addition to five rock units in the Grand Canyon region of Arizona (Austin and Snelling 1998; Snelling 1998, 2003a, 2003b; Snelling et al. 2003; Austin 2005; Snelling 2005). All but one of these rock units were derived from basaltic magmas generated in the mantle. The results revealed that each radioisotope method yielded concordant ages internally (e.g. between whole-rock and mineral ages) but significant discordance between ages from different dating systems. Examples were found of all four categories of isochron discordance described by Austin (2000): (1) two or more discordant whole-rock isochron ages; (2) a whole-rock isochron age older than the associated mineral isochron ages; (3) two or more discordant mineral isochrons from the same rock; and (4) a whole-rock isochron age younger than the associated mineral isochron ages. Moreover, they identified systematic discordances between radioisotope dating systems, so that for the same rock unit Sm-Nd ages > U-Pb ages > Rb-Sr ages > K-Ar ages. In short, α-emitting radioisotopes (238U, 235U, 147Sm) gave consistently older ages than β-emitting radioisotopes (87Rb, 40K), and isotopes with longer half-lives (and/or heavier atomic masses) tended to yield older ages than those with shorter half-lives (and/or lighter atomic masses). The RATE group explained these systematic trends by hypothesising one or more episodes of accelerated nuclear decay in the Earth’s past, in which the amount of acceleration had depended on the type of decay involved (α versus β) and the length of the half-life of each parent isotope. However, the pattern is somewhat complicated by other factors such as the inheritance and mixing of radioisotopes from mantle and crustal sources. Snelling (2005, pp. 462-464) concluded that because the fundamental assumptions of radioisotope dating‒known initial conditions, lack of contamination, and constant rates of decay‒have been shown to be questionable, the resulting ages cannot be trusted as absolute ages but may still be applied, with caution, for relative dating. III. METHODS The National Geochronological Database (Zartman et al. 2003) was created by the United States Geological Survey (USGS) to provide a central repository for published radioisotope ages of rocks from across the United States. With over 18,000 records and almost 30,000 K-Ar, Rb-Sr, Sm-Nd, Th-Pb, Pb-Pb, U-Pb, and fission track ages, it is estimated to contain half of the radioisotope ages published through 1991. The data represent determinations on a wide variety of igneous and metamorphic rocks, as well as a few sedimentary rocks (322 records). Our study uses the 2003 version of the database; an update was released in 2011, but the changes were insignificant enough to make no difference to our analysis. Hillenbrand et al. (2023) published a major revision of the database after our analysis was completed and submitted for review. The basic organizational unit of the database is “the record,” each identifying a particular dated rock sample and containing location, rock description, and age information (Zartman et al. 2003). Record numbers link information contained in separate files for each method, a merged “allages” file, and a location file. To determine whether two calculated ages from the same record agree, we used a standardized definition of concordance. If two such ages had uncertainty ranges that overlapped, then they were considered concordant with one another. If there was no overlap, the two ages were considered to be discordant. For cases in which no uncertainty range was given, we assumed a range of ±10% of the reported age. For comparison, the average uncertainty range in the database was ±6.3% of the corresponding age. Using this definition of concordance, our first step was to calculate a “Concordance Metric” for each record or portion of a record containing two or more ages. Each unique pair of ages in a given record was labeled either 1.00 (concordant) or 0.00 (discordant). By dividing the number of concordant comparisons by the number of comparisons in the record, the metric yields a concordance score for the record. The concordance score can range from 1.00 to 0.00, where 1.00 means total concordance within the record (all the age ranges overlap) and 0.00 means total discordance (none of the age ranges overlap). This metric was directly applied to all records in the database, and this information was used to calculate the average concordance score of the records. We used the concordance metric to find the overall concordance score of the database. After that we adopted three approaches to identifying and quantifying trends in the frequency of concordance and discordance in the database, all based on our concordance metric. Our first approach was to isolate a particular method and the records with two or more ages calculated using that method. Using only the ages from that method, we calculated a new concordance score for each of these records. This was done for eight of the nine methods. We did not perform any analysis of the Sm-Nd ages because there were only 32 records in the database that included Sm-Nd ages. Our second approach was to filter the database for any records that had ages calculated using at least two methods, referred to as the “Two Methods Comparison.” We assembled the data for each unique pair of methods into a spreadsheet, which allowed us to directly compare one method to another. For each record, each calculated age by one method was compared to each calculated age by the other method to check for concordance. The proportion of concordant comparisons was then recorded. Our third approach, called the “Three Methods Comparison” included records with ages calculated using at least three different methods, at least two of which were not in the U-Th-Pb decay chain. Of the 18,575 records in the database, only 34 met this criterion. These 34 records were compiled into a single spreadsheet and plots made of the radioisotope ages vs. present half-lives of the parent radioisotopes, along with atomic weight and type of decay. Our fourth approach, called the “U-Th-Pb Comparison,” was similar to the “Three Methods Comparison.” It included records with ages calculated using three or more of the four U-Th-Pb methods. 998 records met this criterion. Concordance scores were calculated for each record and these were compared to the concordance scores of the database as a whole. To perform our analysis, several pieces of software were used. Microsoft Excel was used to store and access data, perform general calculations, and generate preliminary charts. Processing, a programming language and environment, was used for searching, reformatting, and adding calculated values to the database. Grapher, a data visualization tool, was used to generate the charts used in this paper. IV. RESULTS The total number of unique records in the database is 18,575. For these records there are 29,043 distinct age calculations using eight different methods: 40K-40Ar, 87Rb-87Sr, 147Sm-143Nd, 232Th-208Pb, PbPb, 235U-207Pb, 238U-206Pb, and fission tracks. Appendix A explains how the number of unique age determinations in the database was estimated and includes the source code used to generate our main data file. Six hundred and thirty-six (4.5%) of the ages included in the K-Ar category were actually some type of argon-argon (Ar-Ar) analysis, but we followed the organization of the database in grouping them together. For 12% of K-Ar and FT, 22% of Rb-Sr, 69% of Th-Pb, and 78% of Pb-Pb, 235U-207Pb, and 238U-206Pb ages, no uncerBEACHY, KINARD AND GARNER How often do radioisotope ages agree? 2023 ICC 388
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