Determination of the Depth of Localized Radioactive Contamination by ¹³⁷Cs and ⁶⁰Co in Sand with Principal Component Analysis

Abstract

A method to determine the depth of buried localized radioactive contamination nonintrusively and nondestructively using principal component analysis is described. The γ-ray spectra from two radionuclides, cesium-137 and cobalt-60, have been analyzed to derive the two principal components that change most significantly as a result of varying the depth of the sources in a bespoke sand-filled phantom. The relationship between depth (d) and the angle (θ) between the first two principal component coefficients has been derived for both cases, viz. d(Φ) = x + y log(e) Φ where x and y are constants dependent on the shielding material and the γ-ray energy spectrum of the radioactivity in question, and φ is a function of θ. The technique enables the depth of a localized radioactive source to be determined nonintrusively in the range 5 to 50 mm with an accuracy of ±1 mm.

Finding the depth of radioactivity in construction materials

“…To exploit the additional information that exists as a result of this, principal component analysis (PCA) has been used to highlight the two lowest-order components of this dependence. When these are plotted as a function of depth, a dependence is observed that can be used as a calibration curve in a similar way to the approach depicted in Figure 4 (Adams et al, 2011). This is shown in Figure 5 for the case of 137 Cs.…”

“…Two spectra for a sealed, point caesium-137 source inserted at depths 5 mm (circles) and 50 mm (triangles) in a silica-sand filled phantom. The X-ray photopeak at 5 mm (circles trace, left) is absent at 50 mm, while the 662-keV photon (both traces, right) is present at both depths, but significantly attenuated at 50 mm compared with 5 mm by approximately 50% (Adams et al, 2011) Figure 3. A photograph of the sand-filled phantom designed and commissioned to support this research, with most of the sand removed to expose the calibrated slider (Adams et al, 2011;Shippen and Joyce, 2011) Figure 4.…”

“…The X-ray photopeak at 5 mm (circles trace, left) is absent at 50 mm, while the 662-keV photon (both traces, right) is present at both depths, but significantly attenuated at 50 mm compared with 5 mm by approximately 50% (Adams et al, 2011) Figure 3. A photograph of the sand-filled phantom designed and commissioned to support this research, with most of the sand removed to expose the calibrated slider (Adams et al, 2011;Shippen and Joyce, 2011) Figure 4. A plot of log e R 0 /R X/g against depth d for a sealed, point source entrained in dry silica sand together with a linear fit to the data Joyce, 2010, 2011) the environment) and also those photons that scatter within the material in which the contamination is entrained, losing some of their energy before being detected.…”

“…The specific advantage of this approach over the approach described earlier that is based on Equation 2 is that, in principle, any g-ray spectra subject to the effects of scattering as a result of being entrained at some depth in a material can be calibrated to derive the parameters x, y and w, and thus an estimate of depth can be extracted. This approach has been subject to blind tests in which the previous depth of sealed source locations were not known, in which it performed very well estimating the depths of the source radioactivity to within an average of 2 mm uncertainty down to depths of 45 mm (Adams et al, 2011).…”

Nonintrusive Depth Estimation of Buried Radioactive Wastes Using Ground Penetrating Radar and a Gamma Ray Detector

“…However, traditional methods of depth estimation such as core sampling and logging are slow and have limited spatial sampling extent because of their intrusive nature. Furthermore, the nonintrusive methods reported in [5,[7][8][9][10][11][12][13][14] are either based on regressional models whose parameters typically have no physical significance or are limited to specific radioactive sources. Also, other nonintrusive methods reported in [15,16] use specialised shielding and collimator arrangements while those that employ machine learning [17][18][19] require significant amount of data to train the algorithms.…”