogenic material is in secular radioactive equilibrium and thus carries a significant amount of ²³⁰Th. The effect of ‘inherited’ ²³⁰Th on the overall calculated age of a sample depends on the age of the sample and on the uranium concentration. These effects can be illustrated with some simple calculations.

In this example it is assumed that the authigenic phase has a U=1μg.g^-1 and no thorium and the allogenic phase has 6.6 μg.g^-1 Th, a U/Th=0.238 and is in secular radioactive equilibrium. Ages can be calculated for assumed (²³⁰Th/²³⁴U) and (²³⁴U/²³⁸U) and a range of allogenic contributions by artificially increasing the thorium contribution. Results of such calculations are plotted in the Figure below. For the oldest plotted age of 177 ka the effect of 5 weight % of allogenic contribution is a reduction in the calculated age of around 1%, comparable to the overall uncertainty of the age. However, the effect of only a 0.5 weight % contribution of the same allogenic material is larger than the uncertainty for the 3 ka example.

Higher thorium concentration in the allogenic contribution results in a roughly proportional reduction of the age. Recalculating the age effect for the 10 ky sample but with an assumed Th=13.2 μg.g^-1 shows that with an allogenic contribution of 1.25 weight %, the calculated age is 3.1% lower where with Th=6.6 μg.g^-1 the calculated age is 6.5% lower. Again, for younger samples the concentration effect is more pronounced than for the older samples.

Many types of carbonate deposits, such as tufa and calcrete that are important in Earth and environmental sciences also contain allogenic components, whereas corals and speleothem are usually less affected. Correct interpretation of U-series data requires that the effects of the allogenic contribution on ²³⁰Th are adequately corrected. Three categories of approach can be distinguished: chemical separation, mathematical correction or empirical correction.

The intention of chemical separation is to selectively dissolve the authigenic carbonate without attacking the other phases. The usual method is to use a weak mineral acid, or acetic or formic acid, or strong ligands such as EDTA that dissolve carbonate but not silicates. But even if the authigenic carbonate can be dissolved quantitatively without leaching the silicate (and that is doubtful given the nature and grain-size of the likely silicates), the dissolved authigenic ²³⁰Th is highly particle reactive and precipitates onto the silicate grains. Stronger reagents that would stabilise ²³⁰Th in solution, increase the likelihood of leaching of the allogenic phases. Moreover, even with mild reagents it is impossible to completely avoid dissolving the almost invariable present detrital carbonate, resulting in a ‘mixed age’ that is always older than the true authigenic age. Small variations in the strength of the reagents, the duration of the reaction, the grain size and even the amount of material, all affect the selective dissolution process. Consequently, it is very difficult to obtain reproducible results using selective dissolution protocols.

Mathematical correction

The most used way forward is mathematical modelling (Bischoff and Fitzpatrick, 1991; Luo and Ku, 1991). A number of samples of the same age (or very nearly so) but with different allogenic contributions are analysed. Data are plotted in activity diagrams such as (²³⁰Th /²³²Th) vs (²³⁴U /²³²Th) and of (²³⁴U /²³²Th) vs (²³⁸U /²³²Th). The slopes of best-fit lines through the data-points give (²³⁰Th /²³⁴U), and (²³⁴U /²³⁸U), respectively, and these are the input parameters for the classical Kaufman and Broecker (1965) age equation. The underlying assumption is that there is no ²³²Th in the authigenic mineral and that all ²³²Th is in one allogenic phase with a constant U/Th ratio in secular radioactive equilibrium. There are four different ways to arrange the relevant isotopes in ratios that can be used to calculate ages from either slope or intercept of best-fit lines, all giving equivalent results.
Ludwig (2003) and Ludwig and Titterington (1995) advocate fitting a plane through the (²³⁰Th /²³⁸U), (²³⁴U /²³⁸U) and (²³²Th /²³⁸U) data-points and this is usually referred to as the ‘three-dimensional isochron approach’. However, the Kaufman and Broecker (1965) evaluation method considers the samples to be a mixture of two phases, authigenic and allogenic, not a radioactively evolving closed system, as the use of the word ‘isochron’ implies. Ludwig and Titterington (1995) forms the basis for a regularly updated software package that is available from KR Ludwig and which has become the de-facto standard for calculating U-series ages and uncertainties.

Simpler mathematical correction

Least-squares best-fit line routines are available in many spreadsheet software packages and give adequate answers for the two input parameters of the Broecker Equation.

Uncertainty considerations

Two independent factors have to be considered for uncertainty evaluation: analytical uncertainty and scatter of the data-points around the mixing lines. Total analytical uncertainty can be simply propageted by taking the square root of the sum of the squares of the individual uncertainties. Scatter of the data-points around the least-squares line is given by the minimised deviation. These two uncertainties can then be propagated to calculate an overall uncertainty estimate. In situations of simple two-component mixing of the authigenic material with variable amounts of one other component, the analytical uncertainty will dominate to total uncertainty. Where there is a limited range of mixing ratios, or variable proportions of more than one type of allogenic material, the uncertainty will be dominated by the scatter of the data-points around the mixing line.
In clean samples with a very limited allogenic contamination, the analytical uncertainty in the ²³²Th contribution can become large, especially if the used analytical technique is alpha spectrometry, and can dominate the overall uncertainty unfairly. For such samples it is adequate to simply subtract the small ‘inherited’ ²³⁰Th contribution and ignore the uncertainty magnification.

Empirical correction

Another approach is the ‘minimised standard deviation’ method. This requires analysing the ²³²Th concentration in the samples and assuming a Th/U ratio, such as a global average for shale, for the allogenic material, and secular radiogenic equilibrium. It is then simple to calculate the ‘inherited’ ²³⁰Th and subtract the appropriate amount from the total ²³⁰Th inventory. The assumed Th/U ratio that gives the lowest standard deviation in the calculated ages of a set of coeval samples, is the most appropriate. Analysis of the actual Th/U in the allogenic phase usually confirms the empirical Th/U ratio and the average age is within the uncertainty of the age obtained with best-fit methods. For clean samples the empirical correction would be preferable. The standard deviation of the ages is an acceptable estimate of the uncertainty on the average age. It is tempting to use the empirical Th/U to correct single samples from different horizons in the same sequence but the resulting calculated individual ages are then model-dependant and only analytical uncertainty should be reported.

Last updated: December 23, 2011 11:37