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Upside-down bananas

March 30, 2017

If you are reading this, you are probably familiar with the two-nuclide diagram commonly used to represent paired Be-10 and Al-26 data:

This example is from a review article by Darryl Granger from 2006 (in GSA Special Paper 415) that gives a good description of what the diagram is and how it is supposed to work. Basically, the diagram shows Be-10 concentration on the x-axis and the Al-26/Be-10 ratio on the y-axis, although commonly both quantities are shown in normalized units computed by dividing observed concentrations by the respective production rates at the sample site – this normalization allows plotting data from different sites, with different production rates, on the same axis. The basic concept here is that if your sample stays at the surface and experiences steady exposure with or without erosion, nuclide concentrations are confined to the “simple exposure region” highlighted with dark lines in the above figure. In certain manifestations of this diagram (primarily when plotted with a log x-axis and a linear y-axis), the simple exposure region vaguely resembles a banana, for example:

This resemblance, perhaps unfortunately, has resulted in the common use of the term “banana diagram.”  Then the important aspect of this diagram is that if the sample gets buried after a period of surface exposure, both Al-26 and Be-10 concentrations decrease due to radioactive decay, and Al-26 decreases faster than Be-10. This is represented by a trajectory that goes down and to the left, as shown above in the Granger example. So samples that are “below the banana” have experienced both a period of exposure and a period of burial. Here’s an example:

The lines are contours of burial time in Myr. So these samples have been buried for 2.5 Myr. This is the foundation of the method of cosmogenic-nuclide burial dating.

So, basically, in the Al-26/Be-10 two-nuclide diagram (let’s not use “banana diagram” any more…historically, it probably should be called a “Lal-Klein-Nishiizumi diagram,” although that is a bit cumbersome), exposure goes to the right and burial goes down. Easy. The problem arises when other nuclides are involved. Here is an example of a Be-10/Ne-21 two-nuclide diagram from one of my papers:

Here I have put Ne-21 (the longer-lived nuclide) on the x-axis and the Be-10/Ne-21 ratio on the y-axis. So, again, exposure goes to the right and burial goes down. On the other hand, here is a Ne-21/Be-10 diagram from a very cool paper by Florian Kober and Vasily Alfimov:

This figure has a lot of data in it that are beside the point from the perspective of this post, but the point is that it has the opposite axes: Be-10 concentration on the x-axis and Ne-21/Be-10 ratio on the y-axis. Thus, exposure still goes to the right (at least for a while), but burial goes UP. Not down. Not what we expect from our previous experience with the Al-26/Be-10 diagram. Very weird.

At present, the choice of axes in two-nuclide diagrams involving Ne-21 in the literature appears to reflect your position in relation to the Atlantic Ocean. US researchers generally plot [Ne-21] vs. Be-10/Ne-21, whereas Europeans plot [Be-10] vs. Ne-21/Be-10. Although I have not made a systematic historiographic study of this phenomenon, I believe that the European style is largely just due to the fact that the “CosmoCalc” software put together by Pieter Vermeesch does it this way.

So the question here is which one to use. I have a pretty clear opinion on this. I think no matter what the nuclides involved, you should always do it the same way as is commonly done for Al-26/Be-10 diagrams, so that burial goes down. Nearly all the two-nuclide diagrams in the existing literature involve the normal implementation of the Al-26/Be-10 diagram, so anyone familiar with this literature expects exposure to go to the right on a tw0-nuclide diagram, and burial to go down. I think inverting the diagram so that burial goes up just confuses readers. Why confuse readers when you don’t have to? Thus, I advocate always plotting the longer-lived nuclide of the pair on the x-axis, and the ratio of the shorter-lived to longer-lived nuclide on the y-axis. Then burial always goes down, as we expect. Of course, I am in the US, but I am not just cheering for my own team here. It really does make more sense for two-nuclide diagrams to always behave the same way no matter what nuclide pair is involved. I’ve done it this way in the version 3 online exposure age calculator, which will generate two-nuclide diagrams for all combinations of Ne-21, Be-10, Al-26, and C-14 in quartz, and also in the ICE-D database which makes use of the v3 calculator as a back end.

Summary: Draw two-nuclide diagrams so that burial always goes the same way. Why confuse people?

 

 

 

 

 

 

 

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