get_al_be_age.m

results = get_al_be_age(sample,consts,nuclide)

This is the main control function that carries out the exposure age calculation. al_be_age_one and
al_be_age_many call it.

The argument sample is a structure containing sample information. The fields are as follows:

sample.sample_name	Sample name	string
sample.lat	Latitude	double
sample.long	Longitude	double
sample.elv	elevation in meters	double
sample.pressure	pressure in hPa (optional if sample.elv is set)	double
sample.aa	Flag that indicates how to interpret the elevation value.	string
sample.thick	Sample thickness in cm	double
sample.rho	Sample density, g $\cdot$ cm$^{-3}$	double
sample.othercorr	Shielding correction.	double
sample.E	Erosion rate, cm $\cdot$ yr$^{-1}$	double
sample.N10	$^{10}$Be concentration, atoms $\cdot$ g $^{-1} \cdot$ yr$^{-1}$	double
sample.delN10	standard error of $^{10}$Be concentration	double
sample.N26	$^{26}$Al concentration, atoms $\cdot$ g $^{-1} \cdot$ yr$^{-1}$	double
sample.delN26	standard error of $^{26}$Al concentration	double

The argument consts is a structure containing the constants. It is typically the structure created by
make_al_be_consts_v12.m, although only a subset of the fields in that structure are actually used by this function.

The argument nuclide tells the function which nuclide is being used; allowed values are 10 or 26. This is a numerical value, not a string.

This function returns a structure called results that contains the following fields:

results.main_version	Version number for this function	string
results.simplet	Exposure age (yr)	double
results.delt_int	Internal uncertainty (yr)	double
results.delt_ext	External uncertainty (yr)	double
results.thick_sf	Thickness correction	double
results.simple_sf	Geographic scaling factor	double
results.Psp	Thickness-integrated surface production rate due to spallation	double
results.Pmu	Thickness-integrated surface production rate due to muons	double

The exposure age calculation goes as follows:

Calculate the thickness scaling factor $S_{thick}$ by calling the function thickness.m.

If sample.pressure is not set, calculate it by calling either stdatm.m or antatm.m.

Calculate the geographic scaling factor $S_{i,geo}$ for nuclide $i$ by calling the function stone2000.m.

The production rate of nuclide $i$ in the sample $P_{i}$ (atoms $\cdot$ g $^{-1} \cdot$ yr$^{-1}$) is :

$$P_{i} = P_{i,ref} * S_{thick} * S_{T} * S_{i,geo}$$ (5)

where $P_{i,ref}$ is the reference production rate for nuclide $i$ and $S_{T}$ is the topographic shielding correction.

The exposure age $t_{i}$ for nuclide $i$ is then:

$$t_{i} = \frac{1}{\lambda_{i}+\frac{\rho \epsilon}{\Lambda_{sp}}} ... ...{P_{i}} \left( \lambda_{i}+\frac{\rho \epsilon}{\Lambda_{sp}} \right) \right] }$$ (6)

where $N_{i}$ is the measured concentration of nuclide $i$ (atoms $\cdot$ g$^{-1}$), $\epsilon$ is the erosion rate (g $\cdot$ cm $^{-2} \cdot$ yr$^{-1}$), $\lambda_{i}$ is the decay constant for nuclide $i$ (yr$^{-1}$), $\rho$ is the sample density (g $\cdot$ cm$^{-3}$), and $\Lambda_{sp}$ is the effective attenuation length for prodution by neutron spallation.

The internal uncertainty in the exposure age $\sigma_{int}t_{i}$ is:

$$\left( \sigma_{int}t_{i} \right)^{2} = \left( \frac{\partial t_{i}}{\partial N_{i}} \right) ^{2} \sigma N_{i}^{2}$$ (7)

where $\sigma N_{i}$ is the standard error in the measured nuclide concentration and:

$$\frac{\partial t_{i}}{\partial N_{i}} = \left[ P_{i} - N_{i} \left( \lambda_{i}+\frac{\rho \epsilon}{\Lambda_{sp}} \right) \right]^{-1}$$ (8)

The external uncertainty in the exposure age $\sigma_{ext}t_{i}$ is:

$$\left( \sigma_{ext}t_{i} \right)^{2} = \left( \frac{\partial t_{i... ...^{2} + \left( \frac{\partial t_{i}}{\partial P_{i}}\right)^{2} \sigma P_{i}^{2}$$ (9)

where

$$\frac{\partial t_{i}}{\partial P_{i}} = -N_{i} \left[ P_{i}^{2} -... ..._{i} \left( \lambda_{i}+\frac{\rho \epsilon}{\Lambda_{sp}} \right) \right]^{-1}$$ (10)

$$\sigma P_{i} = \sigma P_{i,ref} * S_{thick} * S_{T} * S_{i,geo}$$ (11)

and $\sigma P_{i,ref}$ is the standard error in the reference production rate of nuclide $i$.