A Practical Framework for Depth and Profile Assessment of Cs-137 in Soil Using Scintillation Detectors and Composite Spectrum Analysis

A Practical Framework for Depth and Profile Assessment of Cs-137 in Soil Using Scintillation Detectors and Composite Spectrum Analysis | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article A Practical Framework for Depth and Profile Assessment of Cs-137 in Soil Using Scintillation Detectors and Composite Spectrum Analysis Vahid Sadeghi Zali, Saleh Ashrafi, Aydin Ghalehasadi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7186113/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract For environmental monitoring and radiation protection, it is important to know exactly how deep and where radioactive materials like Cs-137 are in the soil. Conventional approaches are often invasive and provide only average depth estimates, limiting their reliability. In this study, a novel, non-destructive method is proposed based on a hexagonal close-packed configuration to simulate a surface-distributed Cs-137 source. Measurements were conducted at multiple depths using NaI(Tl) and plastic scintillation detectors, and the system was calibrated using Monte Carlo simulations. Composite spectra were analyzed using an inverse modeling approach to estimate both the depth and layer-wise distribution of contamination. Blind tests demonstrated the method’s high accuracy in reconstructing realistic contamination profiles. The suggested method is easy to use, cheap, and works with different types of detectors, so it can be used in real-world situations to measure environmental radioactivity. Physical sciences/Engineering Earth and environmental sciences/Environmental sciences Physical sciences/Materials science Physical sciences/Physics Cesium-137 Depth distribution Gamma-ray spectroscopy MCNP simulation Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Introduction Determining how deeply radioactive contaminants penetrate soil is essential for effective radiation protection and informed decision-making regarding necessary decontamination actions 1 . Nuclear testing, along with accidents such as the 1986 Chernobyl disaster and the 2011 Fukushima incident, has led to widespread environmental contamination by radioactive substances 2 . Among these contaminants, Cs-137 is especially significant due to its long half-life and specific radiological properties. The penetration of Cs-137 into deeper soil layers can facilitate its uptake by plants, consequently causing internal radiation exposure to humans through the food chain 3 . Moreover, the depth distribution of Cs-137 in soil is a critical factor influencing external radiation exposure received by humans 4 . Therefore, continuous monitoring of Cs-137 depth distribution in soil remains essential. Several studies have been conducted to determine the depth distribution of radioactive contaminants in soil. Isaksson and Erlandsson (1995) investigated the spatial distribution of Cs-137 from nuclear fallout using a three-point core sampling technique, with soil cores sliced into 2–3 cm layers and analyzed via Ge(Li) detection. While their method minimized sampling time and reduced compaction and cross-contamination, modeling the vertical distribution with a simple exponential function proved inadequate, leading to noticeable discrepancies between predicted and measured values 5 . Adams et al. (2011) proposed a non-destructive technique for estimating the depth of Cs-137 and Co-60 sources in sand using Principal Component Analysis (PCA) of gamma spectra collected by a CdTe detector. Their method successfully correlated source depth (5–50 mm) with the angular relationship between spectral components and showed promising accuracy up to 5 cm depth, even in blind tests. However, limitations included the method’s untested performance for distributed or multiple sources and its reliance on advanced instrumentation and statistical processing, which may hinder broader field deployment 6 . A simulation-based method was developed to estimate the average depth of Cs-137 in soil using the GEANT Monte Carlo code. By analyzing the ratio of scattered to fully absorbed photons, researchers inferred the depth of the source without requiring direct sampling. While the method demonstrated good accuracy in realistic settings, it was limited by its reliance on precise simulation models, inability to resolve layered contamination, and reduced performance in soils with low Cs-to-background radionuclide ratios 7 . A post-accident field study in Fukushima examined the vertical distribution of I-131 and Cs-137 in soils from three distinct sites. Measurements using high-purity germanium (HPGe) detectors revealed that the majority of both radionuclides, over 87% for Cs-137 and 76% for I-131, were confined to the top 5 cm. Although the study offered important empirical data, it was limited to short-term conditions and lacked a non-invasive depth estimation approach. 8 . A more recent study from 2023 looked into the depth distribution of Sr-90 in polluted soils around the Fukushima Daiichi Nuclear Power Plant. This topic had previously received limited research attention. Core samples were taken from 32 different places, going down to a depth of 30 cm. Samples were analyzed using Geiger–Müller counters and α/β spectrometry following chemical separation. The results showed that more than 80% of Sr-90 was concentrated in the top 0–5 cm of soil in most cases. This means that the distribution was mostly surface-bound, like that of Cs-137. However, in specific soil types such as sandy soils, downward migration to deeper layers was observed. The study's main limitations were its exclusive reliance on destructive sampling and the absence of non-invasive depth profiling techniques 9 . Ukaegbu et al. (2018) explored the use of a portable plastic scintillation detector to estimate Cs-137 depth in soil. By combining in-situ gamma spectroscopy with Monte Carlo simulations, they identified correlations between spectral features, such as the low-energy photon ratio, and source depth. The method proved effective for point sources in dry sand up to 5 cm deep. While the system’s simplicity and portability were notable strengths, the approach assumed a fixed depth for the radioactive source, overlooking potential vertical distribution within the soil 10 . One of the key factors contributing to the infiltration of radioactive materials into soil is the phenomenon of radioactive fallout. This occurs as a result of the atmospheric dispersion and subsequent deposition of radionuclides, such as Cs-137, following nuclear weapons testing or nuclear accidents around the world 11 . Previous studies have often been conducted under the assumption that radioactive materials are concentrated at a specific depth, without access to detailed experimental information regarding their actual distribution in soil. Moreover, most of these methods have relied on invasive sampling techniques using HPGe detectors, which are costly and technically demanding. In this work, we propose an innovative calibration method for plastic scintillators and sodium iodide detectors based on simulated surface and depth-distributed Cs-137 sources—reflecting more realistic environmental conditions. The method’s accuracy in identifying complex vertical contamination profiles is assessed using blind tests and comparative algorithmic analysis, demonstrating high reliability in reconstructing depth distributions with minimal error. Method The surface distribution of the radioisotope Cs-137 at various soil depths was simulated. This approach took into account the nature of nuclear fallout and the chemical behavior of the element within the soil. To achieve this, small standard Cs-137 source was arranged using a hexagonal close packing (HCP) method within a circular area with a diameter of 23 cm, at varying depths in the soil. The HCP arrangement allows for efficient two-dimensional coverage of up to 91% of the target area 12 , enabling the representation of a large-area surface source using small individual sources. The specific configuration employed in this study is illustrated in Figure 1. In Figure 1, regions with the same color and labeled with identical English letters correspond to source positions that are equidistant from the detector center and symmetrically arranged around it. Due to this axial symmetry, these positions are expected to yield similar detector responses. The number of repeated positions for each distance group is indicated on the right side of the figure. The diameter of each circle was set equal to that of the individual Cs-137 source (17 mm). Therefore, it is sufficient to measure the gamma spectrum at only one representative point for each group (A through R), and then multiply the resulting response by the number of repetitions corresponding to that group. By summing the weighted spectra of all representative points, the overall response spectrum of the extended surface source can be reconstructed. The validity of this approach was tested through MCNP simulations. The simulation process was carried out for both sodium iodide (NaI) and plastic scintillation detectors. These detectors are widely used in studies involving radionuclide identification as well as depth and location estimation of radioactive sources. Plastic scintillators offer the advantage of being cost-effective and easily fabricated in large sizes, whereas sodium iodide detectors provide superior energy resolution and higher intrinsic efficiency 13 . In this study, a rectangular glass-walled container with dimensions of 30 cm × 50 cm was filled with soil and used as a phantom to model a realistic environmental setting for subsequent measurements. The effectiveness of such phantoms in simulating soil environments has been demonstrated in previous studies 14 . The configuration of this setup is illustrated in Figures 2 and 3, corresponding to the sodium iodide and plastic scintillation detectors, respectively. To conduct the experiment, a full-scale printout of the surface source configuration was placed directly on the soil surface. The Cs-137 source was then positioned at the various non-redundant points indicated in the configuration. We performed measurements at different depths: 0 cm (the surface without soil cover), 1 cm, 2 cm, 3 cm, and 4 cm by adding layers of soil on top of the printed configuration map. Table 1 shows that the Cs-137 source was put in 18 different places at each depth, each one at a different distance from the center of the 23 cm circular test area. The data presented in Table 1 were obtained through analytical calculations. Measurement durations were set to 20 seconds for the sodium iodide scintillation detector and 150 seconds for the plastic scintillation detector. These intervals were determined by placing the Cs-137 source at the most distant lateral point and at a depth of 5 cm in the soil, and then identifying the minimum acquisition time needed to obtain a spectrum with sufficient shape and resolution. From a physics standpoint, the longer measurement time required for the plastic scintillation detector is primarily due to its lower energy resolution and reduced intrinsic efficiency compared to the sodium iodide detector. At each depth, the source was placed at different positions, and for repeated positions in the configuration, the measurement time was scaled proportionally to the number of repetitions. For example, for point B, which appears six times in the configuration, the total measurement time was set to 120 seconds for the sodium iodide detector and 900 seconds for the plastic scintillation detector. For each measurement cycle, background radiation was recorded for the same duration as the corresponding sample and then subtracted from the acquired spectrum. Rather than multiplying a single spectrum by the number of repetitions, repeated positions were measured for extended durations to account for cumulative effects such as scattering and buildup. To ensure uniformity across depths, the soil surface in front of the detector was precisely leveled and smoothed with a trowel prior to every measurement. A total of approximately 200 measurements were conducted utilizing both scintillation detectors. To maximize the detector’s solid-angle coverage, the sodium iodide scintillation detector was positioned 3 cm above the soil surface. Due to the plastic scintillator's sensitivity to beta radiation, it was placed directly in contact with the soil surface 15 . By summing the spectra from all measurement points within the configuration, the composite spectrum of the surface source at each depth was obtained. The simulated spectra were compared with the total measured spectra to calibrate the response of each detector. Once calibrated, these datasets enabled not only the estimation of Cs-137 burial depth, but also the reconstruction of its relative distribution across multiple soil layers. To differentiate between the resulting spectra, various classification algorithms were applied, and their performance was compared. The process of identifying the depth and stratified distribution of cesium follows an approach analogous to radionuclide identification techniques 16 . A library of simulated spectra corresponding to different source depths was used as a reference dataset. The composite spectrum obtained from either measurements or simulations, representing a surface-distributed Cs-137 source spread across multiple soil layers with varying contributions, was treated as the input to the inverse problem. The algorithm performs spectral deconvolution to estimate the relative contribution of Cs-137 in each layer by comparing the input spectrum against the spectral library. The optimization problem is formulated as follows: (1) where cᵢ represents the relative contribution of Cs-137 in the i th soil layer, Rᵢ denotes the detector response for a source distributed exclusively in that layer (based on the spectral library), and S is the measured or simulated composite input spectrum. Different algorithms approach the solution of this equation using various optimization strategies. The performance of the proposed method is evaluated through a series of blind tests. Results and Discussion The measurement results for each depth using the HCP configuration are presented in Figures 4 and 5. The significant difference observed between the 0 cm depth and the other depths in Figure 5 is attributed to the presence of beta radiation in the spectrum, as well as the disparity in attenuation coefficients between soil and air. With the experimental data in hand, Monte Carlo simulations were carried out to calibrate the detector for various source depths. The MCNP code was used to carry out the simulations. A critical factor in achieving accurate results was defining the elemental composition of the soil, which serves as the main attenuating material for nuclear radiation. To characterize the soil, its elemental content was determined based on results obtained from X-ray fluorescence (XRF) analysis. For lighter elements not detectable by XRF, reference data from the literature 17 were utilized to complete the composition model. The simulated NaI(Tl) detector consisted of several key components: an aluminum housing with a density of 2.7 g/cm³, a magnesium oxide (MgO) reflector at 3.58 g/cm³, the NaI scintillation crystal itself with a density of 3.67 g/cm³, and a glass window for the photomultiplier tube (PMT) with a density of 2.23 g/cm³. The glass was chosen for its high mechanical durability and its ability to transmit radiation at wavelengths beyond the ultraviolet range. The detector dimensions were 63 mm in diameter and 63 mm in height. For the plastic scintillation detector, all materials and structural details were also simulated based on reference data provided in 17 . The dimensions of the plastic scintillation detector were set to 128 mm in diameter and 8 mm in thickness. The density of the electronic components and photomultiplier tube (PMT) housing for both detectors were assumed to be 1.207 g/cm³ 18 . Additionally, the electronic components of the detectors were modeled as polyester-equivalent material in simulation 19 . The results of the comparison between the scaled simulated and experimental spectra are presented in Figures 6 and 7. The differences observed between the simulated and measured spectra are the result of several contributing factors, including the statistical nature of the Monte Carlo method, background radiation subtraction, the inherent randomness of radioactive decay, and discrepancies between the idealized simulation configuration and the actual surface source setup 20 . Additionally, to improve the agreement between the experimental and simulated data, counts in some of the lower-energy channels were excluded from the analysis 21 . Therefore, in this study, the simulation of radioactive material at various depths was successfully performed with good accuracy. The simulated data were used not only for detector calibration but also for evaluating source localization performance. We now proceed to predict the depth and layer-wise distribution of radioactive material using various computational algorithms. For demonstration purposes, and considering its practical applicability, the sodium iodide detector is used in the following analysis. It is evident, however, that given the validated simulation results for the plastic scintillator and the identical formulation and methodology used for both detectors, similar results, albeit with slightly lower accuracy due to its poorer energy resolution, can also be expected from the plastic scintillation detector. The gamma spectra recorded by the sodium iodide detector for various depth distributions of the Cs-137 source are shown in Figure 8. The results obtained from multiple algorithms for predicting the contribution of each depth distribution in the composite spectra shown in Figure 8 are presented in Table 2. A detailed description of the algorithms used to obtain the results presented in this table has been previously provided in Reference 21 . The results demonstrate the high accuracy of the multi-step approach in determining the distribution of radioactive material in soil, both in terms of minimizing false-positive detections of activity at various depths and in accurately estimating the depth-wise distribution of the radionuclide. Conclusion The determination of radionuclide depth in soil has been addressed in previous studies, most of which have relied on direct sampling methods that are inherently invasive and destructive. Moreover, these studies often report only an average depth for Cs-137, which does not accurately reflect the true distribution of surface contamination. In this work, we employed an HCP configuration to simulate a realistic surface-distributed Cs-137 source using a low-activity standard source. The MCNP simulation results, based on defining a realistic surface source using the *SF* card and accurately specifying the material properties, confirmed the feasibility and effectiveness of the proposed approach. Building upon this successful simulation, the calibration of the measurement system was performed for both types of scintillation detectors using the simulated data. Our blind tests showed that the method performs reliably when analyzing full gamma spectra, especially with the multi-step approach. However, the plastic scintillation detector, although cost-effective and portable, exhibits limited energy resolution, which may affect spectral deconvolution accuracy for more complex contamination profiles. The results highlight that simulation-based calibration can effectively estimate both the depth and the vertical spread of Cs-137 in soil. What makes this approach even more practical is that it isn’t limited to a specific isotope and could work just as well for identifying other surface contaminants. The accuracy of the proposed method heavily depends on the precise modeling of the soil composition, which may vary significantly across different geographical regions. Future work may focus on addressing the mentioned challenges. Declarations The authors declare no competing interests. This research received no specific grand from any funding agency in the public, commercial, or not-for-profit sectors. Data Availability All data generated or analysed during this study are included in this published article. Additionally, any further datasets used or analysed during the current study are available from the corresponding author upon reasonable request. References Liu, S. et al. A State-of-the-Art Review of Radioactive Decontamination Technologies: Facing the Upcoming Wave of Decommissioning and Dismantling of Nuclear Facilities. Sustainability 14, 4021 (2022). Ukaegbu, I. K., Gamage, K. A. A. & Aspinall, M. D. Nonintrusive Depth Estimation of Buried Radioactive Wastes Using Ground Penetrating Radar and a Gamma Ray Detector. Remote Sens (Basel) 11, 141 (2019). Ahmad, A. Y., Al-Ghouti, M. A., AlSadig, I. & Abu-Dieyeh, M. Vertical distribution and radiological risk assessment of 137Cs and natural radionuclides in soil samples. Sci Rep 9, (2019). Ramzaev, V., Mishine, A., Golikov, V., Brown, J. E. & Strand, P. Surface ground contamination and soil vertical distribution of 137Cs around two underground nuclear explosion sites in the Asian Arctic, Russia. J Environ Radioact 92, 123–143 (2007). Isaksson, M. & Erlandsson, B. Experimental determination of the vertical and horizontal distribution of 137Cs in the ground. J Environ Radioact 27, 141–160 (1995). Adams, J. C., Mellor, M. & Joyce, M. J. Determination of the Depth of Localized Radioactive Contamination by 137 Cs and 60 Co in Sand with Principal Component Analysis. Environ Sci Technol 45, 8262–8267 (2011). Likar, A., Omahen, G., Vidmar, T. & Martinčič, R. Method to determine the depth of Cs-137 in soil from in-situ gamma-ray spectrometry. J Phys D Appl Phys 33, 2825–2830 (2000). TANAKA, K. et al. Vertical profiles of Iodine-131 and Cesium-137 in soils in Fukushima Prefecture related to the Fukushima Daiichi Nuclear Power Station Accident. Geochem J 46, 73–76 (2012). Kavasi, N., Arae, H., Aono, T. & Sahoo, S. K. Distribution of strontium-90 in soils affected by Fukushima dai-ichi nuclear power station accident in the context of cesium-137 contamination. Environmental Pollution 326, 121487 (2023). Ukaegbu, I. & Gamage, K. A Novel Method for Remote Depth Estimation of Buried Radioactive Contamination. Sensors 18, 507 (2018). Aoyama, M., Hirose, K. & Igarashi, Y. Re-construction and updating our understanding on the global weapons tests 137Cs fallout. Journal of Environmental Monitoring 8, 431–438 (2006). Atkins, P. & De Paula, J. Elements of Physical Chemistry . (Oxford University Press, USA, 2013). Siciliano, E. R. et al. Comparison of PVT and NaI(Tl) scintillators for vehicle portal monitor applications. Nucl Instrum Methods Phys Res A 550, 647–674 (2005). Kim, J., Lim, K. T., Park, K. & Cho, G. A bayesian approach for remote depth estimation of buried low-level radioactive waste with a nai(Tl) detector. Sensors (Switzerland) 19, (2019). Bae, J. W. & Kim, H. R. Plastic scintillator beta ray scanner for in-situ discrimination of beta ray and gamma ray radioactivity in soil. Nuclear Engineering and Technology 52, 1259–1265 (2020). Ghalehasadi, A., Ashrafi, S., Alizadeh, D. & Meriç, N. Gamma ray interactions based optimization algorithm: Application in radioisotope identification. Nuclear Engineering and Technology 53, 3772–3783 (2021). Detwiler, R. S., McConn, R. J., Grimes, T. F., Upton, S. A. & Engel, E. J. Compendium of Material Composition Data for Radiation Transport Modeling . (2021). Baré, J. & Tondeur, F. Gamma spectrum unfolding for a NaI monitor of radioactivity in aquatic systems: Experimental evaluations of the minimal detectable activity. Applied Radiation and Isotopes 69, 1121–1124 (2011). Cinelli, G., Tositti, L., Mostacci, D. & Baré, J. Calibration with MCNP of NaI detector for the determination of natural radioactivity levels in the field. J Environ Radioact 155–156, 31–37 (2016). Östlund, K., Samuelsson, C. & Rääf, C. L. Experimentally determined vs: Monte Carlo simulated peak-to-valley ratios for a well-characterised n-type HPGe detector. Applied Radiation and Isotopes 95, 94–100 (2015). Alizadeh, D. & Ashrafi, S. New hybrid metaheuristic algorithm for scintillator gamma ray spectrum analysis. Nucl Instrum Methods Phys Res A 915, 1–9 (2019). Tables Table 1. Distances of various positions in the HCP configuration from the center. r denotes the radius of the source or the small circles used in the configuration. Distance from Center Location Label 0r A 2r B 4r C 6r D 8r E 10r F 12r G 2(3) 1/2 r H 4(3) 1/2 r K 6(3) 1/2 r N 2(7) 1/2 r I 4(7) 1/2 r P 2(13) 1/2 r J 2(19) 1/2 r M 2(21) 1/2 r L 2(31) 1/2 r O 2(37) 1/2 r R 2(39) 1/2 r Q Table 2. Results of various algorithms used to identify the depth distribution of Cs-137 in soil. The multi-step method combines two optimization techniques: Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) Method / Spectrum Cs (4 cm) Cs (3 cm) Cs (2 cm) Cs (1 cm) Cs (0 cm) True – Sample 1 (Fig. a) 0.0 0.0 0.0 50.0 50.0 MLEM 0.31 0.39 1.23 49.27 48.8 Gold 0.26 0.67 0.0 49.69 49.38 GA 0.15 0.74 0.0 49.58 49.53 Multi-step 0.0 0.0 0.0 50.16 49.84 True – Sample 2 (Fig. b) 0.0 10.0 0.0 0.0 90.0 MLEM 4.13 17.32 5.94 1.54 71.07 Gold 0.0 10.48 0.27 0.0 89.25 GA 0.88 9.51 1.27 1.68 87.93 Multi-step 0.0 10.21 0.0 0.0 89.79 True – Sample 3 (Fig. c) 30.0 0.0 10.0 60.0 0.0 MLEM 31.58 0.0 7.92 53.99 6.51 Gold 31.63 0.0 9.06 58.18 1.13 GA 30.69 0.0 8.86 56.81 3.64 Multi-step 30.43 0.0 10.23 59.34 0.0 Additional Declarations No competing interests reported. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7186113","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":495627077,"identity":"f6711e02-ea28-47e6-9f94-e820721b0b98","order_by":0,"name":"Vahid Sadeghi Zali","email":"","orcid":"","institution":"University of Tabriz","correspondingAuthor":false,"prefix":"","firstName":"Vahid","middleName":"Sadeghi","lastName":"Zali","suffix":""},{"id":495627078,"identity":"2ecd7955-d5b9-4354-b7df-27d9fb0050c0","order_by":1,"name":"Saleh Ashrafi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA40lEQVRIie3RsWvCQBTH8V8QdHmS9RVK/BcitwgK/itPAmZR504lW5eAq/41Rh7YJcU1Y/8AKXbLkKGX0K3ltFuH+w7H4+DDOzjA5/uH9UH2nHGEdpDv28JFwo4s2dDd5CHrCBZ5Z+8pPr+drrVM0sPADu+NInwpAn1ykWqT7HPhdU6bZCek4FJwLJ2EDIa1JVgZCCtQAcfMQebn0gSNcErhxZJYMbpF4mJleiQsxO0WUbv3FqkseRQe59VHAilSGpeLzE3ah13keTTYrjWom2kUvap+usiP7O8EfwI+n8/n+6UvmsRKzuUirjIAAAAASUVORK5CYII=","orcid":"","institution":"University of Tabriz","correspondingAuthor":true,"prefix":"","firstName":"Saleh","middleName":"","lastName":"Ashrafi","suffix":""},{"id":495627079,"identity":"3ca1a1d8-f8d3-4c62-805c-4509b3ba9d3c","order_by":2,"name":"Aydin Ghalehasadi","email":"","orcid":"","institution":"University of Tabriz","correspondingAuthor":false,"prefix":"","firstName":"Aydin","middleName":"","lastName":"Ghalehasadi","suffix":""}],"badges":[],"createdAt":"2025-07-22 10:53:17","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7186113/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7186113/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":88354784,"identity":"b6dd2fc2-69b1-4475-8e61-d78a00ef3d10","added_by":"auto","created_at":"2025-08-05 15:02:22","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":138324,"visible":true,"origin":"","legend":"\u003cp\u003eHexagonal close-packed (HCP) configuration used for simulating a surface-distributed Cs-137 source.\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7186113/v1/86a38a259265e59cdff32968.jpg"},{"id":88354551,"identity":"7caa9132-0f2b-44d5-925f-394abba1853d","added_by":"auto","created_at":"2025-08-05 14:54:22","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":77363,"visible":true,"origin":"","legend":"\u003cp\u003eExperimental measurement setup for recording the Cs-137 spectrum in soil using a Thallium-dopped sodium iodide (NaI(Tl)) scintillation detector.\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7186113/v1/650b0c335080b62541db5e3c.jpg"},{"id":88354553,"identity":"bcf77e23-8f45-422e-a3ef-5ce920363f5d","added_by":"auto","created_at":"2025-08-05 14:54:22","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":73935,"visible":true,"origin":"","legend":"\u003cp\u003eExperimental measurement setup for recording the Cs-137 spectrum in soil using a plastic scintillation detector.\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7186113/v1/2138500c67d32dee774a6b92.jpg"},{"id":88354557,"identity":"c946e0c8-37c8-41aa-83b9-764b69432f34","added_by":"auto","created_at":"2025-08-05 14:54:22","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":50298,"visible":true,"origin":"","legend":"\u003cp\u003eExperimental data from the sodium iodide (NaI) scintillation detector for a Cs-137 source at various depths, represented by different colors. The horizontal axis shows the channel number, and the vertical axis indicates the count rate.\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7186113/v1/6b7bafb0f9186505f83c90bf.jpg"},{"id":88354552,"identity":"1da4cfa5-c2a7-4149-ad67-9275874c3549","added_by":"auto","created_at":"2025-08-05 14:54:22","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":34376,"visible":true,"origin":"","legend":"\u003cp\u003eExperimental data from the plastic scintillation detector for a Cs-137 source at various depths, represented by different colors. The horizontal axis corresponds to the channel number, and the vertical axis shows the count rate.\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7186113/v1/5aa8724aa03060f5f291e3b7.jpg"},{"id":88354786,"identity":"31197767-ed78-42bd-8309-e5f059e92584","added_by":"auto","created_at":"2025-08-05 15:02:22","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":140183,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFigure 7.\u003c/strong\u003eComparison of simulated and experimental spectra for the plastic scintillation detector at depths ranging from 0 to 4 cm in 1 cm increments. Blue curves represent experimental data, while red curves indicate simulation results. The horizontal axis shows the channel number, and the vertical axis represents scaled count values normalized to the simulation results.\u003c/p\u003e","description":"","filename":"7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7186113/v1/3be74b6f476d87a3a089f08b.jpg"},{"id":88354554,"identity":"cbf10491-878e-4973-ad65-31d60dcb25e9","added_by":"auto","created_at":"2025-08-05 14:54:22","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":142042,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFigure 8.\u003c/strong\u003eComparison of simulated and experimental spectra for NaI(Tl) detector at depths ranging from 0 to 4 cm in 1 cm increments. Blue curves represent experimental data, while red curves correspond to simulation results. The horizontal axis shows the channel number, and the vertical axis indicates scaled count values normalized to the simulation results.\u003c/p\u003e","description":"","filename":"8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7186113/v1/9f3d1119ca80c35ffed83a5f.jpg"},{"id":88354560,"identity":"fa741140-5838-4368-bd5c-6934d1a2653b","added_by":"auto","created_at":"2025-08-05 14:54:22","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":5713,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFigure 9.\u003c/strong\u003eComposite gamma spectra resulting from different depth distributions of surface-deposited Cs-137 in soil: (a) 50% at the surface and 50% at 1 cm depth, (b) 90% at the surface and 10% at 3 cm depth, and (c) 60% at 1 cm, 10% at 2 cm, and 30% at 4 cm depth.\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-7186113/v1/1b13a6cc0a0f011dabc428ce.png"},{"id":88437899,"identity":"9c28fdda-5dcd-4636-a4b3-b735ca54d181","added_by":"auto","created_at":"2025-08-06 12:09:05","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1140239,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7186113/v1/1c91fd0d-fa29-4c00-864a-c779ef9b0074.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Practical Framework for Depth and Profile Assessment of Cs-137 in Soil Using Scintillation Detectors and Composite Spectrum Analysis","fulltext":[{"header":"Introduction","content":"\u003cp\u003eDetermining how deeply radioactive contaminants penetrate soil is essential for effective radiation protection and informed decision-making regarding necessary decontamination actions \u003csup\u003e1\u003c/sup\u003e. Nuclear testing, along with accidents such as the 1986 Chernobyl disaster and the 2011 Fukushima incident, has led to widespread environmental contamination by radioactive substances \u003csup\u003e2\u003c/sup\u003e. Among these contaminants, Cs-137 is especially significant due to its long half-life and specific radiological properties. The penetration of Cs-137 into deeper soil layers can facilitate its uptake by plants, consequently causing internal radiation exposure to humans through the food chain \u003csup\u003e3\u003c/sup\u003e. Moreover, the depth distribution of Cs-137 in soil is a critical factor influencing external radiation exposure received by humans \u003csup\u003e4\u003c/sup\u003e. Therefore, continuous monitoring of Cs-137 depth distribution in soil remains essential.\u003c/p\u003e\n\u003cp\u003eSeveral studies have been conducted to determine the depth distribution of radioactive contaminants in soil. Isaksson and Erlandsson (1995) investigated the spatial distribution of Cs-137 from nuclear fallout using a three-point core sampling technique, with soil cores sliced into 2\u0026ndash;3 cm layers and analyzed via Ge(Li) detection. While their method minimized sampling time and reduced compaction and cross-contamination, modeling the vertical distribution with a simple exponential function proved inadequate, leading to noticeable discrepancies between predicted and measured values \u003csup\u003e5\u003c/sup\u003e. Adams et al. (2011) proposed a non-destructive technique for estimating the depth of Cs-137 and Co-60 sources in sand using Principal Component Analysis (PCA) of gamma spectra collected by a CdTe detector. Their method successfully correlated source depth (5\u0026ndash;50 mm) with the angular relationship between spectral components and showed promising accuracy up to 5 cm depth, even in blind tests. However, limitations included the method\u0026rsquo;s untested performance for distributed or multiple sources and its reliance on advanced instrumentation and statistical processing, which may hinder broader field deployment\u003csup\u003e\u0026nbsp;6\u003c/sup\u003e. A simulation-based method was developed to estimate the average depth of Cs-137 in soil using the GEANT Monte Carlo code. By analyzing the ratio of scattered to fully absorbed photons, researchers inferred the depth of the source without requiring direct sampling. While the method demonstrated good accuracy in realistic settings, it was limited by its reliance on precise simulation models, inability to resolve layered contamination, and reduced performance in soils with low Cs-to-background radionuclide ratios \u003csup\u003e7\u003c/sup\u003e. A post-accident field study in Fukushima examined the vertical distribution of I-131 and Cs-137 in soils from three distinct sites. Measurements using\u0026nbsp;high-purity germanium (HPGe)\u0026nbsp;detectors revealed that the majority of both radionuclides, over 87% for Cs-137 and 76% for I-131, were confined to the top 5 cm. Although the study offered important empirical data, it was limited to short-term conditions and lacked a non-invasive depth estimation approach. \u003csup\u003e8\u003c/sup\u003e. A more recent study from 2023 looked into the depth distribution of Sr-90 in polluted soils around the Fukushima Daiichi Nuclear Power Plant. This topic had previously received limited research attention. Core samples were taken from 32 different places, going down to a depth of 30 cm. Samples were analyzed using Geiger\u0026ndash;M\u0026uuml;ller counters and \u0026alpha;/\u0026beta; spectrometry following chemical separation. The results showed that more than 80% of Sr-90 was concentrated in the top 0\u0026ndash;5 cm of soil in most cases. This means that the distribution was mostly surface-bound, like that of Cs-137. However, in specific soil types such as sandy soils, downward migration to deeper layers was observed. The study\u0026apos;s main limitations were its exclusive reliance on destructive sampling and the absence of non-invasive depth profiling techniques \u003csup\u003e9\u003c/sup\u003e.\u0026nbsp;Ukaegbu et al. (2018) explored the use of a portable plastic scintillation detector to estimate Cs-137 depth in soil. By combining in-situ gamma spectroscopy with Monte Carlo simulations, they identified correlations between spectral features, such as the low-energy photon ratio, and source depth. The method proved effective for point sources in dry sand up to 5 cm deep. While the system\u0026rsquo;s simplicity and portability were notable strengths, the approach assumed a fixed depth for the radioactive source, overlooking potential vertical distribution within the soil\u003cspan dir=\"RTL\"\u003e\u0026nbsp;\u003c/span\u003e\u003csup\u003e10\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eOne of the key factors contributing to the infiltration of radioactive materials into soil is the phenomenon of radioactive fallout. This occurs as a result of the atmospheric dispersion and subsequent deposition of radionuclides, such as Cs-137, following nuclear weapons testing or nuclear accidents around the world \u003csup\u003e11\u003c/sup\u003e. Previous studies have often been conducted under the assumption that radioactive materials are concentrated at a specific depth, without access to detailed experimental information regarding their actual distribution in soil. Moreover, most of these methods have relied on invasive sampling techniques using HPGe detectors, which are costly and technically demanding.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIn this work, we propose an innovative calibration method for plastic scintillators and sodium iodide detectors based on simulated surface and depth-distributed Cs-137 sources\u0026mdash;reflecting more realistic environmental conditions. The method\u0026rsquo;s accuracy in identifying complex vertical contamination profiles is assessed using blind tests and comparative algorithmic analysis, demonstrating high reliability in reconstructing depth distributions with minimal error.\u003c/p\u003e"},{"header":"Method","content":"\u003cp\u003eThe surface distribution of the radioisotope Cs-137 at various soil depths was simulated. This approach took into account the nature of nuclear fallout and the chemical behavior of the element within the soil. To achieve this, small standard Cs-137 source was arranged using a hexagonal close packing (HCP) method within a circular area with a diameter of 23 cm, at varying depths in the soil. The HCP arrangement allows for efficient two-dimensional coverage of up to 91% of the target area\u003csup\u003e12\u003c/sup\u003e, enabling the representation of a large-area surface source using small individual sources. The specific configuration employed in this study is illustrated in Figure 1.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIn Figure 1, regions with the same color and labeled with identical English letters correspond to source positions that are equidistant from the detector center and symmetrically arranged around it. Due to this axial symmetry, these positions are expected to yield similar detector responses. The number of repeated positions for each distance group is indicated on the right side of the figure. The diameter of each circle was set equal to that of the individual Cs-137 source (17 mm). Therefore, it is sufficient to measure the gamma spectrum at only one representative point for each group (A through R), and then multiply the resulting response by the number of repetitions corresponding to that group. By summing the weighted spectra of all representative points, the overall response spectrum of the extended surface source can be reconstructed. The validity of this approach was tested through MCNP simulations. The simulation process was carried out for both sodium iodide (NaI) and plastic scintillation detectors. These detectors are widely used in studies involving radionuclide identification as well as depth and location estimation of radioactive sources. Plastic scintillators offer the advantage of being cost-effective and easily fabricated in large sizes, whereas sodium iodide detectors provide superior energy resolution and higher intrinsic efficiency \u003csup\u003e13\u003c/sup\u003e. In this study, a rectangular glass-walled container with dimensions of 30 cm \u0026times; 50 cm was filled with soil and used as a phantom to model a realistic environmental setting for subsequent measurements. The effectiveness of such phantoms in simulating soil environments has been demonstrated in previous studies \u003csup\u003e14\u003c/sup\u003e. The configuration of this setup is illustrated in Figures 2 and 3, corresponding to the sodium iodide and plastic scintillation detectors, respectively.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTo conduct the experiment, a full-scale printout of the surface source configuration was placed directly on the soil surface. The Cs-137 source was then positioned at the various non-redundant points indicated in the configuration. We performed measurements at different depths: 0 cm (the surface without soil cover), 1 cm, 2 cm, 3 cm, and 4 cm by adding layers of soil on top of the printed configuration map. Table 1 shows that the Cs-137 source was put in 18 different places at each depth, each one at a different distance from the center of the 23 cm circular test area. The data presented in Table 1 were obtained through analytical calculations. Measurement durations were set to 20 seconds for the sodium iodide scintillation detector and 150 seconds for the plastic scintillation detector. These intervals were determined by placing the Cs-137 source at the most distant lateral point and at a depth of 5 cm in the soil, and then identifying the minimum acquisition time needed to obtain a spectrum with sufficient shape and resolution.\u003c/p\u003e\n\u003cp\u003eFrom a physics standpoint, the longer measurement time required for the plastic scintillation detector is primarily due to its lower energy resolution and reduced intrinsic efficiency compared to the sodium iodide detector. At each depth, the source was placed at different positions, and for repeated positions in the configuration, the measurement time was scaled proportionally to the number of repetitions. For example, for point B, which appears six times in the configuration, the total measurement time was set to 120 seconds for the sodium iodide detector and 900 seconds for the plastic scintillation detector. For each measurement cycle, background radiation was recorded for the same duration as the corresponding sample and then subtracted from the acquired spectrum. Rather than multiplying a single spectrum by the number of repetitions, repeated positions were measured for extended durations to account for cumulative effects such as scattering and buildup. To ensure uniformity across depths, the soil surface in front of the detector was precisely leveled and smoothed with a trowel prior to every measurement. A total of approximately 200 measurements were conducted utilizing both scintillation detectors. To maximize the detector\u0026rsquo;s solid-angle coverage, the sodium iodide scintillation detector was positioned 3 cm above the soil surface. Due to the plastic scintillator\u0026apos;s sensitivity to beta radiation, it was placed directly in contact with the soil surface\u0026nbsp;\u003csup\u003e15\u003c/sup\u003e. By summing the spectra from all measurement points within the configuration, the composite spectrum of the surface source at each depth was obtained. The simulated spectra were compared with the total measured spectra to calibrate the response of each detector. Once calibrated, these datasets enabled not only the estimation of Cs-137 burial depth, but also the reconstruction of its relative distribution across multiple soil layers. To differentiate between the resulting spectra, various classification algorithms were applied, and their performance was compared. The process of identifying the depth and stratified distribution of cesium follows an approach analogous to radionuclide identification techniques\u003csup\u003e16\u003c/sup\u003e. A library of simulated spectra corresponding to different source depths was used as a reference dataset. The composite spectrum obtained from either measurements or simulations, representing a surface-distributed Cs-137 source spread across multiple soil layers with varying contributions, was treated as the input to the inverse problem. The algorithm performs spectral deconvolution to estimate the relative contribution of Cs-137 in each layer by comparing the input spectrum against the spectral library. The optimization problem is formulated as follows:\u003c/p\u003e\n\u003cp\u003e\u003cimg width=\"73\" height=\"45\" src=\"data:image/wmf;base64,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\" alt=\"image\"\u003e\u0026nbsp;(1)\u003c/p\u003e\n\u003cp\u003ewhere \u003cem\u003ecᵢ\u003c/em\u003e represents the relative contribution of Cs-137 in the \u003cem\u003ei\u003c/em\u003eth soil layer, \u003cem\u003eRᵢ\u003c/em\u003e denotes the detector response for a source distributed exclusively in that layer (based on the spectral library), and \u003cem\u003eS\u003c/em\u003e is the measured or simulated composite input spectrum. Different algorithms approach the solution of this equation using various optimization strategies. The performance of the proposed method is evaluated through a series of blind tests.\u003c/p\u003e"},{"header":"Results and Discussion","content":"\u003cp\u003eThe measurement results for each depth using the HCP configuration are presented in Figures 4 and 5. The significant difference observed between the 0 cm depth and the other depths in Figure 5 is attributed to the presence of beta radiation in the spectrum, as well as the disparity in attenuation coefficients between soil and air. With the experimental data in hand, Monte Carlo simulations were carried out to calibrate the detector for various source depths. The MCNP code was used to carry out the simulations.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eA critical factor in achieving accurate results was defining the elemental composition of the soil, which serves as the main attenuating material for nuclear radiation. To characterize the soil, its elemental content was determined based on results obtained from X-ray fluorescence (XRF) analysis. For lighter elements not detectable by XRF, reference data from the literature\u003cspan dir=\"RTL\"\u003e\u0026nbsp;\u003c/span\u003e17\u003cspan dir=\"RTL\"\u003e\u0026nbsp;\u003c/span\u003ewere utilized to complete the composition model. The simulated NaI(Tl) detector consisted of several key components: an aluminum housing with a density of 2.7 g/cm\u0026sup3;, a magnesium oxide (MgO) reflector at 3.58 g/cm\u0026sup3;, the NaI scintillation crystal itself with a density of 3.67 g/cm\u0026sup3;, and a glass window for the photomultiplier tube (PMT) with a density of 2.23 g/cm\u0026sup3;. The glass was chosen for its high mechanical durability and its ability to transmit radiation at wavelengths beyond the ultraviolet range. The detector dimensions were 63 mm in diameter and 63 mm in height. For the plastic scintillation detector, all materials and structural details were also simulated based on reference data provided in \u003csup\u003e17\u003c/sup\u003e. The dimensions of the plastic scintillation detector were set to 128 mm in diameter and 8 mm in thickness. The density of the electronic components and photomultiplier tube (PMT) housing for both detectors were assumed to be 1.207 g/cm\u0026sup3; \u003csup\u003e18\u003c/sup\u003e. Additionally, the electronic components of the detectors were modeled as polyester-equivalent material in simulation \u003csup\u003e19\u003c/sup\u003e.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe results of the comparison between the scaled simulated and experimental spectra are presented in Figures 6 and 7. The differences observed between the simulated and measured spectra are the result of several contributing factors, including the statistical nature of the Monte Carlo method, background radiation subtraction, the inherent randomness of radioactive decay, and discrepancies between the idealized simulation configuration and the actual surface source setup \u003csup\u003e20\u003c/sup\u003e. Additionally, to improve the agreement between the experimental and simulated data, counts in some of the lower-energy channels were excluded from the analysis \u003csup\u003e21\u003c/sup\u003e.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTherefore, in this study, the simulation of radioactive material at various depths was successfully performed with good accuracy. The simulated data were used not only for detector calibration but also for evaluating source localization performance. We now proceed to predict the depth and layer-wise distribution of radioactive material using various computational algorithms. For demonstration purposes, and considering its practical applicability, the sodium iodide detector is used in the following analysis. It is evident, however, that given the validated simulation results for the plastic scintillator and the identical formulation and methodology used for both detectors, similar results, albeit with slightly lower accuracy due to its poorer energy resolution, can also be expected from the plastic scintillation detector.\u003c/p\u003e\n\u003cp\u003eThe gamma spectra recorded by the sodium iodide detector for various depth distributions of the Cs-137 source are shown in Figure 8.\u003c/p\u003e\n\u003cp\u003eThe results obtained from multiple algorithms for predicting the contribution of each depth distribution in the composite spectra shown in Figure 8 are presented in Table 2.\u003c/p\u003e\n\u003cp\u003eA detailed description of the algorithms used to obtain the results presented in this table has been previously provided in Reference \u003csup\u003e21\u003c/sup\u003e. The results demonstrate the high accuracy of the multi-step approach in determining the distribution of radioactive material in soil, both in terms of minimizing false-positive detections of activity at various depths and in accurately estimating the depth-wise distribution of the radionuclide.\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThe determination of radionuclide depth in soil has been addressed in previous studies, most of which have relied on direct sampling methods that are inherently invasive and destructive. Moreover, these studies often report only an average depth for Cs-137, which does not accurately reflect the true distribution of surface contamination. In this work, we employed an HCP configuration to simulate a realistic surface-distributed Cs-137 source using a low-activity standard source. The MCNP simulation results, based on defining a realistic surface source using the *SF* card and accurately specifying the material properties, confirmed the feasibility and effectiveness of the proposed approach. Building upon this successful simulation, the calibration of the measurement system was performed for both types of scintillation detectors using the simulated data. Our blind tests showed that the method performs reliably when analyzing full gamma spectra, especially with the multi-step approach. However, the plastic scintillation detector, although cost-effective and portable, exhibits limited energy resolution, which may affect spectral deconvolution accuracy for more complex contamination profiles. The results highlight that simulation-based calibration can effectively estimate both the depth and the vertical spread of Cs-137 in soil. What makes this approach even more practical is that it isn\u0026rsquo;t limited to a specific isotope and could work just as well for identifying other surface contaminants. The accuracy of the proposed method heavily depends on the precise modeling of the soil composition, which may vary significantly across different geographical regions. Future work may focus on addressing the mentioned challenges.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003cp\u003eThis research received no specific grand from any funding agency in the public, commercial, or not-for-profit sectors.\u003c/p\u003e\n\u003cp\u003eData Availability\u003c/p\u003e\n\u003cp\u003eAll data generated or analysed during this study are included in this published article. Additionally, any further datasets used or analysed during the current study are available from the corresponding author upon reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eLiu, S. \u003cem\u003eet al.\u003c/em\u003e A State-of-the-Art Review of Radioactive Decontamination Technologies: Facing the Upcoming Wave of Decommissioning and Dismantling of Nuclear Facilities. \u003cem\u003eSustainability\u003c/em\u003e 14, 4021 (2022).\u003c/li\u003e\n\u003cli\u003eUkaegbu, I. K., Gamage, K. A. A. \u0026amp; Aspinall, M. D. Nonintrusive Depth Estimation of Buried Radioactive Wastes Using Ground Penetrating Radar and a Gamma Ray Detector. \u003cem\u003eRemote Sens (Basel)\u003c/em\u003e 11, 141 (2019).\u003c/li\u003e\n\u003cli\u003eAhmad, A. Y., Al-Ghouti, M. A., AlSadig, I. \u0026amp; Abu-Dieyeh, M. 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Determination of the Depth of Localized Radioactive Contamination by 137 Cs and 60 Co in Sand with Principal Component Analysis. \u003cem\u003eEnviron Sci Technol\u003c/em\u003e 45, 8262\u0026ndash;8267 (2011).\u003c/li\u003e\n\u003cli\u003eLikar, A., Omahen, G., Vidmar, T. \u0026amp; Martinčič, R. Method to determine the depth of Cs-137 in soil from in-situ gamma-ray spectrometry. \u003cem\u003eJ Phys D Appl Phys\u003c/em\u003e 33, 2825\u0026ndash;2830 (2000).\u003c/li\u003e\n\u003cli\u003eTANAKA, K. \u003cem\u003eet al.\u003c/em\u003e Vertical profiles of Iodine-131 and Cesium-137 in soils in Fukushima Prefecture related to the Fukushima Daiichi Nuclear Power Station Accident. \u003cem\u003eGeochem J\u003c/em\u003e 46, 73\u0026ndash;76 (2012).\u003c/li\u003e\n\u003cli\u003eKavasi, N., Arae, H., Aono, T. \u0026amp; Sahoo, S. K. Distribution of strontium-90 in soils affected by Fukushima dai-ichi nuclear power station accident in the context of cesium-137 contamination. \u003cem\u003eEnvironmental Pollution\u003c/em\u003e 326, 121487 (2023).\u003c/li\u003e\n\u003cli\u003eUkaegbu, I. \u0026amp; Gamage, K. A Novel Method for Remote Depth Estimation of Buried Radioactive Contamination. \u003cem\u003eSensors\u003c/em\u003e 18, 507 (2018).\u003c/li\u003e\n\u003cli\u003eAoyama, M., Hirose, K. \u0026amp; Igarashi, Y. Re-construction and updating our understanding on the global weapons tests 137Cs fallout. \u003cem\u003eJournal of Environmental Monitoring\u003c/em\u003e 8, 431\u0026ndash;438 (2006).\u003c/li\u003e\n\u003cli\u003eAtkins, P. \u0026amp; De Paula, J. \u003cem\u003eElements of Physical Chemistry\u003c/em\u003e. (Oxford University Press, USA, 2013).\u003c/li\u003e\n\u003cli\u003eSiciliano, E. R. \u003cem\u003eet al.\u003c/em\u003e Comparison of PVT and NaI(Tl) scintillators for vehicle portal monitor applications. \u003cem\u003eNucl Instrum Methods Phys Res A\u003c/em\u003e 550, 647\u0026ndash;674 (2005).\u003c/li\u003e\n\u003cli\u003eKim, J., Lim, K. T., Park, K. \u0026amp; Cho, G. A bayesian approach for remote depth estimation of buried low-level radioactive waste with a nai(Tl) detector. \u003cem\u003eSensors (Switzerland)\u003c/em\u003e 19, (2019).\u003c/li\u003e\n\u003cli\u003eBae, J. W. \u0026amp; Kim, H. R. Plastic scintillator beta ray scanner for in-situ discrimination of beta ray and gamma ray radioactivity in soil. \u003cem\u003eNuclear Engineering and Technology\u003c/em\u003e 52, 1259\u0026ndash;1265 (2020).\u003c/li\u003e\n\u003cli\u003eGhalehasadi, A., Ashrafi, S., Alizadeh, D. \u0026amp; Meri\u0026ccedil;, N. Gamma ray interactions based optimization algorithm: Application in radioisotope identification. \u003cem\u003eNuclear Engineering and Technology\u003c/em\u003e 53, 3772\u0026ndash;3783 (2021).\u003c/li\u003e\n\u003cli\u003eDetwiler, R. S., McConn, R. J., Grimes, T. F., Upton, S. A. \u0026amp; Engel, E. J. \u003cem\u003eCompendium of Material Composition Data for Radiation Transport Modeling\u003c/em\u003e. (2021).\u003c/li\u003e\n\u003cli\u003eBar\u0026eacute;, J. \u0026amp; Tondeur, F. Gamma spectrum unfolding for a NaI monitor of radioactivity in aquatic systems: Experimental evaluations of the minimal detectable activity. \u003cem\u003eApplied Radiation and Isotopes\u003c/em\u003e 69, 1121\u0026ndash;1124 (2011).\u003c/li\u003e\n\u003cli\u003eCinelli, G., Tositti, L., Mostacci, D. \u0026amp; Bar\u0026eacute;, J. Calibration with MCNP of NaI detector for the determination of natural radioactivity levels in the field. \u003cem\u003eJ Environ Radioact\u003c/em\u003e 155\u0026ndash;156, 31\u0026ndash;37 (2016).\u003c/li\u003e\n\u003cli\u003e\u0026Ouml;stlund, K., Samuelsson, C. \u0026amp; R\u0026auml;\u0026auml;f, C. L. Experimentally determined vs: Monte Carlo simulated peak-to-valley ratios for a well-characterised n-type HPGe detector. \u003cem\u003eApplied Radiation and Isotopes\u003c/em\u003e 95, 94\u0026ndash;100 (2015).\u003c/li\u003e\n\u003cli\u003eAlizadeh, D. \u0026amp; Ashrafi, S. New hybrid metaheuristic algorithm for scintillator gamma ray spectrum analysis. \u003cem\u003eNucl Instrum Methods Phys Res A\u003c/em\u003e 915, 1\u0026ndash;9 (2019).\u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Tables","content":"\u003cp\u003eTable 1. Distances of various positions in the HCP configuration from the center. r denotes the radius of the source or the small circles used in the configuration.\u003c/p\u003e\n\u003ctable dir=\"rtl\" border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003eDistance from Center\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003eLocation Label\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003e0r\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003eA\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003e2r\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003eB\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003e4r\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003eC\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003e6r\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003eD\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003e8r\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003eE\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003e10r\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003eF\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003e12r\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003eG\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003e2(3)\u003csup\u003e1/2\u003c/sup\u003er\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003eH\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003e4(3)\u003csup\u003e1/2\u003c/sup\u003er\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003eK\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003e6(3)\u003csup\u003e1/2\u003c/sup\u003er\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003eN\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003e2(7)\u003csup\u003e1/2\u003c/sup\u003er\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003eI\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003e4(7)\u003csup\u003e1/2\u003c/sup\u003er\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003eP\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003e2(13)\u003csup\u003e1/2\u003c/sup\u003er\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003eJ\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003e2(19)\u003csup\u003e1/2\u003c/sup\u003er\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003eM\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003e2(21)\u003csup\u003e1/2\u003c/sup\u003er\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003eL\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003e2(31)\u003csup\u003e1/2\u003c/sup\u003er\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003eO\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003e2(37)\u003csup\u003e1/2\u003c/sup\u003er\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003eR\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003e2(39)\u003csup\u003e1/2\u003c/sup\u003er\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 240px;\"\u003e\n \u003cp dir=\"LTR\"\u003eQ\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003cstrong\u003eTable 2.\u003c/strong\u003e Results of various algorithms used to identify the depth distribution of Cs-137 in soil. The multi-step method combines two optimization techniques: Particle Swarm Optimization (PSO) and Genetic Algorithm (GA)\u003c/p\u003e\n \u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\" class=\"fr-table-selection-hover\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 118px;\"\u003e\n \u003cp\u003eMethod / Spectrum\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003eCs (4 cm)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003eCs (3 cm)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003eCs (2 cm)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003eCs (1 cm)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003eCs (0 cm)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 118px;\"\u003e\n \u003cp\u003eTrue \u0026ndash; Sample 1 (Fig. a)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.0\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.0\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.0\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e50.0\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e50.0\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 118px;\"\u003e\n \u003cp\u003eMLEM\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e0.31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e0.39\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e1.23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e49.27\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e48.8\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 118px;\"\u003e\n \u003cp\u003eGold\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e0.26\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e0.67\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e0.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e49.69\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e49.38\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 118px;\"\u003e\n \u003cp\u003eGA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e0.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e0.74\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e0.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e49.58\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e49.53\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 118px;\"\u003e\n \u003cp\u003eMulti-step\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e0.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e0.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e0.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e50.16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e49.84\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 118px;\"\u003e\n \u003cp\u003eTrue \u0026ndash; Sample 2 (Fig. b)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.0\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e10.0\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.0\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.0\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e90.0\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 118px;\"\u003e\n \u003cp\u003eMLEM\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e4.13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e17.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e5.94\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e1.54\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e71.07\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 118px;\"\u003e\n \u003cp\u003eGold\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e0.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e10.48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e0.27\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e0.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e89.25\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 118px;\"\u003e\n \u003cp\u003eGA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e0.88\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e9.51\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e1.27\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e1.68\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e87.93\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 118px;\"\u003e\n \u003cp\u003eMulti-step\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e0.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e10.21\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e0.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e0.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e89.79\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 118px;\"\u003e\n \u003cp\u003eTrue \u0026ndash; Sample 3 (Fig. c)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e30.0\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.0\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e10.0\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e60.0\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.0\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 118px;\"\u003e\n \u003cp\u003eMLEM\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e31.58\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e0.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e7.92\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e53.99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e6.51\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 118px;\"\u003e\n \u003cp\u003eGold\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e31.63\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e0.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e9.06\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e58.18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e1.13\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 118px;\"\u003e\n \u003cp\u003eGA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e30.69\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e0.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e8.86\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e56.81\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e3.64\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 118px;\"\u003e\n \u003cp\u003eMulti-step\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e30.43\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e0.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e10.23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e59.34\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 82px;\"\u003e\n \u003cp\u003e0.0\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Cesium-137, Depth distribution, Gamma-ray spectroscopy, MCNP simulation","lastPublishedDoi":"10.21203/rs.3.rs-7186113/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7186113/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"For environmental monitoring and radiation protection, it is important to know exactly how deep and where radioactive materials like Cs-137 are in the soil. Conventional approaches are often invasive and provide only average depth estimates, limiting their reliability. In this study, a novel, non-destructive method is proposed based on a hexagonal close-packed configuration to simulate a surface-distributed Cs-137 source. Measurements were conducted at multiple depths using NaI(Tl) and plastic scintillation detectors, and the system was calibrated using Monte Carlo simulations. Composite spectra were analyzed using an inverse modeling approach to estimate both the depth and layer-wise distribution of contamination. Blind tests demonstrated the method’s high accuracy in reconstructing realistic contamination profiles. The suggested method is easy to use, cheap, and works with different types of detectors, so it can be used in real-world situations to measure environmental radioactivity.","manuscriptTitle":"A Practical Framework for Depth and Profile Assessment of Cs-137 in Soil Using Scintillation Detectors and Composite Spectrum Analysis","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-08-05 14:54:17","doi":"10.21203/rs.3.rs-7186113/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"3228af92-b868-4c77-98bf-88ea424436a8","owner":[],"postedDate":"August 5th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":52637268,"name":"Physical sciences/Engineering"},{"id":52637269,"name":"Earth and environmental sciences/Environmental sciences"},{"id":52637270,"name":"Physical sciences/Materials science"},{"id":52637271,"name":"Physical sciences/Physics"}],"tags":[],"updatedAt":"2025-08-06T12:08:47+00:00","versionOfRecord":[],"versionCreatedAt":"2025-08-05 14:54:17","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7186113","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7186113","identity":"rs-7186113","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}