Statistical Analysis of Lead Isotope Data in Provenance Studies
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ABSTRACT Tracing artifacts to ore sources is different from assigning ore samples to time epochs. Until now, archaeometrists working with lead isotopes have used the ratio methods developed by geochronologists. For provenance studies, however, the use of composition data (the fraction of each of the four isotopes) leads to fewer arbitrary choices, two standard types of plots (labelled ternary and canonical variable), and a consistent method of discriminant analysis for separating groups of samples from different sources.
INTRODUCTION Lead (Pb) has four stable isotopes. 204pb is a direct product of stellar fusion. 206pb,20?pb and 208pb are the endpoints of decay series which start with uranium 238, uranium 235, and thorium 232 respectively. The lead isotope composition of an ore sample depends upon the composition at the time of deposition, the relative amounts of precursors in the decay series, and the time since deposition. Since the 1920s, geochronologists have used lead isotope ratios to 12 calculate the age of the earth and of particular ore deposits' . They primarily 206 207 208 express and analyze their data in terms of the ratios of Pb, Pb, and Pb to 204pb, with secondary use of similar ratios to 206pbo In a plot of two of these ratios, samples generally fall at a position along a curved line that can be related to time since deposition. Use of lead isotope analysis for provenance studies began in the 1970s, to identify the source of metals used to produce artifacts. The analytical method typically used so far has been visual identification of source areas on bivariate plots of isotope ratios. The plots are based upon those of geochronologists, with a shift of emphasis from 204pb ratios to 206pb ratios. Only recently have serious statistical methods been attempted. Matching artifacts to geographically dispersed sources is different from matching sources to a time scale. We have therefore taken a fresh look at statistical methods for handling lead isotope data in provenance studies. Here we discuss the use of (i) fractional composition data; (2) standard statistical summary measures; (3) labelled ternary and canonical variable plots; and (4) discriminant analysis to objectively identify source areas. Items 4, 3, and 1 contrast with visual examination of bivariate plots of ratios.
LEAD ISOTOPE DATA IN PROVENANCE STUDIES The statistical issues were examined and tested with three datasets, based on published materials, of lead isotopes in ore deposits and artifacts: Mediterranean 56 samples of Mediterranean artifacts from Italy to Egypt, 800 B.C. to 1500 A.D. (bronzes, coins, lead objects, and glass), drawn together as part of an authentication study of a bronze horse in the Metropolitan Museum of Art attributed to classical Greece3. Aegean Region and Anatolia 314 Aegean and Anatolian mixed artifact and sourcerelated analyses (after elimination of duplicates, which sometimes had different samples numbers in different publications)4"12. East Asia 230 Chinese, Japanese and Korean artifacts (with a few
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