A Bayesian Approach for Remote Depth Estimation of Buried Low-Level Radioactive Waste with a NaI(Tl) Detector

Abstract

This study reports on the implementation of Bayesian inference to improve the estimation of remote-depth profiling for low-level radioactive contaminants with a low-resolution NaI(Tl) detector. In particular, we demonstrate that this approach offers results that are more reliable because it provides a mean value with a 95% credible interval by determining the probability distributions of the burial depth and activity of a radioisotope in a single measurement. To evaluate the proposed method, the simulation was compared with experimental measurements. The simulation showed that the proposed method was able to detect the depth of a Cs-137 point source buried below 60 cm in sand, with a 95% credible interval. The experiment also showed that the maximum detectable depths for weakly active 0.94-μCi Cs-137 and 0.69-μCi Co-60 sources buried in sand was 21 cm, providing an improved performance compared to existing methods. In addition, the maximum detectable depths hardly degraded, even with a reduced acquisition time of less than 60 s or with gain-shift effects; therefore, the proposed method is appropriate for the accurate and rapid non-intrusive localization of buried low-level radioactive contaminants during in situ measurement.

Radioisotope Identification and Nonintrusive Depth Estimation of Localized Low-Level Radioactive Contaminants Using Bayesian Inference

“…This function is based on the energy emitted by the primordial radioisotope of K-40 (1461 keV). The automatic calibration function was not used for the acquisition of the test spectra because this method automatically compensates the gain-shift effects because of changes in ambient temperature or calibration drifts [19]. Figure 2 shows the joint probability distributions between the depth and activity of the radioisotopes analyzed for a spectrum, measured for 300 s for a Cs-137 source buried at a depth of 3 cm.…”

“…This function is based on the energy emitted by the primordial radioisotope of K-40 (1461 keV). The automatic calibration function was not used for the acquisition of the test spectra because this method automatically compensates the gain-shift effects because of changes in ambient temperature or calibration drifts [19].…”

“…By defining a mathematical model that describes an observed spectrum in terms of the burial depth, activity, and shift degree of the spectrum, we can identify buried radioisotopes and obtain the posterior distribution of the depth and activity of the identified sources. Such a model can be established by extending the model defined by Kim et al [19,25]…”

“…Computation of f (z, ηi) requires a spectrum measurement at depths ranging from 0 to D cm at certain intervals to determine the K × D response matrix for a radioisotope. Consequently, f (z, ηi) can be interpolated using the closest points to the f (z, ηi) among the known values of depths and channels from the K × D response matrix [19]. The parameter δ can be obtained experimentally by placing a source on the material surface (that is, at 0 cm depth), which can be expressed as:…”

“…The availability of prior distributions for z, A, η, c, and, σ 2 , which represents our knowledge of the parameters before taking any measurements, is assumed by Kim et al [19]. That is, A, c, and σ 2 followed gamma distributions with parameters (1, 1); z and η followed uniform distributions with parameters (0, 18) and (0.85, 1.15), respectively.…”