Simulation of the gamma radiation field in lumpy environments

Many of the environments used for ESR and luminescence dating are inhomogeneous over the distances up to 0.3 m which contribute to gamma doses, and the consequent variability in gamma dose usually cannot be ascertained on a sample by sample basis. In this paper we examine the characteristics of such “lumpy” environments by simulation. Random environments were generated in which spherical source-free calcite inclusions were embedded in a source-rich sediment matrix. Using dose point kernels based on build-up factors, the gamma dose rate at a large number of random points in the sediment was then calculated. Various values for the sphere radius and volume fraction of the inclusions were tested.The gamma dose rate frequency distributions exhibit negative skewness, with the low outliers arising from points close to one or more inclusions. The variance of the distribution and the significance of the negative tail increase with the inclusion radius. Lognormal and gamma distributions were found to fit these histograms quite well.By sampling from the dose rate distribution, it was possible to repeatedly generate two hypothetical samples representing the positions of contemporaneous datable objects (and thus their accumulated doses) and of dose meters. Various statistical estimators were trialled to establish the optimum approach to extracting a site age from given sets of accumulated dose and gamma dose rate values. For ease of analysis, it was assumed that the gamma dose is the total dose, but the techniques can be generalised to realistic dose environments also. Most estimators produced values accurate to a few percent for typical environment parameters, and the one with the least variance was based on a two-stage maximum likelihood approach to age estimation. In the absence of such a sophisticated approach, culling of low valued outliers for both accumulated dose and dose rate leads to improved site age estimation.