Full-spectrum modeling of mobile gamma-ray spectrometry systems in scattering media

TL;DR

The paper addresses the heavy computational cost of full-spectrum analysis for mobile gamma-ray spectrometry in scattering media by introducing a generalized framework that uses dynamic anisotropic instrument response functions (IRFs) convolved with double-differential gamma-ray flux banks to generate spectral templates in near real-time. By discretizing the IRF and flux on grids over energy, direction, and time, and performing multithreaded matrix convolutions, the method achieves a computational speedup of about $\mathcal{O}(10^7)$ while maintaining Monte Carlo–level accuracy with median spectral deviations below $6\%$ relative to high-fidelity benchmarks. The SAGRS airborne system serves as a detailed implementation case, including IRF generation, flux calculations, and uncertainty propagation, with benchmark results confirming substantial improvements over traditional isotropic models. The framework is platform-agnostic and poised to enhance near-real-time full-spectrum analyses for environmental monitoring, geophysical exploration, nuclear safeguards, and radiological emergency response across terrestrial, marine, and aerial domains.

Abstract

Mobile gamma-ray spectrometry (MGRS) systems are essential for localizing, identifying, and quantifying gamma-ray sources in complex environments. Full-spectrum template matching offers the highest accuracy and sensitivity for these tasks but is limited by the computational cost of generating the required spectral templates. Here, we present a generalized full-spectrum modeling framework for MGRS systems in scattering media, enabling near-real-time template generation through dynamic, anisotropic instrument response functions. Benchmarked against high-fidelity brute-force Monte Carlo simulations, our method yields a computational speedup by a factor of $\mathcal{O}(10^7)$, while achieving comparable accuracy with median spectral deviations below 6%. The methodology presented is platform-agnostic and applicable across marine, terrestrial, and airborne domains, unlocking new capabilities for MGRS in a variety of applications, such as environmental monitoring, geophysical exploration, nuclear safeguards, and radiological emergency response.

Figures (5)

• Figure 1: Graphical illustration of the configuration used to derive instrument response functions (IRFs) for the SAGRS system via Monte Carlo simulations. The main elements in the setup include the Monte Carlo mass model of the MGRS platform and the circular gamma-ray plane wave characterized by the source radius $r_{\text{src}}$ as well as the angular variables ($\phi'$, $\theta'$) in the local platform-fixed coordinate system. The local coordinate system is defined by the platform's principal axes $x'$, $y'$, $z'$ and parameterized by the Tait-Bryan angles $\alpha'$ (yaw), $\beta'$ (pitch), and $\gamma'$ (roll) relative to the global inertial reference frame. The inset highlights the mass model of the gamma-ray spectrometer integrated into the SAGRS system, with the local frame's origin positioned at the scintillator array's center of mass. All mass model visualizations were generated using the graphical interface FLAIRVlachoudis2009a for the SAGRS Monte Carlo model derived in our previous work Breitenmoser2022eBreitenmoser2025a. For improved visibility and interpretability, semitransparent false colors were applied.
• Figure 2: Angular dispersion of the SAGRS system's instrument response $R$ as a function of the polar angle $\theta'$ and the azimuthal angle $\varphi'$ with respect to the local noninertial platform-fixed coordinate system $x'$, $y'$, $z'$. The angular dispersion was computed for a gamma-ray energy $E_{\gamma}=\qty{662}{\keV}$ and normalized by its maximum, $R/\operatorname*{max}{R}$, with $\operatorname*{max}{R}$ indicated in each graph. Three different spectral bands were evaluated: (a) full-spectrum band ($\mathoms{B}_{\mathrm{tot}}$); (b) full-energy band ($\mathoms{B}_{\gamma}$); (c) Compton band ($\mathoms{B}_{\mathrm{C}}$). The angular dispersion graphs are interpolated on a regular $\qty{6}{\degree}\times\qty{6}{\degree}$ angular grid and displayed using the Mollweide projection.
• Figure 3: Spectral dispersion of the SAGRS system's instrument response $R$ as a function of the spectral energy $E'$ and the gamma-ray energy $E_{\gamma}$ with a constant spectral energy bin width $\Updelta{E'}\sim\qty{3}{\keV}$. The IRF was computed for the six cardinal incident directions (see also \ref{['fig:IRFscheme']}): (a) antinormal ($\theta'=\qty{180}{\degree}$); (b) normal ($\theta'=\qty{0}{\degree}$); (c) starboard ($\theta'=\qty{90}{\degree}$, $\phi'=\qty{0}{\degree}$); (d) port ($\theta'=\qty{90}{\degree}$, $\phi'=\qty{180}{\degree}$); (e) forward ($\theta'=\qty{90}{\degree}$, $\phi'=\qty{90}{\degree}$); (f) backward ($\theta'=\qty{90}{\degree}$, $\phi'=\qty{-90}{\degree}$). Characteristic spectral features typical of inorganic scintillator responses are indicated Knoll2010aBreitenmoser2024. For visualization purposes, the IRF is constrained to the spectral energy range $E'<E_{\gamma}+3\sigma_{E}$ with $\sigma_{E}$ being the spectral resolution standard deviation at $E_{\gamma}$. The line drawing of the AS332 helicopter displayed in the individual subfigures was adapted from Jetijones, https://creativecommons.org/licenses/by/3.0, via Wikimedia Commons.
• Figure 4: Relative deviation in the angular dispersion of the SAGRS system’s instrument response, defined as $\Updelta{R}_{\mathrm{rel}}=\Updelta{R}/R(\boldsymbol{\mathrm{\xi}}_0)$ with $\Updelta{R}\coloneqq R(\boldsymbol{\mathrm{\xi}}_1)-R(\boldsymbol{\mathrm{\xi}}_0)$, shown as a function of selected state variable changes $\boldsymbol{\mathrm{\xi}}_0 \rightarrow \boldsymbol{\mathrm{\xi}}_1$. Three perturbation scenarios are considered: (a--c) fuel state from empty ($\boldsymbol{\mathrm{\xi}}_0$) to full ($\boldsymbol{\mathrm{\xi}}_1$); (d--f) crew loading from unoccupied ($\boldsymbol{\mathrm{\xi}}_0$) to maximum capacity ($\boldsymbol{\mathrm{\xi}}_1$); (g--i) landing gear deployment from retracted ($\boldsymbol{\mathrm{\xi}}_0$) to extended ($\boldsymbol{\mathrm{\xi}}_1$). All remaining parameters are kept at their fiducial value $\boldsymbol{\mathrm{\xi}}_{\text{fid}}$ (see \ref{['subsec:IRFmethod']}). For each state variable change, the instrument response is evaluated in three distinct spectral bands at a gamma-ray energy of $E_{\gamma}=\qty{662}{\keV}$: (a, d, g) full-spectrum band ($\mathoms{B}_{\mathrm{tot}}$); (b, e, h) full-energy band ($\mathoms{B}_{\gamma}$); (c, f, i) Compton band ($\mathoms{B}_{\mathrm{C}}$). All graphs are interpolated on a regular $\qty{6}{\degree}\times\qty{6}{\degree}$ angular grid and displayed using the Mollweide projection. Additionally, characteristic dynamic subsystems are annotated for reference, for example the main landing gear (MLG) and the nose landing gear (NLG) in (g--i) (see also \ref{['app:SwissAGRS']}).
• Figure 5: Spectral signature computation results obtained by isotropic IRFs, anisotropic IRFs, as well as brute-force Monte Carlo simulations for four selected source-detector configurations, adopting a monoenergetic, isotropic gamma-ray source with energy $E_\gamma$ and located at ($r=\qty{30}{\m}, \phi_\gamma=\qty{0}{\degree}, \theta_\gamma$): (a) $E_\gamma=\qty{120}{\keV}$, $\theta_\gamma=\qty{180}{\degree}$; (b) $E_\gamma=\qty{2.7}{\MeV}$, $\theta_\gamma=\qty{180}{\degree}$; (c) $E_\gamma=\qty{120}{\keV}$, $\theta_\gamma=\qty{45}{\degree}$; (d) $E_\gamma=\qty{2.7}{\MeV}$, $\theta_\gamma=\qty{45}{\degree}$. For each configuration, the mean spectral template $\boldsymbol{\mathrm{\uppsi}}$ is displayed as a function of the spectral energy $E'$ with a spectral bin width $\Updelta E'\sim\qty{3}{\keV}$. Uncertainties are provided as 1 standard deviation shaded areas. In addition, the coefficient of variation (CV) as well as the relative deviation (RD) between the isotropic/anisotropic IRF and the brute-force Monte Carlo simulation results are provided (see also \ref{['app:UQ']}). The displayed line drawings of the AS332 helicopter were adapted from Jetijones, https://creativecommons.org/licenses/by/3.0, via Wikimedia Commons.