# Exotic burial dating methods

This post is about cosmogenic-nuclide burial dating, and how to make it better. I say “theoretically” a lot below — because mostly no one has done any of these things. However, most of them are feasible and should be tried.

The general concept of cosmogenic-nuclide burial-dating is that one has a pair of cosmogenic nuclides that are produced at a fixed ratio in some rock or mineral target, but have different decay constants. If a sample is exposed at the surface for a time, no matter what the production rate or how long the exposure, the concentrations of the two nuclides conform to the production ratio. Then if you bury the sample deeply enough to stop new nuclide production, inventories of both nuclides (or at least one of the nuclides, if the other is stable) decrease due to radioactive decay. Because they decay at different rates, the actual ratio of the two nuclides gradually diverges from the production ratio. Measuring this ratio tells you the length of time the sample has been buried.

So far, nearly all applications of burial dating have used the Al-26/Be-10 pair in quartz. The 26/10 production ratio is 6.75. The half-lives of Al-26 and Be-10 are 0.7 and 1.4 Ma, respectively. This turns out to be a very useful nuclide pair because quartz is so common — nearly all sedimentary deposits contain quartz that has been exposed for a time and then buried as the deposit accumulated.

However, there are a lot of other nuclide pairs that could potentially be used for this purpose. There are really two reasons one might want to use a different nuclide pair — first, one can’t find quartz; second, the new nuclide pair would give a more precise age in the time range of interest. Because it’s pretty rare not to be able to find quartz, the second reason — potentially reduced uncertainty or a wider age range — is really the key reason to think about burial-dating with other nuclide pairs. The uncertainty of a cosmogenic-nuclide burial age is set by a number of factors: measurement precision for the nuclides in question; the actual values of the production ratios and decay constants; how precisely the decay constants of the nuclides in question are known; how precisely the production ratios are known; and geological factors, mainly to do with the burial history of the sample. Geological factors don’t depend on the nuclides that are being used — they would have a similar effect no matter what the nuclide pair — so because the point of this discussion is to discuss why you would want to use one nuclide pair rather than another, we’ll ignore geological factors and assume that whatever we’re dating gets immediately buried at infinite depth and stays there until the time of measurement.

So to compare the precision of burial dates with various nuclide pairs over different age ranges, a few ingredients are needed.

One is the precision of the half-life determinations. I’ll consider four commonly used cosmogenic nuclides: Ne-21, Be-10, Al-26, and Cl-36 (both He-3 and Ne-21 are stable, so they’re pretty much equivalent for purposes of this discussion and I’ll only talk about Ne-21). Of these, Ne-21 is stable, so there is no uncertainty in its half-life. The half-life of Be-10 has recently been very precisely measured to about 0.8% precision. That of Cl-36 is also fairly accurately known (0.7%). That of Al-26 is somewhat less well known (ca. 2.5%).

Another is measurement precision. The following plot shows the concentration-measurement uncertainty relationship for all the Al-26 and Be-10 concentrations I could assemble from readily available data.

Red and blue dots are actual Be-10 and Al-26 measurements from the past few years. Nearly all these measurements include chemical processing at the University of Washington, and AMS analysis at LLNL-CAMS. The solid lines show model uncertainty relationships fit to these data; they have approximately a square-root dependence at high concentrations (the log-linear part of the curve) and then diverge upward from that relationship at low concentrations as one approaches the detection limit. I don’t have similar data readily to hand for Cl-36, so I’ll assume for now that Cl-36 measurements have the same statistics as Al-26. Ne-21 measurement precision depends on the geomorphic situation and will be discussed later. The final ingredient we need is an estimate of the uncertainty in the production ratios of these nuclides. This is hard to estimate in a general way — it depends on the rock or mineral in question and its composition — so for purposes of the following discussion I’ll assume that we know these ratios accurately (however, this is a major issue for some nuclide pairs).

Given these ingredients, we can make an uncertainty estimate for all six nuclide pairs implied by these four nuclides. My point in doing this calculation in the first place was to carry out a feasibility study for burial-dating of sediments derived from ignimbrites in the western US, so the basic assumptions are tailored to that scenario. The target mineral for Cl-36 production is a K-rich feldspar. That for all other nuclides is quartz. The sediment source is at 1300 m elevation and is eroding at 3 m/Myr. This results in a cosmogenic Ne-21 concentration near 10 Matoms/g, which we can measure with approximately 5% precision. I use the measurement uncertainties for the other nuclides as discussed above, assume no geologic uncertainty, and assume we know the production ratios accurately. This yields the following burial age-uncertainty relationship for the six nuclide pairs we are considering:

Here is the same plot with a different axis, focusing on the Pleistocene:

OK, what do we learn from this? First of all, the general structure of this plot is as follows. For a particular nuclide pair, relative age uncertainties are large at young ages (this is just a consequence of the radioactive decay equation and the fact that if the age uncertainty is more or less constant in absolute terms, it blows up in relative terms as the age approaches zero), and then become large at old ages again (because at least one of the nuclides decays to concentrations too low to measure accurately). There is a relatively flat “sweet spot” in the middle. The location, width, and uncertainty of the sweet spot depend in a fairly complicated way on the production ratios and decay constants themselves as well as on the measurement uncertainty characteristics of each nuclide. One thing that is interesting is that it generally pays to pick a stable nuclide (Ne-21) as one of the pair, for three reasons: first, it doesn’t decay, so there’s no loss of measurement precision with burial age; second, it doesn’t decay, so one less half-life uncertainty gets propagated into the burial age; third, its ‘decay constant’ is zero, which maximizes the difference between decay constants (an important part of the uncertainty) relative to anything else you could choose. So this is a good reason to focus on Ne-21 measurements (or on He-3 measurements, which would work similarly except that He-3 is not retained in quartz).

Regardless, two things are clear, at least in theory for this particular scenario:

First, with this scenario, for any time period it is (again, theoretically) possible to improve on the precision of Al-26/Be-10 burial dating by choosing a different nuclide pair. Mainly this is for two reasons: i) the uncertainty is inversely proportional to the difference between decay constants (this falls out of the math) and the difference between Al-26 and Be-10 decay constants is not as large as for other nuclide pairs; ii) the half-life of Al-26 is the least precisely measured of all the nuclides.

Second, different nuclide pairs are the optimal choice for different time ranges. Pairs where the half-life difference is larger are useable at younger ages; pairs that include one nuclide with a short half-life become unusable faster. So this sort of a plot can serve as a guide for which nuclide pair one ought to apply to a particular problem. In this example, we’re looking at Pleistocene alluvial terraces so in theory we should like either the Cl-36/Ne-21 or the Cl-36/Be-10 pair.

Of course, there are a couple more points here. Besides the fact that I am ignoring geologic complications, all of these pairs might not be feasible because the targets don’t occur together, or because of complications in figuring the production ratios. Nuclide pairs involving Cl-36 are only feasible for targets where Cl-36 production by thermal neutron capture is negligible; this most likely means K- or Ca-rich feldspars with very low Cl-35 concentrations. Ne-21 can only be measured precisely at relatively high concentrations, such as in this example; at low concentrations precision degrades rapidly because of interference from non-cosmogenic Ne-21 trapped in the target mineral. Al-26, Be-10, and Ne-21 all can be measured and have well-characterized production rates in quartz, so those three nuclides can commonly be used together. Cl-36 and Ne-21 both occur in K-feldspars, although production rates are not as well characterized as in quartz. This pair is potentially quite precise, and could be used to good effect in sanidine from ignimbrites. However, if a nuclide pair has different target minerals, for example if combining Cl-36 in feldspar with something else in quartz, then the sample must consist of a rock that contains both minerals together, to ensure that they have the same exposure history.

Summary: in theory one can tune the burial-dating method to have better precision, and a much wider range of applicability, by using a range of nuclide pairs beyond Al-26/Be-10. This is really interesting.

Other important point: I haven’t discussed at all the possibility of using three nuclides in the same sample. This gets complicated fast, but it is a really interesting idea because it can potentially allow one to be less dependent on the geological assumptions that go into two-nuclide burial dating — so the method would be useful in more geologic situations.

**More information:**

Balco G., Shuster D.L., 2009. Al-26 – Be-10 – Ne-21 burial dating. *Earth and Planetary Science Letters, *v. 286, pp. 570-575. doi:10.1016/j.epsl.2009.07.025

Granger, D., 2006. A review of burial dating methods using Al-26 and Be-10. In: Siame, L., Bourlés, D., Brown, E., eds., *In-situ-produced cosmogenic nuclides and quantification of geological processes: Geological Society of America Special Paper 415.* Geological Society of America, Boulder, CO. pp. 1-16.

Wow, just found this site. I’m just starting to use cosmo for bulk erosion rates and have TONS to learn about the method. I will definitely be reading this blog (and your papers).

Dr. Balco,

I’m using 10Be depth profiles of faulted alluvial and fluvial surfaces for Quaternary slip rate determinations. I have a growing concern about the ability of shallow to moderate (2m) profiles to yield unique exposure age/erosion rate pairs (e.g., Braucher, et al. 2009, Quat. Geochron.). I am wondering if paired nuclide dating in addition to depth profiles would solve the problem. Your discussion here is centered on burial dating but it would seem that there may be some application to estimating erosion rates as well. What are your thoughts on this?

Also, how would the time sensitivity plots work for a 14C/10Be pair? The surfaces I’m working on are probably 10-50 kyr old, so the nuclide pairs discussed above are not particularly suited for these features.

Thanks!

Richard