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I've completed part A of the question below.


Dating fluvial terraces with $^{10}\rm{Be}$

One way to determine the age of an alluvial deposit is to collect a series of samples from a range of depths, from the surface down to a few meters, and analyze the cosmogenic nuclide concentration. The expectation is to find an exponential-like decline in concentration with depth, with an asymptotic value that reflects the inherited concentration. Suppose you sample an alluvial deposit on a mesa surface near Boulder and find the values that are shown in Table 1.

10Be C      26AL C     Depth (m)
4.29E+06    2.62E+07     0.0
2.44E+06    1.64E+07    -0.5
1.88E+06    1.24E+07    -0.9
1.49E+06    9.80E+06    -1.3
1.27E+06    8.32E+06    -1.7
1.12E+06    6.89E+06    -2.5
9.99E+05    6.46E+06    -3.1

C units (atoms/gram*year)

A Use a spreadsheet (or if you prefer, a script in Python, Matlab, etc.) to make a plot that shows the $^{10}\rm{Be}$ and $^{26}\rm{Al}$ concentrations as a function of depth. Make depth your y-axis, and have the values increase downwards.

B Make an initial guess about (1) how old the terrace is, and (2) how much of the Beryllium concentration is inherited from when the sediment was first deposited (the exact numbers you use in your guess don’t matter, since you will change them). Then use your spreadsheet to calculate the expected $^{10}\rm{Be}$ concentration that each sample should have if it had the inheritance and age that you have specified.

C Quantify the error in your guess by calculating, for each sample, the root-mean square error: (i) take the difference between the sample age and your guess, (ii) square it (to make the number positive no matter which way you’re off), (iii) take the square root, (iv) take the average.

D Now, iteratively adjust (1) your guess at the age and (2) your guess at the inheritance, until you find a pair of values that come as close as you feel you can reasonably get.

E In your paper, present and describe a graph of the sample data that also shows your best-guess curve. Discuss this “best fit” estimate of the age of the terrace. What is the root-mean square error? Can you think of a procedure that would be more systematic than trial-and-error guessing?

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    $\begingroup$ What did you try to do so far in B? Help us help you. $\endgroup$ – Gimelist Feb 12 '16 at 11:16
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    $\begingroup$ @Michael I am really struggling with the age component of part B. I began to tackle the problem by making a separate scatter plot for 10Be with its concentration on the x-axis and depth on the y-axis. Given this, I saw the logarithmic trend asymptote at ~1E6. This, I take to be the samples inheritance. I've also been toying with this formula: C=C0+P0e^(-z/z*)t where, C = concentration, C0 = inherited concentration (atoms/gramyear), P0 = production rate (30 atoms/gramyear), z= elevation at site and z*= natural length scale (.762 m). I really appreciate the help, thank you. $\endgroup$ – Justin Grant Feb 12 '16 at 14:24

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