The objective of this work is to simulate the spectral gamma-ray response of NaI(Tl) scintillation detectors for airborne gamma-ray spectrometry (AGRS) using the state-of-the-art multi-purpose Monte Carlo code FLUKA. The study is based on a commercial airborne gamma-ray spectrometry detector system with four individual NaI(Tl) scintillation crystals and a total volume of 16.8 L.
To validate the developed model, radiation measurements were conducted using
The simulation results show superior accuracy and precision compared to previous AGRS simulation models with a median relative spectral error
These findings imply that the linear energy deposition model applied in this and previously developed AGRS simulation models should be revised and considered to be replaced by more accurate non-proportional models.
Airborne gamma-ray spectrometry (AGRS) is an established technique to identify and quantify terrestrial radionuclides using a gamma-ray spectrometer mounted in an aerial vehicle
As pointed out by
Up to now, experimental calibration procedures based on calibration pads are the suggested approach according to the technical guidelines published by the International Atomic Energy Agency (IAEA)
With increasing computational capabilities and development of high-fidelity Monte Carlo based radiation transport codes over the past two decades, simulation-based calibration approaches are now commonly used for laboratory and in-situ spectrometry
First attempts to simulate the detector response of a standard AGRS system were performed by
As it emerges from this introduction, studies covering simulation-based calibration of standard AGRS systems are scarce. Moreover, most of the studies focus on full energy peak characterization for single radionuclides, adopted significant geometrical as well as physical simplifications, did not assess systematic uncertainties and, for some cases, lack experimental validation.
To address this gap, we performed high-resolution Monte Carlo simulations of a standard AGRS system under laboratory conditions using the state-of-the-art radiation transport code FLUKA
The goal of the laboratory-based radiation measurements are twofold. First, the spectral measurements are used to derive crystal-specific energy calibration and detector resolution parameters. Second, the radiation measurements can be adopted to validate the simulated spectral detector response and thereby quantify the model accuracy and precision.
This study focuses on a commercial AGRS system, which is used regularly in annual survey campaigns by civil and military institutions in Switzerland for nuclear facility monitoring, geophysical studies and radiological emergency response training
Experimental setup in the calibration laboratory at the Paul Scherrer Institute (PSI).
Radiation measurements where performed in the calibration laboratory at the Paul Scherrer Institute in Switzerland using standard calibration disk sources from the Eckert & Ziegler Nuclitec GmbH (
The detector box was placed on an aluminum frame and vertically oriented along the detector axis of symmetry, i. e. the
During measurements, additional instruments and laboratory equipment were located in the calibration laboratory, e. g. shelves, a workbench, a source scanner or a boiler as shown in Fig.
As a first step in the postprocessing of the measured pulse-height spectra, the gross count spectra
The dead time corrected background and gross count rate spectra
To characterize the relationship between the spectral energy and the detector channel as well as to quantify the detector resolution, statistical measures for the center and dispersion of the full energy peaks (FEP) in the pulse height spectra are required. In this study, the center and dispersion of the FEP are quantified by the mean
Spectral postprocessing of the experimental data for the scintillation crystal 3.
Using the Gaussian mean parameters
The quantification of the spectral resolution was achieved by deriving an analytical resolution model adopting an exponential function:
For both models, WNLLS regression using the interior-reflective Newton method
In this study, we adopt a single-stage stochastic model using the state-of-the-art multi-purpose Monte Carlo code FLUKA
In this study, the most accurate physics mode available in FLUKA, i. e. “precisio”, was used featuring a fully coupled photon, electron and positron radiation transport for our source-detector configuration. Lower transport thresholds were set to 1
It is important to add that for the
The energy deposition events in the scintillation crystals are scored individually on an event-by-event basis using the custom user routine “usreou” together with the “detect” card. The number of primaries
The simulation model includes all relevant detector components such as scintillation crystals, reflectors, aluminum casings, insulation materials, PMT and MCA in high detail (cf. Fig.
To assess the effect of the individual model elements on the detector response, a sensitivity analysis was performed changing one set of model elements at the time (OAT) for the
In addition, there are some uncertainties regarding the elemental composition and mass density of the reflector, which is located between the aluminum casing and the scintillation crystals. Based on publicly available sources for our detector, the reflector is modelled with a polytetrafluoroethylene (PTFE) foil with an equivalent mass density of 2.25
The obtained event-by-event energy deposition data is transformed to channel-based count rate spectra in three distinct steps for each of the four scintillation crystals. First, the individual energy deposition events are transformed from the spectral energy space
Second, to account for the finite detector resolution, the individual energy deposition events are broadened according to the derived resolution models for the individual crystals (Eq.
The broadening, sometimes also referred to as Gaussian broadening
As a last step, a lower level discriminator (LLD) model is applied to the generated count rate spectrum
Fig.
In general, the agreement in both absolute count rate and shape is striking considering the significant deviations previous studies have reported, especially in the lower part of the spectra
Despite these improvements, there are some systematic deviations between the measured and simulated spectra for certain sources, specifically around the Compton edges (CE), the backscatter peaks (BSP) and the characteristic
Spectral comparison of the experimental and simulated detector response for different radiation sources using the summed scintillation crystal spectra.
To quantify the relative spectral error over the entire spectra between simulations and measurements, the corresponding adjusted box plots
Model accuracy and precision analysis for the summed scintillation crystal spectra.
This statistical analysis shows a median relative spectral error
This increased deviation can be explained by two factors. First, the empirical detector models, i. e. the energy calibration in Eq. (
We want to point out that some of the previous studies adopted integrated detector channels around the FEP to estimate the model accuracy
To quantitatively assess the statistical significance of the deviations in the BSP and the CE, a detailed spectral uncertainty analysis is presented in Fig.
First, the systematic uncertainty for the simulated spectrum
Second, the residuals normalized by the total uncertainty
In contrast, the difference between the simulated and measured CE and BSP regions are statistically significant. It is worth adding that these findings are also supported by the statistical analysis of the
As discussed in Sect.
Monte Carlo model sensitivity analysis for the summed
The results from these sensitivity analysis can be summarized as follows: In the low spectral window featuring the backscatter peak and tail of the Compton continuum, the laboratory room (model B) has by far the highest impact on the spectrum followed by the detector box (model C) and source materials (model D). In the middle spectral window featuring the Compton continuum, the detector box (model C) shows the highest sensitivity followed by the source materials (model D). For the high spectral window containing the two FEPs, only the detector box materials (model C) seem to have a significant sensitivity on the spectral detector response. The two remaining models, i. e. the laboratory equipment (model E) and the reflector (model F) have negligible impact on the detector response for all three spectral windows.
These findings imply that the laboratory room, the source and the detector box elements are essential parts of the Monte Carlo model for an accurate detector response simulation. In contrast, the additional laboratory equipment and the reflector seem to be of less importance considering the adopted source-detector configuration. It is worth noting that the calibration sources in this study exhibit comparably low attenuation and self-shielding. Consequently, for sources with metal shields or bigger active volume sources, the sensitivity of the source elements on the spectral detector response is expected to be even higher.
Based on this sensitivity analysis results from the previous section, the bias in the BSP can be explained by the systematic uncertainties in the laboratory room, detector box and source elements. On the other hand, the CE region seems to be unaffected by all analyzed model elements (cf. Fig.
Interestingly, related studies adopting specialized Monte Carlo codes for NaI(Tl) scintillation detector response simulations under laboratory conditions have reported exactly the same deviations in the CE
These findings suggest that the neglected scintillator non-proportionality is also in this study the cause for the observed bias in the CE. This conjecture is supported by the fact that standard AGRS systems contain typically the largest commercially available prismatic scintillation crystals and based on the results of other studies
The Monte Carlo model developed to simulate the spectral detector response of a standard AGRS system shows excellent accuracy and precision with a median relative spectral error
Moreover, compared to previous studies
A sensitivity analysis confirmed the conjecture that the laboratory room, the source and the detector box elements are essential parts of the Monte Carlo model for an accurate detector response simulation. In consequence, neglecting the detector box elements, i. e. equipment surrounding the scintillation crystals such as aluminum casings, PMT, MCA or insulating foam as it was done by
Based on a thorough uncertainty analysis incorporating statistical and systematic uncertainties, two important conclusions could be drawn. First, the systematic uncertainty for the simulated spectrum is the dominant contributor to the total uncertainty in the FEP and the BSP exceeding the statistical uncertainty by more than 1 order of magnitude. This systematic uncertainty is likely to be even larger for previous studies due to the reduced number of calibration sources used to derive the empirical detector models in those studies. Consequently, the incorporation of systematic uncertainties is essential in the assessment of the statistical significance for detector response simulations of AGRS systems. Second, deviations between the simulations and the measurements in the FEP as well as in the major part of the Compton continuum are statistically insignificant.
In contrast, differences in the BSP and the CE regions are statistically significant and can be attributed to the systematic uncertainties in the laboratory room model on the one hand and the neglected scintillator non-proportionality on the other hand. Previous studies have shown that the effect of the scintillator non-proportionality on the spectral detector response is increasing for larger scintillation crystals
The developed and validated detector model presented herein is an important step towards a simulation-based calibration methodology for AGRS systems. In contrast to previous studies
In summary, the developed model shows superior accuracy and precision compared to previous models and is an important step towards a simulation-based calibration of AGRS systems. Moreover, thorough model validation and uncertainty analysis revealed statistically significant deviations in the BSP and the CE regions. Embedding of scintillator non-proportionality models in the Monte Carlo codes, characterizing and validating the angular spectral gamma-ray response as well as incorporating material and geometrical uncertainties in the systematic uncertainty analysis are necessary steps to improve the model accuracy and uncertainty estimates further and correct for the discussed biases.
Following the standard methodology of uncertainty and uncertainty propagation
For the simulations, the statistical uncertainty of the net count rate spectrum
Physical properties of the calibrated radiation sources adopted for detector characterization and simulation model validation measurements. Uncertainty values are stated as 1 SD values and provided as last significant figures, e. g. 0.12(3) corresponds to 0.12
The propagation of the systematic uncertainties in the post-processing steps discussed in Sect.
We want to point out that, given the spectral trends in the sensitivity analysis presented in Sect.
In Fig.
Uncertainty quantification of the spectral detector response for the summed scintillation crystal spectra.
As already reported in previous studies
The LLD model parameters
The custom FLUKA user routines adopted in the Monte Carlo simulations are deposited on the ETH Research Collection repository for open access:
The radiation measurement data presented herein are deposited on the ETH Research Collection repository for open access:
DB and GB planned the study and performed the measurements; DB performed the Monte Carlo simulations, analyzed the data, and wrote the manuscript draft; EGY and SM acquired the funding for this study; DB, EGY, GB, MMK, SM reviewed and edited the manuscript.
The contact author has declared that none of the authors has any competing interests.
Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This article is part of the special issue “Geoscience applications of environmental radioactivity (EGU21 GI6.2 session)”.
The authors would like to thank Kilian Meier for his support in designing and constructing the source holder for the calibration source disks. Furthermore, the authors gratefully acknowledge the technical support by Dominik Werthmüller for the execution of the Monte Carlo simulations on the computer cluster at PSI.
This research has been supported by the Swiss Federal Nuclear Safety Inspectorate (grant no. CTR00836).
This paper was edited by Gerti Xhixha and reviewed by two anonymous referees.