Combined linear-regression and Monte Carlo approach to modeling exposure age depth profiles

Abstract

We introduce a set of methods for analyzing cosmogenic-nuclide depth profiles that formally integrates denudation and muogenic production, while retaining the advantages of linear inversion for surfaces with inheritance and age much greater than zero. For surfaces with denudation, we present solutions for both denudation rate and total denudation depth, each with their own advantages. By combining linear inversion with Monte Carlo simulation of error propagation, our method jointly assesses uncertainty arising from measurement error and denudation constraints. Using simulated depth profiles and natural-example depth profile data sets from the Beida River, northwest China, and Lees Ferry, Arizona, we show that our methods robustly produce accurate age and inheritance estimations for surfaces under varying circumstances. For surfaces with very low inheritance or age, it is important to apply a constrained inversion to obtain the correct result distributions. The denudation-depth approach can theoretically produce reasonably accurate age estimates even when total denudation reaches 5 times the nucleon attenuation length. The denudation-rate approach, on the other hand, has the advantage of allowing direct exploration of trade-offs between exposure age and denudation rate. Out of all the factors, lack of precise constraints for denudation rate or depth tends to be the largest contributor of age uncertainty, while negligible error results from our approximation of muogenic production using the denudation-depth approach.