Activity ratios of paired isotopes detected at IMS radionuclide stations can be used to not only discriminate a nuclear test from civil nuclear releases, but also determine the explosion time under assumed scenarios. A function of the isotopic ratio with time from the explosion time up to the stop of collection can be derived, based on Bateman equations of given decay chains. It is not a linear relationship between activities collected in the sample and concentrations in the plume. Activities in the sample are determined by spectra analysis. Non-linear relationships of isotopic ratios can also be caused by the division algorithm when denominators have larger measurement uncertainties. Covariances between isotope concentrations might be another reason for non-linearity. Correlations of two concentrations could be caused by decay corrections of parent-daughter chain, interference corrections between two isotopes and subtractions of the same detector background measurement. This presentation demonstrates Monte-Carlo procedures estimating the probability distributions of isotopic ratios, based on input distributions related to spectrum measurements and decay chains. Then the isotopic ratio, associated uncertainty and limits of the coverage interval can be estimated accordingly. Furthermore, the explosion time can be estimated in the same way, if applicable.
This presentation is about calculation procedures of isotopic ratios by the Monte-Carlo method. It is a simple and direct way to perform uncertainty estimation for numerical solutions of the isotopic ratio and explosion time.