Determination of both exposure time and denudation rate from an in situ-produced 10Be depth profile: A mathematical proof of uniqueness. Model sensitivity and applications to natural cases

Measurements of radioactive in situ-produced cosmogenic nuclide concentrations in surficial material exposed to cosmic rays allow either determining the long-term denudation rate assuming that the surface studied has reached steady-state (where production and losses by denudation and radioactive decay are in equilibrium) (infinite exposure time), or dating the initiation of exposure to cosmic rays, assuming that the denudation and post-depositional processes are negligible. Criteria for determining whether a surface is eroding or undergoing burial as well as quantitative information on denudation or burial rates may be obtained from cosmogenic nuclide depth profiles. With the refinement of the physical parameters involved in the production of in situ-produced cosmogenic nuclides, a unique well-constrained depth profile now permits determination of both the exposure time and the denudation rate affecting a surface. In this paper, we first mathematically demonstrate that the exponential decrease of the in situ-produced ¹⁰Be concentrations observed along a depth profile constrains a unique exposure time and denudation rate when considering both neutrons and muons. In the second part, an improved chi-square inversion model is described and tested in the third part with actual measured profiles.