In the previous post, we showed how to determine the sensitivity of sample ages to erosion. We used a stable nuclude (^{21}Ne) with a large cosmogenic inventory. The sensitivity is shown below:

The sensitivity of sample ages (y axis, years) to erosion rate (x axis, centimeters per year) appears to be linear. This can be verified by exporting the samples to a csv file using the **Export Samples **button and then reading the file into into excel/openoffice/matlab:

As a linear relationship, the sensitivity has a correlation between erosion rate and computed age with R^{2}=0.9923. Why?

Perhaps it should first be noted that with the large inventory, the sample is quite old and temporal variability in things like geomagnetic intensity/polarity tends to integrate towards a constant value. However further insight can be gained by examining the samples production rate profile, which can be invoked by using the Production Rate Utility:

The production rate utility is useful as it highlights the sensitivity of the sample to erosion. For the case of our ^{21}Ne sample, production is due exclusively to spallation, and at least for the upper part of the surface of the Earth it can be approximated as a straight line. Could this explain the apparent linearity between erosion rate and age for this sample? The sample has a cosmogenic inventory of 21.7 x 10^{6} a / g, and ACE calculates an age for no erosion of 374560 yr. For a stable nuclide, where inventory = mean production rate x age, ACE calculates an average production rate of about 57.9 a / g / yr, which is the near surface value for the production rate profile shown above. However if the sample was eroding, the production rate would be less and the sample age would be older, as indicated by the correlation.

If the sample was eroding, how much would the production rate change? Let’s use the ACE computed age of 464360 yr for corresponding to the erosion rate of 0.0001 cm / yr. In this case, over this time 46.4 cm of erosion would have occurred. By zooming into the production rate plot we find that the production rate at this depth is 38 a / g / yr:

In terms of the sample history, this would suggest that at 464360 years before the present the sample was at a depth of 46.4 cm below the surface, and experienced a production rate at this time of ~38 a / g / yr. So the surface (present day) production rate is 58 a / g / yr, the production rate at 46.4 cm (initial exposure time) is 38 a / g / yr, and assuming a linear production rate profile the mean production rate between present day and 464360 yr would therefore be (58 + 38)/2 = 48 a / g / yr. In this case the sample age would be 21.7 x 10^{6} / 48 = 452 000 yr, quite close to the ACE calculated value of 464360 yr. Why the difference? The figure below shows the actual change in spallation production rate with time for this sample:

The effects of erosion and temporal variability are evident in this plot as the slowly increasing production rate with time as the sample approaches the surface, and also the fluctuations on shorter timescales resulting (mostly) from changes in geomagnetic intensity. The mean production rate (black line) here is 46.7 a / g / yr, corresponding to a sample age of 21.7 x 10^{6} / 46.7 = 464 700 yr, as predicted by ACE.

So the production rate profile can be useful when examining the sample sensitivity to erosion. The above example is a little simplistic as ^{21}Ne is a stable nuclide without production from muons/low energy neutrons and the sample is quite old, so temporal variability play a lesser role. Also, the sample is reported as thickness corrected cosmogenic inventory. The next post will repeat this exercise for a finite width ^{36}Cl sample, with very different results.