Calibration and Error Analysis for Spectral Radiation Detectors

In every type of radiological monitoring, the fundamental goal is to relate the number of nuclear disintegrations observed in a detector to the concentration of radioactive elements actually present. The process of "calibrating" the detector is usually straightforward, but the uncertainties in the resulting calibration are often inadequately considered. Ignoring these uncertainties can produce an erroneous confidence in the calibration-dependent results, and consequently deficiencies in the data or in the data analysis can be missed. A technique using matrices for spectral data handling has been developed in which uncertainties originating in the input data are traced through the matrices to the final calculations. Uncertainties in the calculated concentrations are provided by a calibration matrix with an accompanying uncertainly matrix that relates countrate to radioelement concentrations. This analysis procedure was specifically developed for uranium and thorium exploration methods using radiation detectors equipped for spectral observations. In this application, the three elements potassium (K), uranium (U), and thorium (T) are of interest and the matrices have a 3×3 dimension. The method can be used directly for different sets of three radioelements, or it can be adapted to other dimensions.