Snow shielding factors for cosmogenic nuclide dating inferred from Monte Carlo neutron transport simulations

https://doi.org/10.1016/j.epsl.2013.07.023Get rights and content

Highlights

  • The conventional mass-shielding approach underestimates the effect of snow cover for spallation by ∼40%.

  • The conventional mass-shielding approach is inappropriate for nuclide production via low-energy neutron capture.

  • Because of low-energy neutron diffusion, choosing the tops of boulders as snow-free regions cannot be justified for 36Cl.

Abstract

Conventional formulations of changes in cosmogenic nuclide production rates with snow cover are based on a mass-shielding approach, which neglects the role of neutron moderation by hydrogen. This approach can produce erroneous correction factors and add to the uncertainty of the calculated cosmogenic exposure ages. We use a Monte Carlo particle transport model to simulate fluxes of secondary cosmic-ray neutrons near the surface of the Earth and vary surface snow depth to show changes in neutron fluxes above rock or soil surface. To correspond with shielding factors for spallation and low-energy neutron capture, neutron fluxes are partitioned into high-energy, epithermal and thermal components. The results suggest that high-energy neutrons are attenuated by snow cover at a significantly higher rate (shorter attenuation length) than indicated by the commonly-used mass-shielding formulation. As thermal and epithermal neutrons derive from the moderation of high-energy neutrons, the presence of a strong moderator such as hydrogen in snow increases the thermal neutron flux both within the snow layer and above it. This means that low-energy production rates are affected by snow cover in a manner inconsistent with the mass-shielding approach and those formulations cannot be used to compute snow correction factors for nuclides produced by thermal neutrons. Additionally, as above-ground low-energy neutron fluxes vary with snow cover as a result of reduced diffusion from the ground, low-energy neutron fluxes are affected by snow even if the snow is at some distance from the site where measurements are made.

Introduction

For over half a century the relationship between cosmogenic nuclide concentrations and landform ages has been explored (Davis and Schaeffer, 1955), and its application met with considerable success, with several nuclides (3He, 10Be, 14C, 26Al, 36Cl) used routinely to date landforms over Earthʼs surface (Muzikar et al., 2003). Recent efforts, such as the CRONUS project (Phillips, 2012), focus on reducing total methodological uncertainty to permit more precise and accurate assessment of ages and production rates. First- and second-order effects using physically-based parameterizations have been accounted for. These include the effects of erosion and inheritance (Lal, 1991), topographic shielding (Dunne et al., 1999), mass shielding (Cerling and Craig, 1994), spatio-temporal variability in cosmic-ray flux (Dunai, 2001, Desilets and Zreda, 2003, Lifton et al., 2005, Lifton et al., 2008) and atmospheric pressure (Staiger et al., 2007). However, despite these successes, other uncertainties remain. One of these uncertainties, the effect of moisture at the land surface on cosmogenic production rates, is addressed here.

We use a Monte Carlo particle transport model to examine how snow affects secondary cosmic-ray neutron intensity near Earthʼs surface. Models such as these have been used to estimate rates of cosmogenic nuclide production (Masarik and Reedy, 1995) and other effects such as temporal changes in Earthʼs geomagnetic intensity (Masarik et al., 2001) and boulder size (Masarik and Wieler, 2003). Although snow cover represents only a small (10–15%) effect (Gosse and Phillips, 2001), it is considered necessary when dating boulders within moraine complexes, as the presence of moraines indicates recently glaciated environments. We place particular emphasis on low-energy neutron capture, which is a production pathway for 36Cl. Cosmogenic nuclide techniques give the ‘apparent’ age of a sample, the age computed under the assumption of continuous exposure at Earthʼs surface. If the period of exposure was punctuated by times when the sample was shielded, for example by soil, snow, ash or sand (Fig. 1), neutron fluxes and corresponding cosmogenic nuclide production rates near the surface will be affected. As a result, the apparent age will not be the same as the true exposure age, and a shielding correction factor must be computed to convert apparent age to exposure age. Covering materials can have a significant effect on computed exposure ages. For example Schildgen et al. (2005) estimate a spallation snow cover correction factor of 14% for a 15.5 ka sample from the Cairngorm Mountains in Scotland. Similarly, Gosse et al. (1995) present snow cover correction factors ranging from 0.6% to 15% for samples from the Wind River Range, Wyoming.

Prior research into the role of snow cover in moderating neutron fluxes is sparse, presumably because more rigorous formulations of snow scaling would be hampered by a lack of observational data regarding snow cover over the period of sample exposure. Generally, snow shielding is grouped into the more general category of mass shielding (Cerling and Craig, 1994, Schildgen et al., 2005), where the important characteristic of the shielding material is its ‘mass length’, reported as density times thickness (g cm−2). For cosmogenic nuclides generated by spallation, it is conventional to invoke a generic mass-shielding approach, in which the high-energy neutron flux beneath covering material ϕcover is computed from (e.g. Gosse and Phillips, 2001, Eq. 3.75):ϕcoverϕ=e(Zcover/Λf) where ϕ is the high-energy neutron flux (neutrons cm−2 yr−1) in the absence of cover, Zcover the mass length of the material covering the surface (g cm−2), and Λf the attenuation length for high-energy neutrons, thought to vary between 140 g cm−2 at Earthʼs poles to 170 g cm−2 near the equator (Cerling and Craig, 1994), as Earthʼs magnetic field blocks fewer low-energy, less penetrating cosmic rays near the poles.

For seasonal cover such as snow, the shielding factor Ssnow is calculated as the sum of fractional components from a time discretization, such that in each time interval the cover can be assumed to be constant. For example monthly snow cover (e.g. Gosse and Phillips, 2001) is calculated as:Ssnow=ϕsnowϕ=112i12ezsnow,iρsnow,i/Λf where zsnow,i is the snow thickness during the ith month (cm) and ρsnow,i the density of snow during the ith month (g cm−3). Implicit in Eq. (2) is the notion that if the sample site is above the snowline, such as at the top of a large boulder, the sample can be considered snow free with no correction factor applied.

The above approach is reasonable for spallation because high-energy neutrons responsible for spallation reactions are attenuated by the mass length of materials above a dated surface. However, for low-energy neutrons, which are not only attenuated but also moderated, a different approach to correcting for snow cover is necessary.

Section snippets

Numerical simulations

To simulate changes in neutron flux resulting from changes in surface cover we use MCNPX (Monte Carlo N-Particle eXtended; Pelowitz, 2005) Version 2.5.0, a 3-D Monte Carlo particle transport code that can track 34 different particle types and more than 2000 heavy ions at nearly all energies. Interactions between neutrons and earth elements are computed using empirically derived, energy dependent cross sections of scattering and absorption; when these are not available, nuclear models are used.

Results

In the absence of surface ground cover, high-energy neutron fluxes decrease exponentially with depth, whereas thermal and epithermal concentrations increase to reach broad maxima at depths between 50 g cm−2 and 100 g cm−2 (Liu et al., 1994, Phillips et al., 2001; Fig. 1 LHS). In the absence of any cover, the exponential attenuation with depth for high-energy neutrons is computed here as 156 g cm−2, which for a cutoff rigidity of 6 GV compares reasonably with the 170 g cm−2 determined

Discussion

As mentioned in the introduction, the utility of revising snow attenuation factors for spallation and low-energy neutron capture is hampered by a lack of observational data of past snow cover. However, differences between the formulations can give some insight into our understanding of real versus apparent cosmogenic sample ages. For example, the 14% snow correction factor for an 11.5 ka sample from the Cairngorm Mountains (Schildgen et al., 2005) is based on Eq. (1) with Λf=165gcm2, from

Conclusions

As water contains hydrogen, a highly efficient moderator of secondary cosmic-ray neutrons, cosmogenic nuclide production rates for samples shielded by snow, ice or water differ to those for other shielding types, such as sand, soil or ash. This is especially true for nuclides which have an appreciable production component by low-energy neutrons, such as 36Cl. Our modeling results indicate that for spallation a 30% reduction, compared with rock, in attenuation length is sufficient to account for

Acknowledgments

Research supported by the US National Science Foundation (grants 0325929, 0345440, 0636110 and 0838491). Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energyʼs National Nuclear Security Administration under contract DE-AC04-94AL85000. We would like to thank Patrick Applegate and an anonymous reviewer for providing thoughtful and constructive reviews.

References (38)

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