Modelling dose rate to single grains of quartz in well-sorted sand samples: The dispersion arising from the presence of potassium feldspars and implications for single grain OSL dating

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Single grain OSL has become a widely used approach in Quaternary geochronology. However, the origins of De distributions and the sources of variation in individual dose estimates are still poorly understood. The amount of scatter in these distributions on top of the known uncertainties in measurement and analysis is defined by overdispersion and this quantity is generally used for weighting individual De values to calculate a central equivalent dose. In this study, we address the nature and amount of different sources of dispersion in quartz single grain De estimates, by (i) using appropriate statistical tools to characterize De populations and (ii) modelling, with a specifically designed Geant4 code, dose rate distributions arising from the presence of potassium feldspar grains in well-sorted sands. The model uses Monte Carlo simulations of beta emissions and interactions in a random close packing of quartz and feldspar spheres representing a sand sample. Based on the simulation results, we explain the discrepancy between intrinsic and natural overdispersion values in a well-bleached sample, thus validating the model. The three parameters having the most influence on dispersion in dose rate distributions, and modelled in this study, appear to be grain size, potassium content and total dose rate.Finally an analysis of measurement uncertainties and other sources of variations in equivalent dose estimates lead us to conclude that all age models (both logged and unlogged) which include an overdispersion value to weight individual De values rely mainly on unknown parameters; this ignorance may lead to an inadvertent bias in De estimates. Assuming counting statistics make a small contribution to dispersion (as is often the case), we suggest that in some cases it is most appropriate to use unweighted averages of equivalent doses when dividing by commonly measured average dose rates.