Mathematics – Probability
Scientific paper
Apr 2004
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004e%26psl.220..265s&link_type=abstract
Earth and Planetary Science Letters, Volume 220, Issue 3-4, p. 265-275.
Mathematics
Probability
12
Unspiked K-Ar Dating, Resolution, Historical Age, Positivity Constraint
Scientific paper
An evaluation of the precision and resolution of the unspiked K-Ar dating method is presented with particular regard to the statistical significance of ages that are measured near or at the detection limit of the technique. Near-zero (historical) ages can be measured by the unspiked K-Ar technique with a precision that is essentially controlled by the precision with which the 40Ar/36Ar of the sample can be resolved from the present-day atmospheric value of 295.5. The best analytical precision on the isotopic ratio is +/-0.05% (1σ) by this technique, which currently limits the lower detection limit of unspiked K-Ar ages to samples featuring at least 0.14% of radiogenic 40Ar. The corresponding youngest resolvable K-Ar age depends on the K content and atmospheric contamination of the sample. Total-fusion analysis of high-K refractory minerals like sanidine is not practicable via K-Ar, and the lowest resolvable age for medium-K samples more amenable to complete fusion is around 1.5 ka (on a single-run basis). It is argued that near-zero age measured with a probability density straddling or narrowing the time-origin cannot be handled without accounting for the non-negativity constraint imposed by the physical requirement of a positive age. The pertinent equations are derived both for the single-run case and for the case of independent replicates made on a single sample. We show that pooled K-Ar replicates can theoretically reduce the nominal uncertainty of individual unspiked ages (typically +/-1.5 ka, 2σ) to a value that is close to the smallest 40Ar/39Ar isochron age uncertainty achievable on sanidine in the 0-2 ka range (+/-0.2 ka, 2σ). However, this performance is obtained at the cost of prohibitively large-sample statistics (n>=15) for medium-K feldspars datable via K-Ar. Coupled with the inability of the K-Ar approach to obviate the problems of excess/fractionated 40Ar and/or xenocrystic contamination, this makes the 40Ar/39Ar technique the method of choice for dating historical events by the K-Ar scheme.
Guillou Hervé
Scaillet Stéphane
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