A Software Package for Carbon-14 Dating

[摘要] In processing data pertaining to the radiocarbon dating context, there are many statistical methods which may be applied in the treatment of data, all of which are usually intended to produce reliable radiocarbon ages. In the pursuit of a suitable treatment of data, this work has produced some new methods in managing radiocarbon data. A major feature which is developed here is the incorporation of a certain number of statistical quality controls into the data management process. The culmination of this work is the presentation of a software package which has been successfully employed for over 6 years at the Scottish Universities Research and Reactor Centre at East Kilbride. The work can be described according to the various sections of this report. There are 8 sections in this report altogether. Section 1 is an introduction to the work and provides a brief description of the radiocarbon dating principle with particular emphasis on the liquid scintillation approach. Aspects of the method are examined including some basic axioms which give rise to the method, the chemistry of the liquid scintillation method and some statistical avenues which have already been explored in the pursuit of refining the production of radiocarbon ages. In section 2 some preliminary tests are conducted on a number of background counting samples. Two simple tests are conducted: a limited test for correlation patterns in the background counting data; a test for the normality of the background counting data. The problem of outliers in counting data is examined next in section 3. With an aim to filtering out spurious counting data, a method is developed here for small data samples which screens the data for the presence of outliers and removes them on discovery. The method is extremely simple and is based on the linear regressions of the estimated percentage points of two outlier detection statistics on the natural logarithms of sample sizes. Its simplicity makes it relatively easy to program which is the advantage of the method. In section 4 a new way of estimating the background activity using a pool of background samples is developed. The estimation, which is referred to as retrospect estimation, essentially involves drawing on a knowledge of the history of the samples and through that knowledge making corrections in the data which assist in the production of a mean background activity. Section 5 explores an alternative method for calculating the radiocarbon age of a sample. This method considers the correlation introduced into the counting data once corrections for the background activity have been applied to that data. The method basically involves deriving a weighted least squares estimate of the sample age taking into account the correlation introduced by the corrections for background. Section 6 follows this up with a simulation study which seeks to compare the alternative method of age estimation with a conventional method and finds favour for the alternative method. In section 7 there is a useful description of the software package which encapsulates some of the work presented in this report. The final section presents some brief conclusions and looks at possibilities for future modification and expansion of the software. This work is by no means a complete or definitive work since it would be virtually impossible to exhaust all possible treatments of radiocarbon data. What is achieved, instead, is a software package which covers a selected range of statistical aspects in radiocarbon dating and which hopefully produces reliable radiocarbon ages which is the primary aim of the radiocarbon method.

[发布机构] University:University of Glasgow

[关键词] Statistics, Computer science