Open University UraniumSeries Laboratory  
Earth and Environmental Sciences, The Open University, Milton Keynes, UK  
Correction of allogenic or 'inherited' ^{230}Th  
A
disadvantage of many authigenic precipitates suchs as lake marls is that
they contain significant amounts of ‘inherited’ ^{230}Th
from allogenic material. This can include detrital material such as carbonate
or clay from the drainage area, or windblown 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 ^{230}Th. The
effect of ‘inherited’ ^{230}Th 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. 



Effect of ‘inherited’ ^{230}Th on the calculated age. In these model calculations a 5 wt % allogenic contribution has negligible effect on an age of 177 ka. A 0.5 wt % contribution is already resolvable on an age of 10 ka and would be significant on an age of 3 ka. 

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 Useries data requires that the effects of the allogenic contribution
on ^{230}Th are adequately corrected.
Three categories of approach can be distinguished: chemical separation,
mathematical correction or empirical correction. 

Chemical
separation 

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 grainsize of the likely silicates),
the dissolved authigenic ^{230}Th
is highly particle reactive and precipitates onto the silicate grains. Stronger
reagents that would stabilise ^{230}Th 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 (^{230}Th
/^{232}Th) vs (^{234}U /^{232}Th) and of
(^{234}U /^{232}Th) vs (^{238}U /^{232}Th).
The slopes of bestfit lines through the datapoints give (^{230}Th
/^{234}U), and (^{234}U /^{238}U), respectively,
and these are the input parameters for the classical Kaufman and Broecker
(1965) age equation. The underlying assumption is that there is no ^{232}Th
in the authigenic mineral and that all ^{232}Th 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 bestfit
lines, all giving equivalent results. Ludwig (2003) and Ludwig and Titterington (1995) advocate fitting a plane through the (^{230}Th /^{238}U), (^{234}U /^{238}U) and (^{232}Th /^{238}U) datapoints and this is usually referred to as the ‘threedimensional 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 defacto standard for calculating Useries ages and uncertainties. 

Simpler
mathematical correction 

Leastsquares
bestfit 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 datapoints 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
datapoints around the leastsquares line is given by the minimised deviation.
These two uncertainties can then be propagated to calculate an overall uncertainty
estimate. In situations of simple twocomponent 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 datapoints around
the mixing line. In clean samples with a very limited allogenic contamination, the analytical uncertainty in the ^{232}Th 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’ ^{230}Th contribution and ignore the uncertainty magnification. 

Empirical
correction 

Another approach
is the ‘minimised standard deviation’ method. This requires
analysing the ^{232}Th 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’
^{230}Th and subtract the appropriate
amount from the total ^{230}Th 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 bestfit
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 modeldependant and only analytical
uncertainty should be reported. 



Bischoff
and Fitzpatrick, 1991. Geochimica et Cosmochimica Acta 55(2), 553–555.
Kaufman and Broecker, 1965. Journal of Geophysical Research 70, 4039–4054. Ludwig, 2003. Reviews in Mineralogy & Geochemistry 52, 631–656. Ludwig and Titterington, 1995. Geochimica et Cosmochimica Acta 58 (22), 5031–5052. Luo and TehLung Ku, 1991. Geochimica et Cosmochimica Acta 55(2), 555–565. 


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© Peter van Calsteren  Last
updated:
December 23, 2011 11:37
