Introduction
Radiocarbon dating (RD) of a sample is reduced to measuring the 14C and 13C content in it, introducing a correction to the 14C content for the fractionation of carbon isotopes (calculated from the 13C content) and calculating the radiocarbon age. Based on the calibration curve, the radiocarbon age of the sample is recalculated to the calendar. Thus, the reliability of radiocarbon dating is determined by the reliability of calculating the radiocarbon age of the samples and the reliability of the calibration curve. The latter parameter is determined by the reliability of the radiocarbon and calendar ages of the samples, which were used to construct the calibration curve and the degree of its correspondence to the 14C variations in the CO2 atmosphere of the region in which the dated samples were formed.
By the reliability of RD results, we mean the degree and nature of the correspondence between the estimated and actual age of the dated samples. A direct experimental assessment of the reliability of RD results is fundamentally impossible. This is a fundamental feature of the method. Thus, the assessment of the reliability of the RD results can be performed only by “indirect” methods. But the funds available for such an assessment are significantly limited. We can name only one work in which one of the classic "indirect" methods of assessing the reliability of the RD is relatively correctly implemented - the factors affecting the reliability of dating are identified, the errors introduced by them are estimated and the total contribution of factors to the calendar age of the dated samples is found. There is another group of classical "indirect" methods,based on the analysis of "convergence" of research results. One of the methods of this group, in relation to the RD, we have found.
Method description
The calibration curve of the RD was calculated using wood samples with a known age and reflects the dependence of the radiocarbon age on the calendar. It has local maxima and minima, steps and relatively steep sections. It follows from this that with a uniform distribution of the dated samples along the calendar age scale, their distribution along the radiocarbon age scale will be uneven. The calendar age of the samples, on the basis of which the calibration curve was calculated, is evenly distributed - after 10 years. Therefore, from the calibration curve, we can calculate the standard for the radiocarbon age frequencies of the samples. The calibration curve for the RD and the standard for the radiocarbon-age frequencies of the samples are shown in Figure 1.
Figure: 1. Calibration curve of radiocarbon dating and the standard of frequencies of the radiocarbon age of the samples.
The standard for the frequencies of the radiocarbon age of the samples is calculated for intervals of 100 radiocarbon years. The resulting curve is highly differentiated. The frequencies range from 2 to 29. There are distinct highs and lows. We can compare the standard with the frequencies of the radiocarbon age of samples of specific samples for regions, types of dated materials or laboratories obtained from RD databases. The idea behind this comparison is simple. If the reliability of the estimate of the radiocarbon age of the sample and the calibration curve are close, then the actual and reference frequencies should be expected to coincide. In this case, the degree of coincidence will be determined by the degree of conformity of the actual distribution of the calendar age of the sample samples on the scale of calendar years to their uniform distribution. If there are significant frequency mismatches,then this will mean that the reliability of the calibration curve and the radiocarbon age of the samples of a particular sample are different. Moreover, for some cases of discrepancies, it is possible to substantiate hypotheses about their causes.
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The efficiency of the method is shown on the example of the analysis of three samples of data from the RD, which we named "USA-Canada", "Europe" and "North China". The samples include dates that fall within the interval 0-5999 BP years. All frequencies of the radiocarbon age of the samples were calculated in a window of 100 VR years.
Sample "USA-Canada"
The USA-Canada sample was compiled from the database on the website. There are 22227 dates in the sample: 15452 dates in the USA, 6561 dates in Canada, and 214 dates in Russia. Including: 1438 dates of wood samples, 12675 - charcoal, 2922 - bones, 2655 - calagen bones.
Figure: 2. Sample "USA-Canada". Comparison of the age frequencies of all samples in the sample with the reference.
Figure: 3. Sample "USA-Canada". Comparison of the high-frequency component of the age frequencies of all samples in the sample with the reference.
Figures 2 and 3 show a comparison of the frequencies of age and their high-frequency component of all samples in the sample with the standard. Three intervals are distinguished according to the degree of qualitative coincidence of the curves. In the interval A (250-1400 BP years) the agreement is good, in the interval B (4200-5950 BP years) it is satisfactory. In the interval B (1400-4200 BP years), no coincidence is seen.
Figure 4 shows an example of modeling the accuracy of radiocarbon dating at the age frequencies of all samples from the US-Canada sample for the interval 250-1350 BP years. The model frequency curve is the sum of the normalized low-frequency component of the age frequencies of all samples in the sample and the normalized reference frequencies. Satisfactory agreement between the model and the actual data was obtained provided that 9.2% of the dates have an accuracy approximately equal to the accuracy of the calibration curve. The low-frequency component of the model was calculated by averaging the frequencies of the age of the sample over 5 points (window of 500 years). Based on this, it can be roughly assumed that the accuracy of the remaining 90.8% of the datings of the sample does not exceed plus / minus the first hundreds of years. Since we do not have a criterion for distinguishing from the entire set of dates of thosewhich have an accuracy approximately equal to the accuracy of the calibration curve, the latter value can be taken as the actual accuracy of the RD of a particular sample in a particular time interval.
Figure: 4. Sample "USA-Canada". An example of modeling the accuracy of radiocarbon dating based on the age frequencies of all samples in the range of 250-1350 BP.
The dating frequencies of coal qualitatively coincide with the reference frequencies practically over the entire analysis interval (Figure 5). The dates of the tree in the range of 50-3050 BP years are shifted by 100 BP years in the direction of decreasing radiocarbon age.
Figure: 5. Sample "USA-Canada". Comparison of the frequencies of the age of wood and charcoal samples with the standard.
Figure: 6. Sample "USA-Canada". Comparison of the age frequencies of the bone and calagen samples with the reference.
The bone dating frequencies are fully consistent with the calagen dating frequencies (Figure 6), however, they are shifted relative to the reference frequencies in different time intervals by 0-300 BP years in the direction of increasing radiocarbon age.
Figure 7 shows a comparison of the actual total frequencies of dating of wood, charcoal, bones and calagen and frequencies corrected for shifts with respect to the standard. The corrected frequencies better match the reference frequencies.
Figure: 7. Sample "USA-Canada". Comparison of the actual total frequencies of the age of samples of wood, charcoal, bones, calagen and frequencies corrected for shifts with respect to the standard.
Sample "Europe"
The Europa sample was compiled from radiocarbon dating data published in the journal Archaeometry. The sample includes only those dates for which the content in sample 13C is shown. The sample characterizes all of Europe. The "center of gravity" of the sample is in the UK. There are only 1168 dates in the sample. Including: 83 dates of wood samples, 267 - charcoal, 216 - animal bones, 398 - human bones, 26 - unidentified bones, 133 - seeds, 45 - plant remains.
Figure: 8. Sample "Europe". Comparison of the age frequencies of all samples in the sample with the reference.
Figure 8 shows a comparison of the dating frequencies of all samples in the sample with the reference. According to the degree of qualitative coincidence of the curves, 5 intervals are distinguished. In the intervals A (50-700 VR years), B (1600-2800 VR years) and D (5300-5950 VR years), the agreement is satisfactory. In the intervals B (700-1600 VR years) and D (2800-5300 VR years), the shapes of the curves do not coincide. It should be noted that these intervals are characterized by high dating frequencies. The frequency shifts of the age of wood and charcoal samples relative to each other and the standard by plus / minus 100 BP years are seen (Figure 9). The frequencies of the age of animal bone samples (Figure 10) coincide with the standard only in the interval A (50-1100 BP years).
Figure: 9. Sample "Europe". Comparison of the frequencies of the age of wood and charcoal samples with the standard.
Figure: 10. Sample "Europe". Comparison of the frequencies of the age of animal bone samples with the standard.
Sample "North China"
The North China sample was compiled from the database on the website. The sample includes all dates of archaeological sites in Northwestern (Xinjiang Uygur Autonomous Region) and Northeastern China (Heilongjiang, Jilin, Liaoning Provinces, and Inner Mongolia Autonomous Region) obtained in the laboratories of Beijing. A total of 601 dates. Including: 169 wood samples, 234 - charcoal, 137 - plant residues (seeds, straw, reeds, rotten wood, bark). The remaining samples are represented by animal and human bones, skin, wool and shells.
Figure: 11. Sample "North China". Comparison of the frequencies of the age of all samples of the sample and plant remains with the standard.
Figure 11 shows a comparison of the age frequencies of all samples from the North China sample and plant residues with the reference. Qualitatively, the coincidence of the shapes of the curves is observed only in the interval A (1200-2000 BP years). The frequencies of the age of wood and charcoal samples correspond to each other only in the interval 2800-4200 years and do not correspond to the standard (Figure 12). After a shift in the frequencies of the age of wood and coal by minus 100 BP years, a satisfactory agreement between their sum and the reference curve was obtained (Figure 13).
Figure: 12. Sample "North China". Comparison of the frequencies of the age of wood and charcoal samples with the standard.
Figure: 13. Sample "North China". Comparison of age frequencies (reduced by 100 years) of wood and charcoal samples with the standard.
Evaluating the reliability of the calibration curve
From the discrepancy between the reference frequencies and the actual frequencies of the radiocarbon age of a particular sample in a particular interval of radiocarbon years, it follows that the reliability is low within the interval of the radiocarbon age of the sample and / or the calibration curve. By analyzing a sufficiently large number of samples, it is possible to statistically identify “suspicious” intervals of the calibration curve. Using the analysis of three samples as an example, one such interval can be named - approximately 1700-1900 VR years (Figure 3, interval B1; Figure 8, interval B1). It can be assumed that within this interval it is the calibration curve that has a low reliability.
conclusions
Based on the results of the analysis of three samples of the radiocarbon age of the samples by our proposed method, methodological and practical conclusions can be drawn.
Methodological conclusions
The method for assessing the reliability of the results of radiocarbon dating, based on comparing the reference frequency of the radiocarbon age with the frequencies of the radiocarbon age of samples from the RD databases, is simple, independent and highly efficient. To apply the method, it is not required to involve a priori data for the RD. Based on it, it is possible:
- allocation in the frequencies of the radiocarbon age of samples of specific samples, time intervals and their ranking according to the degree of compliance with the reference frequencies;
- assessment of the accuracy of determining the radiocarbon age of samples based on modeling;
- identification of systemic shifts in the age of samples of various materials;
- identification of areas on the calibration curve characterized by relatively low reliability.
When applying the method, classical procedures for statistical processing of data arrays can be used.
Practical conclusions
Radiocarbon dating is generally quite workable. Two questions remain open - the objective reliability of dating and the influence of subjective factors on the dating results. The error in determining the radiocarbon age of the samples of the "USA-Canada" sample based on the results of modeling in the interval of 250-1350 BP years is plus / minus the first hundreds of years. In other intervals, the dating error is higher than in the interval 250-1350 BP years. The dates of various materials are shifted relative to each other by up to 300 BP years, which also gives an error of plus / minus the first hundreds of years. The errors in determining the radiocarbon age of the samples from the Europe and North China samples roughly correspond to the errors of the Canada sample. In the range 1700-1900 VR years, the calibration curve may have low confidence.