# Integration of Ground- Penetrating Radar and Gamma-Ray Detectors for Nonintrusive Characterisation of Buried Radioactive Objects

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{−1}above the ground [1]. This is about 26,000-times the stipulated effective dose limit of 20 mSv per year [2]. Furthermore, chemical reactions in the soil can lead to the dissolution of these objects and subsequent contamination of groundwater. For example, the high energy penetrators used in ammunition are usually made from depleted uranium, which is a by-product of the nuclear fuel enrichment process. Many of these penetrators get lodged in the ground during military operations and become potential sources of groundwater contamination because of their high solubility in sand and other volcanic rock [3]. Therefore, it is important to promptly detect, and safely dispose these objects.

## 2. Theoretical Framework

^{2}Bq

^{−1}) and is calculated from the flux due to a source of known activity placed at a known distance z along the centerline, i.e.,:

^{2}g

^{−1}), ${\rho}_{a}$ is the density of air (g cm

^{−3}), h is the distance from the ground surface to the centre of the detector and ${\rho}_{b}$ is the bulk density of soil (g cm

^{−3}).

^{−2}).

^{−1}), c is the speed of light (299,792,458 m s

^{−1}) and ${\u03f5}_{b}$ is the relative bulk permittivity of the soil (unitless). It should be noted that Equation (5) assumes that both the transmitting (Tx) and receiving (Rx) antennas are close to each other. Porous materials such as soil can be considered as a three-phase mixture of air, water and solid particles [21]. Therefore, their bulk permittivity is a function of the permittivities of these phases and their proportional composition in the material. Various formulas have been proposed to express this relationship; however, in a comparative study [22], it was shown that the formula based on the exponential mixing rule [21] with the exponent value of 0.65 gave the best result across a variety of materials. This formula is given by:

^{−3}is the solid particle density for soils, ${W}_{c}$ is the volumetric water content (%), ${\u03f5}_{s}=4.7$ is the solid particle relative permittivity for soils [23,24], ${\u03f5}_{a}=1$ is the relative permittivity of air and ${\u03f5}_{w}$ is the relative permittivity of water, which is given by the real part of the modified Debye’s equation [24], i.e.,

## 3. Materials and Methods

#### 3.1. Selection and Modelling of Sensors

^{3}(Figure 4a). The detector was chosen because of its size and good spectroscopic properties. In addition, unlike high purity germanium (HPGe) detectors, CZT detectors do not require a cooling system; therefore, they are very portable and easy to integrate with other systems. Figure 4b shows the simulated and experimental Cs-137 spectrum from the model and real detectors, respectively. A very good alignment of the spectrum key features can be observed. The tailing effect in the Compton valley of the spectrum from the experiment was due to incomplete charge collection caused by poor electron-hole mobility. This is a characteristic feature of CZT detectors. This feature was not modelled because of the additional complexity required. However, this will not affect the results of the study because the ratio of the area under the photo peak for two simulated spectra will be the same as that for two experimental spectra. The difference in the position of the Compton peak was likely due to nonlinearity in the real detector, while the higher background below 300 keV in the spectrum from the experiment can be attributed to backscatter from surrounding objects.

#### 3.2. Measurement Scenario Modelling

^{−3}[33]. The horizontal distance between the gamma detectors was selected such that it can fit the width of the GPR antenna. The antenna was modelled as a propylene box since it was not an active component in the MCNP5 simulation. The soil used in the model was a typical soil (51.4% O, 0.6% Na, 1.3% Mg, 6.8% Al, 27% Si, 1.4% K, 5.1% Ca, 0.5% Ti, 0.07% Mn and 5.6% Fe) with a dry density of 1.52 g cm

^{−3}[34].

^{−1}) and ${\sigma}_{w}$ is the conductivity of pore water (0.05 Sm

^{−1}[36]).

#### 3.3. Simulation and Data Processing

^{−2}, unless otherwise stated. After simulation, a Gaussian function was fitted to the spectra from the gamma ray detectors in order to estimate the number of full energy photons detected. This is the required flux due to the buried radioactive object. The energy range used for the estimation was from 655–672 keV.

## 4. Results and Discussion

^{−2}) of a radius of 3 cm buried at a depth of 20 cm in soil of different densities and and volumetric water contents. The estimates in the first row were obtained using the proposed integrated GPR and gamma ray detectors approach. The values in the second row were obtained using the measurements from only the two gamma-ray detectors by minimising the following function:

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Popp, A.; Ardouin, C.; Alexander, M.; Blackley, R.; Murray, A. Improvement of a high risk category source buried in the grounds of a hospital in Cambodia. In Proceedings of the 13th International Congress of the International Radiation Protection Association, Glasgow, UK, 13–18 May 2012; pp. 1–10. [Google Scholar]
- IAEA. Radiation Protection and Safety of Radiation Sources: International Basic Safety Standards; Technical Report GSR Part 3; International Atomic Energy Agency: Vienna, Austria, 2014. [Google Scholar]
- Bleise, A.; Danesi, P.R.; Burkart, W. Properties, use and health effects of depleted uranium. J. Environ. Radioact.
**2003**, 64, 93–112. [Google Scholar] [CrossRef] - Maeda, K.; Sasaki, S.; Kumai, M.; Sato, I.; Suto, M.; Ohsaka, M.; Goto, T.; Sakai, H.; Chigira, T.; Murata, H. Distribution of radioactive nuclides of boring core samples extracted from concrete structures of reactor buildings in the Fukushima Daiichi Nuclear Power Plant. J. Nucl. Sci. Technol.
**2014**, 51, 1006–1023. [Google Scholar] [CrossRef] [Green Version] - Varley, A.; Tyler, A.; Smith, L.; Dale, P. Development of a neural network approach to characterise226Ra contamination at legacy sites using gamma-ray spectra taken from boreholes. J. Environ. Radioact.
**2015**, 140, 130–140. [Google Scholar] [CrossRef] [PubMed] - Varley, A.; Tyler, A.; Dowdall, M.; Bondar, Y.; Zabrotski, V. An in situ method for the high resolution mapping of137Cs and estimation of vertical depth penetration in a highly contaminated environment. Sci. Total Environ.
**2017**, 605–606, 957–966. [Google Scholar] [CrossRef] [PubMed] - Varley, A.; Tyler, A.; Bondar, Y.; Hosseini, A.; Zabrotski, V.; Dowdall, M. Reconstructing the deposition environment and long-term fate of Chernobyl137Cs at the floodplain scale through mobile gamma spectrometry. Environ. Pollut.
**2018**, 240, 191–199. [Google Scholar] [CrossRef] - Adams, J.C.; Mellor, M.; Joyce, M.J. Depth determination of buried caesium-137 and cobalt-60 sources using scatter peak data. IEEE Trans. Nucl. Sci.
**2010**, 57, 2752–2757. [Google Scholar] [CrossRef] - Iwamoto, Y.; Kataoka, J.; Kishimoto, A.; Nishiyama, T.; Taya, T.; Okochi, H.; Ogata, H.; Yamamoto, S. Novel methods for estimating 3D distributions of radioactive isotopes in materials. Nucl. Instrum. Methods Phys. Res. Sec. A
**2016**, 831, 295–300. [Google Scholar] [CrossRef] - Adams, J.C.; Mellor, M.; Joyce, M.J. Determination of the depth of localized radioactive contamination by 137Cs and 60Co in sand with principal component analysis. Environ. Sci. Technol.
**2011**, 45, 8262–8267. [Google Scholar] [CrossRef] - Adams, J.C.; Joyce, M.J.; Mellor, M. Depth profiling 137Cs and 60Co non-intrusively for a suite of industrial shielding materials and at depths beyond 50 mm. Appl. Radiat. Isot.
**2012**, 70, 1150–1153. [Google Scholar] [CrossRef] - Adams, J.C.; Joyce, M.J.; Mellor, M. The advancement of a technique using principal component analysis for the non-intrusive depth profiling of radioactive contamination. IEEE Trans. Nucl. Sci.
**2012**, 59, 1448–1452. [Google Scholar] [CrossRef] - Varley, A.; Tyler, A.; Smith, L.; Dale, P.; Davies, M. Remediating radium contaminated legacy sites: Advances made through machine learning in routine monitoring of “hot” particles. Sci. Total Environ.
**2015**, 521–522, 270–279. [Google Scholar] [CrossRef] [PubMed] - Varley, A.; Tyler, A.; Smith, L.; Dale, P.; Davies, M. Mapping the spatial distribution and activity of 226Ra at legacy sites through Machine Learning interpretation of gamma-ray spectrometry data. Sci. Total Environ.
**2016**, 545–546, 654–661. [Google Scholar] [CrossRef] [PubMed] - Shippen, A.; Joyce, M.J. Profiling the depth of caesium-137 contamination in concrete via a relative linear attenuation model. Appl. Radiat. Isot.
**2010**, 68, 631–634. [Google Scholar] [CrossRef] [PubMed] - Haddad, K.; Al-Masri, M.S.; Doubal, A.W. Determination of 226Ra contamination depth in soil using the multiple photopeaks method. J. Environ. Radioact.
**2014**, 128, 33–37. [Google Scholar] [CrossRef] [PubMed] - Benke, R.R.; Kearfott, K.J. An improved in situ method for determining depth distributions of gamma-ray emitting radionuclides. Nucl. Instrum. Methods in Phy. Res. Sect. A
**2001**, 463, 393–412. [Google Scholar] [CrossRef] - Dewey, S.C.; Whetstone, Z.D.; Kearfott, K.J. A method for determining the analytical form of a radionuclide depth distribution using multiple gamma spectrometry measurements. J. Environ. Radioact.
**2011**, 102, 581–588. [Google Scholar] [CrossRef] [PubMed] - Whetstone, Z.D.; Dewey, S.C.; Kearfott, K.J. Simulation of a method for determining one-dimensional137Cs distribution using multiple gamma spectroscopic measurements with an adjustable cylindrical collimator and center shield. Appl. Radiat. Isot.
**2011**, 69, 790–802. [Google Scholar] [CrossRef] - Dewey, S.C.; Whetstone, Z.D.; Kearfott, K.J. A numerical method for the calibration of in situ gamma ray spectroscopy systems. Health Phys.
**2010**, 98, 657–671. [Google Scholar] [CrossRef] - Brovelli, A.; Cassiani, G. Effective permittivity of porous media: A critical analysis of the complex refractive index model. Geophys. Prospect.
**2008**, 56, 715–727. [Google Scholar] [CrossRef] - Ukaegbu, I.K.; Gamage, K.A.; Aspinall, M.D. Nonintrusive depth estimation of buried radioactive wastes using ground penetrating radar and a gamma ray detector. Remote Sens.
**2019**, 11, 7–14. [Google Scholar] [CrossRef] - Dobson, M.C.; Ulaby, F.T.; Hallikainen, M.T.; El-Rayes, M.A. Microwave Dielectric Behavior of Wet Soil-Part II: Dielectric Mixing Models. IEEE Trans. Geosci. Remote Sens.
**1985**, GE-23, 35–46. [Google Scholar] [CrossRef] - Peplinski, N.R.; Ulaby, F.T.; Dobson, M.C. Dielectric Properties of Soils in the 0.3–1.3-GHz Range. IEEE Trans. Geosci. Remote Sens.
**1995**, 33, 803–807. [Google Scholar] [CrossRef] - Klein, L.; Swift, C. An improved model for the dielectric constant of sea water at microwave frequencies. IEEE Trans. Antennas and Propag.
**1977**, 25, 104–111. [Google Scholar] [CrossRef] - Stogryn, A. The Brightness Temperature of a Vertically Structured Medium. Radio Sci.
**1970**, 5, 1397–1406. [Google Scholar] [CrossRef] - Ukaegbu, I.K.; Gamage, K.A.A. Ground Penetrating Radar as a Contextual Sensor for Multi-Sensor Radiological Characterisation. Sensors
**2017**, 17, 790. [Google Scholar] [CrossRef] [PubMed] - Pelowitz, D.B. MCNPX User’s Manual: Version 2.7.0; Los Alamos National Laboratory: Los Alamos, NM, USA, 2011. [Google Scholar]
- Warren, C.; Giannopoulos, A.; Giannakis, I. gprMax: Open source software to simulate electromagnetic wave propagation for Ground Penetrating Radar. Comput. Phys. Commun.
**2016**, 209, 163–170. [Google Scholar] [CrossRef] [Green Version] - Warren, C.; Giannopoulos, A. Creating finite-difference time-domain models of commercial ground-penetrating radar antennas using Taguchi’s optimization method. Geophysics
**2011**, 76, G37–G47. [Google Scholar] [CrossRef] - Giannakis, I.; Giannopoulos, A.; Warren, C. Realistic FDTD GPR Antenna Models Optimized Using a Novel Linear/Nonlinear Full-Waveform Inversion. IEEE Trans. Geosci. Remote Sens.
**2019**, 57, 1768–1778. [Google Scholar] [CrossRef] - Keith, C.; Selby, H.; Lee, A.; White, M.; Bandong, B.; Roberts, K.; Church, J. Activation product interpretation of structural material for fast critical assemblies. Ann. Nucl. Energy
**2018**, 119, 98–105. [Google Scholar] [CrossRef] - Gamage, K.A.A.; Joyce, M.J.; Taylor, G.C. A comparison of collimator geometries for imaging mixed radiation fields with fast liquid organic scintillators. In Proceedings of the 2011 2nd International Conference on Advancements in Nuclear Instrumentation, Measurement Methods and their Applications, Ghent, Belgium, 6–9 June 2011; pp. 1–5. [Google Scholar] [CrossRef]
- McConn, R.; Gesh, C.J.; Pagh, R.; Rucker, R.A.; Williams, R. Compendium of Material Composition Data for Radiation Transport Modelling; Technical report; Pacific Northwest National Laboratory: Washington, DC, USA, 2011. [Google Scholar]
- Hilhorst, M.A. A Pore Water Conductivity Sensor. Soil Sci. Soc. Am. J.
**2000**, 64, 1922–1925. [Google Scholar] [CrossRef] [Green Version] - Ciampalini, A.; André, F.; Garfagnoli, F.; Grandjean, G.; Lambot, S.; Chiarantini, L.; Moretti, S. Improved estimation of soil clay content by the fusion of remote hyperspectral and proximal geophysical sensing. J. Appl. Geophys.
**2015**, 116, 135–145. [Google Scholar] [CrossRef]

**Figure 1.**Geometry and parameters for estimating the flux (measured by the detector) due to the point source ${S}_{p}$ in the soil.

**Figure 2.**Operation of a ground-penetrating radar (GPR) system. Signals from the transmitter (Tx) are reflected by objects and detected by the receiver (Rx).

**Figure 3.**Two ways of arranging two detectors to measure the flux from the disk source. The horizontally-separated arrangement allows both fluxes to be measured simultaneously because none of the detectors is obstructed.

**Figure 4.**(

**a**) MCNP5 model of the gamma detector. The crystal volume is 1 cm × 1 cm × 0.5 cm; (

**b**) Experimental and simulated Cs-137 spectrum from the model and real detector.

**Figure 5.**gprMax model of the 1.5-GHz antenna from GSSI Inc. The antenna dimensions are 17 cm × 10.8 cm × 4.3 cm (L×W×H). The skid plate underneath the casing has been removed to show the inside of the antenna.

**Figure 6.**Model of the measurement scenario. The radioactive object is a metallic disk with Cs-137 radioactive contamination. (

**a**) MCNP5 model of the measurement scenario. The gamma detectors are surrounded by 1 cm-thick lead collimators with an inner radius of 2.4 cm and height of 3.3 cm; (

**b**) gprMax model of the measurement scenario. All labels and dimensions are the same as (

**a**).

**Figure 7.**GPR signal for metal disk of a radius of 3 cm buried at 24 cm in dry soil, (

**a**) Raw GPR signal with coupled direct wave and ground reflection; (

**b**) GPR signal after subtraction of the GPR antenna’s system response.

**Figure 8.**Flux ratio (i.e., ${F}_{2}/{F}_{1})$ for sources of radii of 3 cm, 9 cm and 15 cm buried at various depths in dry soil (${\rho}_{b}=1.52$ g cm

^{−3}). The solid lines are calculated values, while the markers are the values from the simulation.

**Table 1.**Simultaneously-estimated depths and soil densities for disk sources of different radii buried at different depths in dry soil. The values in parentheses are the relative error in percentage.

Actual Values | Estimated Values | ||||||
---|---|---|---|---|---|---|---|

r = 3 cm | r = 9 cm | r = 15 cm | |||||

$\mathit{d}$(cm) | ${\mathit{\rho}}_{\mathit{b}}$ (g cm^{−3}) | $\mathit{d}$ (cm) | ${\mathit{\rho}}_{\mathit{b}}$ (g cm^{−3}) | $\mathit{d}$ (cm) | ${\mathit{\rho}}_{\mathit{b}}$ (g cm^{−3}) | $\mathit{d}$ (cm) | ${\mathit{\rho}}_{\mathit{b}}$ (g cm^{−3}) |

12 | 1.52 | 11.8 (2) | 1.36 (11) | 11.9 (1) | 1.34 (12) | 12.2 (1) | 1.25 (18) |

16 | 1.52 | 15.7 (2) | 1.42 (7) | 15.7 (2) | 1.43 (6) | 15.2 (5) | 1.54 (1) |

20 | 1.52 | 19.8 (1) | 1.41 (7) | 19.6 (2) | 1.45 (5) | 19.0 (5) | 1.57 (3) |

24 | 1.52 | 24.0 (0) | 1.38 (9) | 23.1 (4) | 1.52 (0) | 23.5 (2) | 1.46 (4) |

28 | 1.52 | 27.7 (1) | 1.43 (6) | 27.9 (0) | 1.41 (7) | 27.3 (2) | 1.48 (3) |

**Table 2.**Depth and density estimates for a disk source of radius 3 cm buried at a depth of 20 cm in three different soil conditions. The values in parentheses are the relative error in percentage.

Estimation Method | Soil 1 (${\mathit{\rho}}_{\mathit{b}}=1.67$ g cm^{−3}, | Soil 2 (${\mathit{\rho}}_{\mathit{b}}=1.82$ g cm^{−3}, | Soil 3 (${\mathit{\rho}}_{\mathit{b}}=1.97$ g cm^{−3}, | |||
---|---|---|---|---|---|---|

${\mathit{W}}_{\mathit{c}}=15\%$) | ${\mathit{W}}_{\mathit{c}}=30\%$) | ${\mathit{W}}_{\mathit{c}}=45\%$) | ||||

d (cm) | ${\mathit{\rho}}_{\mathit{b}}$ (g cm^{−3}) | d (cm) | ${\mathit{\rho}}_{\mathit{b}}$ (g cm^{−3}) | d (cm) | ${\mathit{\rho}}_{\mathit{b}}$ (g cm^{−3}) | |

gamma detector and GPR | 19.8 (1) | 1.61 (4) | 19.7 (2) | 1.93 (6) | 19.8 (1) | 2.12 (8) |

gamma detector only | 19.17 (4) | 1.48 (11) | 17.6 (12) | 1.5 (18) | 16.83 (16) | 1.5 (18) |

**Table 3.**Estimated depths, densities and radii values for disk sources of varying radii buried in the dry soil at a fixed depth of 12 cm. The values in parentheses are the relative error in percentage.

Actual Values | Estimated Values | ||||
---|---|---|---|---|---|

$\mathit{d}$ (cm) | ${\mathit{\rho}}_{\mathit{b}}$ (g cm^{−3}) | $\mathit{r}$ (cm) | $\mathit{d}$ (cm) | ${\mathit{\rho}}_{\mathit{b}}$ (g cm^{−3}) | $\mathit{r}$ (cm) |

12 | 1.52 | 3 | 10.9 (9) | 1.64 (8) | 6.6 (120) |

12 | 1.52 | 9 | 11.5 (4) | 1.47 (3) | 9.6 (7) |

12 | 1.52 | 15 | 11.6 (3) | 1.43 (6) | 15.1 (1) |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Ukaegbu, I.K.; Gamage, K.A.A.; Aspinall, M.D.
Integration of Ground- Penetrating Radar and Gamma-Ray Detectors for Nonintrusive Characterisation of Buried Radioactive Objects. *Sensors* **2019**, *19*, 2743.
https://doi.org/10.3390/s19122743

**AMA Style**

Ukaegbu IK, Gamage KAA, Aspinall MD.
Integration of Ground- Penetrating Radar and Gamma-Ray Detectors for Nonintrusive Characterisation of Buried Radioactive Objects. *Sensors*. 2019; 19(12):2743.
https://doi.org/10.3390/s19122743

**Chicago/Turabian Style**

Ukaegbu, Ikechukwu K., Kelum A. A. Gamage, and Michael D. Aspinall.
2019. "Integration of Ground- Penetrating Radar and Gamma-Ray Detectors for Nonintrusive Characterisation of Buried Radioactive Objects" *Sensors* 19, no. 12: 2743.
https://doi.org/10.3390/s19122743