Error Propagation in the Derivation of Noble Gas Diffusion Parameters for Minerals From Step Heating Experiments

Abstract

AbstractStep heating is an important tool in the derivation of thermochronologic models based on diffusive noble‐gas loss from minerals. This technique investigates noble‐gas diffusion in minerals at length scales of natural crystals. Like any scientific measurement, step heating requires realistic assessment of assumptions and uncertainties; however, uncertainties are often not presented or roughly approximated. Here we propagate errors associated with temperature, step duration, evolved gas quantity, and diffusion domain size. Other potential error sources (e.g., nonideal shapes, fractures, and zonation of aliquots) are not discussed. We provide error propagation formulas for the derivation of diffusivities and diffusion parameters for infinite plane sheet, spherical, and infinite cylinder geometry. We show that a variance in uncertainty (heteroscedasticity) in diffusivity and temperature may lead to erroneous estimates of activation energy (Ea) and frequency factor (D0) and an underestimation of their uncertainties during unweighted regression. The effect becomes significant if the variance in uncertainty exceeds a factor of two to five. The effect of the difference in D0 values is demagnified in the calculation of closure temperature (which calls on lnD0 rather than D0) and its uncertainty. To make this a practical resource, we provide spreadsheets with a step heating data set, diffusivity calculations with associated analytical error propagation formulas, and unweighted and weighted regression models to derive Ea and D0 for all three geometries. We also provide spreadsheets with Monte Carlo and numerical error propagation for plane sheet geometry.