Source quantification by mobile gamma-ray spectrometry systems: A Bayesian approach

TL;DR

Quantifying gamma-ray sources with mobile detectors is a severely ill-posed inverse problem due to sparse counts, varying geometry, and spectral correlations. The authors solve this with a full-spectrum Bayesian inference framework that combines high-fidelity Monte Carlo generated spectral templates with Bayesian inversion; the forward model $\mathcal{M}(\boldsymbol{\xi},\mathfrak{d})$ is a linear superposition of templates plus background, and counts are modeled by a negative-binomial distribution to capture overdispersion. They compute the posterior distribution $\pi(\boldsymbol{\uptheta}|\mathcal{Y},\mathfrak{D},\mathcal{F})$ using affine-invariant MCMC, apply it to SAGRS airborne data, and demonstrate accurate quantification of both anthropogenic and natural radionuclides with robust uncertainty quantification, achieving objective improvements in accuracy. The method resolves systematic template biases, supports inference for multiple sources, and offers a path to model comparison and broader applicability including extended sources and planetary missions.

Abstract

Accurately quantifying gamma-ray sources from mobile gamma-ray spectrometry surveys has remained a fundamentally elusive, long-standing inverse problem at the interface of nuclear and computational physics. Here, we present a full-spectrum Bayesian inference framework that resolves this inverse problem by combining high-fidelity, platform-dynamic Monte Carlo template generation with Bayesian inversion. Applying this methodology to airborne measurements benchmarked against laboratory and in-situ ground truths, we demonstrate accurate and robust quantification of both natural and anthropogenic radionuclides under field conditions. By improving activity estimates by an order of magnitude, providing principled uncertainty quantification, and rigorously accounting for overdispersion, this framework opens the way to a more statistically rigorous and physics-informed era of mobile gamma-ray spectrometry, unlocking enhanced inference capabilities in emergency response, environmental monitoring, nuclear security, and planetary exploration.

Figures (3)

• Figure 1: Overview of the full-spectrum Bayesian inference framework.a, Characteristic source--detector distances for various mobile platforms utilized in MGRS. b, Gamma-ray-matter interaction mechanisms and associated secondary processes. c, Characteristic spectral features in the full-spectrum pulse-height response to monoenergetic gamma-ray events. d, Hierarchical sequence of physical processes involved in MGRS. e, Instrument response function (IRF) and double differential gamma-ray flux database generation utilizing high-fidelity radiation transport codes Romano2015Allison2016Goorley2016Ahdida2022aSato2024 run on high-performance computing (HPC) infrastructure. f, High-fidelity spectral template generation and Bayesian inference on a local workstation utilizing general-purpose programming languages and dedicated Bayesian numerical codes Marelli2014aCarpenter2017Buchner2021cAbril-Pla2023.
• Figure 2: Posterior predictive distribution results. Prior and posterior predictive distributions are shown alongside the measured pulse-height spectra for two measurement configurations: a, Hover flight above an anthropogenic $\cramped{\prescript{137}{55}{\mathrm{Cs}}}$ source. b, Hover flight above an anthropogenic $\cramped{\prescript{133}{56}{\mathrm{Ba}}}$ source. Results are displayed for all six datasets acquired from these measurements with variable live times of 1 (c,Cs_1s, d,Ba_1s), 5 (e,Cs_5s, f,Ba_5s), and the full acquisition ∼5 (g,Cs_5m, h,Ba_5m). Uncertainties in the measured pulse-height spectra are shown as 1 standard error (SE) error bars. Posterior predictive distributions are accompanied by point predictions based on the posterior median estimates. Spectral signatures scaled by the posterior median source strengths and measurement live time are also indicated for all sources included in the forward model, namely the anthropogenic $\cramped{\prescript{137}{55}{\mathrm{Cs}}}$ and $\cramped{\prescript{133}{56}{\mathrm{Ba}}}$ sources; the three natural terrestrial radionuclides $\cramped{\mathrm{K}_{\mathrm{nat}}}$, $\cramped{\mathrm{Th}_{\mathrm{nat}}}$, and $\cramped{\mathrm{U}_{\mathrm{nat}}}$; and the absolute radon source term $\Updelta{\cramped{\mathrm{Rn}_{\mathrm{nat}}}}$ (partially visible in c and e). For better interpretability, all spectral quantities were corrected for nuisance backgrounds described in \ref{['subsec:forwardresult']}.
• Figure 3: Posterior distribution results. Posterior distributions are shown for two measurement configurations: a, Hover flight above an anthropogenic $\cramped{\prescript{137}{55}{\mathrm{Cs}}}$ source. b, Hover flight above an anthropogenic $\cramped{\prescript{133}{56}{\mathrm{Ba}}}$ source. Results are displayed for all six datasets acquired from these measurements with live times of 1 (Cs_1s, Ba_1s), 5 (Cs_5s, Ba_5s), and ∼5 (Cs_5m, Ba_5m). Each subfigure shows posterior distributions for the related model parameters: source activities of the anthropogenic $\cramped{\prescript{137}{55}{\mathrm{Cs}}}$ and $\cramped{\prescript{133}{56}{\mathrm{Ba}}}$ point sources ($\xi_{\text{Cs-137}}$, $\xi_{\text{Ba-133}}$); activity mass concentrations of the three natural terrestrial radionuclides $\cramped{\mathrm{K}_{\mathrm{nat}}}$, $\cramped{\mathrm{Th}_{\mathrm{nat}}}$, and $\cramped{\mathrm{U}_{\mathrm{nat}}}$ ($\xi_{\text{K-nat}}$, $\xi_{\text{Th-nat}}$, $\xi_{\text{U-nat}}$); activity volume concentration of the radon source term $\Updelta{\cramped{\mathrm{Rn}_{\mathrm{nat}}}}$ ($\Updelta{\xi_{\text{Rn-nat}}}$), as well as the dispersion parameter of the negative binomial distribution ($\alpha_{\text{NB}}$). Off-diagonal panels depict bivariate posterior marginals with 68 and 99 probability contours, while diagonal panels show the corresponding univariate marginals. Gray-shaded regions indicate in-situ gamma-ray spectroscopy constraints on terrestrial radionuclide activity concentrations, and black dashed lines mark best-estimate laboratory gamma-ray assay activities for the two anthropogenic sources.