|“||There are known knowns. These are things we know that we know. There are known unknowns. That is to say, there are things that we now know we don’t know. But there are also unknown unknowns. These are things we do not know we don’t know.||”|
—United States Secretary of Defense Donald Rumsfeld
We have learned in Parts 2 and 3 that radio-isotopic dating is capable of producing very precise dates however full exploitation of these data requires considerations of the associated uncertainties. All measurements have an uncertainty associated therewith regardless of precision and accuracy. This is caused by two factors: the limitation of the measuring instrument (systematic uncertainty) and the skill of the experimenter making the measurements (random/external uncertainty). During the past two decades analytical precision has increased substantially due to improvements in both mass spectrometry and laboratory protocols.
- Systematic uncertainty: biases in a measurement where the mean of individual measurements differs from the true value.
- Random/external uncertainty: aberration in measurements that lacks reproduciblity of a fixed value.
- Accuracy: the correctness of measurements to a quantity's true/accepted value.
- Precision: the degree of reproducibility and repeatibility of measurements.
|Accuracy and Precision|
Sources and types of uncertaintyEdit
Without an accurate estimation of total uncertainty, the radio-isotopic age of a given rock or mineral is of limited value.
It is necessary for users of geochronological data to understand the various sources of error and when one must consider the total uncertainty of a given date as opposed to its constituent parts. Although the uncertainty of each date contains an internal/random component in the total uncertainty, there are also components that are systematic, such as errors from the decay constants. When comparing ages determined by the same isotopic system these can be ignored offering a potential increase in resolving power. In this section we review the different sources of uncertainties and the assumptions that underlie the often quoted (or not) errors. For more detailed treatment of uncertainties in geochronology the following articles are recommended: Ireland and Williams (Ireland and Williams, 2003); Stern and Amelin (Stern and Amelin, 2003), Schmitz and Schoene (Schmitz and Schoene, 2007), and various papers by Ludwig (Ludwig, 1980, 1991, 1998, 2003).
One source of systematic uncertainty that affects all radio-isotopic dates are those related to the uncertainty in the decay constants (Table 1). Three approaches have been taken to determine the decay constants (the probability that a given atom will decay per unit of time) of the long-lived radionuclide; (1) direct counting; (2) ingrowth and (3) geological comparison. Direct counting involves the detection of alpha, beta or gamma activity relative to the total number of radioactive atoms. Ingrowth relies upon the quantification of a decay product that is accumulated from a quantity of high-purity parent nuclide over a well-defined period of time. Geologic comparison involves the analyses of cogeneitc materials with multiple chronometers, knowing that each chronometer should yield the same date. This approach has the potential for relative intercalibration of the decay constants but accurate intercalibration requires that at least one decay constant is accurate and known with some precision. This is usually assumed to be the 238U and 235U due to the precision with which the decay constants have been determined (Jaffey et al., 1971) and the internal check provided by closed system zircon analyses (Mattinson, 2000; Schoene et al., 2006).
The counting experiments of Jaffey et al (1971) determined the 238U and 235U decay constants with uncertainties of 0.11% and 0.14% respectively. These values have been adopted for use in geochronology (Steiger and Jager, 1977). The 187Re and 176Lu decay constants have been determined by both direct counting experiment and through geologic comparison with the U-Pb system and uncertainties are estimated at ca. 0.4 to 0.5% (Scherer et al., 2001; Selby et al., 2007).
The incorporation of decay constant uncertainties are becoming increasingly important as both the internal precision of dates is reduced and multiple geochronometers are being used to investigate the same time intervals. The decay constant uncertainties for isochron dates are typically <20% of the total uncertainty budget, in contrast the uncertainties in the U decay constants are often >50% of the total uncertainty budget of U/Pb ID-TIMS dates (Fig. 2). The situation for the ID-TIMS U/Pb community is that they are now often generating 206Pb/238U and 207Pb/206Pb dates often do not overlap within analytical precision and the U decay constant uncertainties must be considered (Begemann et al., 2001; Ludwig, 2000; Schoene et al., 2006). As the ‘user’ often uses these date interchangeably we are now seeing 206Pb/238U and 207Pb/206Pb age uncertainties presented as ± X/Y/Z and ± X/Z respectively, where X is the analytical/internal uncertainty, Y is the analytical uncertainty plus the systematic tracer calibration uncertainty, and Z is the total uncertainty including X, Y and the decay constant uncertainties. This permits use of the data with the level of uncertainty that is appropriate to the problem being addressed. Mattinson, 2000, 2008 and Schoene et al., 2006 pointed out that sets of high-precision dates from zircons of different ages indicates a difference of approximately 0.2% between 206/238 dates and 207/206 dates due to probable inaccuracy in 235U decay constant. This has led to the suggestion that the 235U decay constant be recalculated to achieve concordance between 206/238 , 207/235, and 207/206 dates. While not officially adopted the authors predict this will become common and users if data must be be aware of this trend.