This article is edited and drawn from:
Davies, B.J., 2022. Dating Glacial Landforms II: Radiometric Techniques, in: Haritashya, U. (Ed.), Treatise in Geomorphology (Second edition). Cryospheric Geomorphology. Elsevier, pp. 249-280. (link)
Energy decreases as it interacts with matter
The high-energy component of cosmic radiation follows an exponential decrease as a function of the cumulative mass penetrated perpendicular to the surface of the rock (Gosse and Phillips, 2001).
The attenuation length (Λ) is the thickness of a slab of material (rock, air, water, sediment, snow) required to attenuate the intensity of the cosmic-ray flux by a factor of e-1, due to scattering and absorption processes. The attenuation length varies with altitude and latitude, because the geomagnetic field and atmosphere change the energy spectrum (Gosse and Phillips, 2001).
Attenuation coefficient
The attenuation coefficient is expressed in terms of units of mass length (g cm-2) because the length depends on the total mass traversed and is therefore a function of the material’s density. The attenuation length of solid rock, with a typical bulk density of 2.7 g cm-3, is 121 – 170 g cm-2, and the thickness of rock required to attenuate the cosmic ray flux by a factor of e-1, is 45 to >65 cm. In practice, the attenuation length (Λ) is usually taken to be a constant, at 160 g cm-2 (Balco, 2011; Balco et al., 2008; Gosse and Phillips, 2001).
Length in units of cm can be determined if densities are known and constant (Table 5), by dividing the attenuation length of 160 g cm-2 by the material density.
| Material (bulk density (ρ)) | Thickness of material required to attenuate intensity flux by a factor of e-1, where Λ = 160 g cm-2 (assumes a constant density) |
| Granite (2.7 g cm-3) | 59.3 cm |
| Granite (2.6 g cm-3) | 61.5 cm |
| Basalt (2.5 g cm-3) | 64.0 cm |
| Soil or tuff (2 g cm-3) | 80 cm |
| Water (1 g cm-3) | 160 cm |
| Ice (0.9167 g cm-3) | 174.5 cm |
| Snow (0.25 g cm-3) | 640 cm |
Account for sample thickness
When calculating an exposure age, the sample thickness is therefore a crucial parameter because production by spallation within the rock is assumed to have an exponential depth-dependence with a single attenuation length (160 g cm-2) (Balco et al., 2008).
In granite, the spallogenic production rate falls by a factor of two with every ~40 cm of depth, and becomes negligible 2 to 3 m below the surface (Balco, 2011).