{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T03:14:44Z","timestamp":1775445284512,"version":"3.50.1"},"reference-count":77,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,2,16]],"date-time":"2021-02-16T00:00:00Z","timestamp":1613433600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000848","name":"University of Edinburgh","doi-asserted-by":"publisher","award":["unknown"],"award-info":[{"award-number":["unknown"]}],"id":[{"id":"10.13039\/501100000848","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Estimating the permittivity of heterogeneous mixtures based on the permittivity of their components is of high importance with many applications in ground penetrating radar (GPR) and in electrodynamics-based sensing in general. Complex Refractive Index Model (CRIM) is the most mainstream approach for estimating the bulk permittivity of heterogeneous materials and has been widely applied for GPR applications. The popularity of CRIM is primarily based on its simplicity while its accuracy has never been rigorously tested. In the current study, an optimised shape factor is derived that is fine-tuned for modelling the dielectric properties of concrete. The bulk permittivity of concrete is expressed with respect to its components i.e., aggregate particles, cement particles, air-voids and volumetric water fraction. Different combinations of the above materials are accurately modelled using the Finite-Difference Time-Domain (FDTD) method. The numerically estimated bulk permittivity is then used to fine-tune the shape factor of the CRIM model. Then, using laboratory measurements it is shown that the revised CRIM model over-performs the default shape factor and provides with more accurate estimations of the bulk permittivity of concrete.<\/jats:p>","DOI":"10.3390\/rs13040723","type":"journal-article","created":{"date-parts":[[2021,2,16]],"date-time":"2021-02-16T22:13:38Z","timestamp":1613513618000},"page":"723","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Optimising the Complex Refractive Index Model for Estimating the Permittivity of Heterogeneous Concrete Models"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4466-1164","authenticated-orcid":false,"given":"Hossain","family":"Zadhoush","sequence":"first","affiliation":[{"name":"School of Engineering, Institute for Infrastructure and Environment, The University of Edinburgh, Edinburgh EH8 9YL, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7108-6997","authenticated-orcid":false,"given":"Antonios","family":"Giannopoulos","sequence":"additional","affiliation":[{"name":"School of Engineering, Institute for Infrastructure and Environment, The University of Edinburgh, Edinburgh EH8 9YL, UK"}]},{"given":"Iraklis","family":"Giannakis","sequence":"additional","affiliation":[{"name":"School of Geosciences, University of Aberdeen, Aberdeen AB24 3UE, UK"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Daniels, D.J. (2005). Ground Penetrating Radar, The University of Michigan. [2nd ed.].","DOI":"10.1002\/0471654507.eme152"},{"key":"ref_2","unstructured":"Jol, H.M. (2008). Ground pEnetrating Radar Theory and Applications, Elsevier."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Annan, A. (2005). Ground-penetrating radar. Near-Surface Geophysics, Society of Exploration Geophysicists.","DOI":"10.1190\/1.9781560801719.ch11"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1542","DOI":"10.1109\/LGRS.2013.2261796","article-title":"Material classification of underground utilities from GPR images using DCT-based SVM approach","volume":"10","author":"Hashim","year":"2013","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_5","first-page":"49","article-title":"GPR surveying method as a tool for geodetic verification of GESUT database of utilities in the light of BSI PAS128","volume":"107","author":"Kryszyn","year":"2019","journal-title":"Rep. Geod. Geoinform."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Kang, M.S., Kim, N., Im, S.B., Lee, J.J., and An, Y.K. (2019). 3D GPR Image-based UcNet for Enhancing Underground Cavity Detectability. Remote Sens., 11.","DOI":"10.3390\/rs11212545"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/S0926-9851(99)00052-X","article-title":"Road evaluation with ground penetrating radar","volume":"43","author":"Saarenketo","year":"2000","journal-title":"J. Appl. Geophys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/S0926-9851(02)00242-2","article-title":"Evaluation of tunnel stability using integrated geophysical methods","volume":"52","author":"Cardarelli","year":"2003","journal-title":"J. Appl. Geophys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/S0950-0618(02)00015-6","article-title":"Concrete bridge inspection with a mobile GPR system","volume":"16","author":"Hugenschmidt","year":"2002","journal-title":"Constr. Build. Mater."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"384","DOI":"10.1016\/j.cemconcomp.2006.02.016","article-title":"GPR inspection of concrete bridges","volume":"28","author":"Hugenschmidt","year":"2006","journal-title":"Cem. Concr. Compos."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"121","DOI":"10.2113\/JEEG22.2.121","article-title":"Concrete bridge deck deterioration assessment using ground penetrating radar (GPR)","volume":"22","author":"Diamanti","year":"2017","journal-title":"J. Environ. Eng. Geophys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1061\/(ASCE)0899-1561(2003)15:3(287)","article-title":"Nondestructive evaluation of concrete infrastructure with ground penetrating radar","volume":"15","author":"Maierhofer","year":"2003","journal-title":"J. Mater. Civ. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"034002","DOI":"10.1088\/1742-2132\/10\/3\/034002","article-title":"GPR identification of voids inside concrete based on the support vector machine algorithm","volume":"10","author":"Xie","year":"2013","journal-title":"J. Geophys. Eng."},{"key":"ref_14","unstructured":"Giannakis, I., Giannopoulos, A., and Davidson, N. (July, January 30). Realistic modelling of ground penetrating radar for landmine detection using FDTD. Proceedings of the 15th International Conference on Ground Penetrating Radar, Brussels, Belgium."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1057","DOI":"10.1016\/j.conbuildmat.2008.05.018","article-title":"Measurement radius of reinforcing steel bar in concrete using digital image GPR","volume":"23","author":"Chang","year":"2009","journal-title":"Constr. Build. Mater."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/j.conbuildmat.2014.12.030","article-title":"Non-destructive evaluation of moisture content of wood material at GPR frequency","volume":"77","author":"Mai","year":"2015","journal-title":"Constr. Build. Mater."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/j.csndt.2015.03.002","article-title":"Evaluating asphalt concrete air void variation via GPR antenna array data","volume":"3","author":"Hoegh","year":"2015","journal-title":"Case Stud. Nondestr. Test. Eval."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1080\/1029843021000041140","article-title":"Effects of asphalt pavement properties on complex permittivity","volume":"3","author":"Shang","year":"2002","journal-title":"Int. J. Pavement Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1016\/j.ndteint.2008.01.001","article-title":"GPR evaluation of the damage found in the reinforced concrete base of a block of flats: A case study","volume":"41","author":"Abad","year":"2008","journal-title":"NDT e Int."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"621","DOI":"10.1016\/j.ndteint.2008.03.011","article-title":"Evaluation of dielectric properties of concrete by a numerical FDTD model of a GPR coupled antenna\u2014parametric study","volume":"41","author":"Klysz","year":"2008","journal-title":"NDT e Int."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/S0950-0618(97)00033-0","article-title":"Analytical modelling of the dielectric properties of concrete for subsurface radar applications","volume":"11","author":"Tsui","year":"1997","journal-title":"Constr. Build. Mater."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"205410","DOI":"10.1088\/0022-3727\/41\/20\/205410","article-title":"Application of Jonscher model for the characterization of the dielectric permittivity of concrete","volume":"41","author":"Bourdi","year":"2008","journal-title":"J. Phys. D Appl. Phys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"405401","DOI":"10.1088\/0022-3727\/45\/40\/405401","article-title":"Modelling dielectric-constant values of concrete: An aid to shielding effectiveness prediction and ground-penetrating radar wave technique interpretation","volume":"45","author":"Bourdi","year":"2012","journal-title":"J. Phys. D Appl. Phys."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"489","DOI":"10.2113\/JEEG23.4.489","article-title":"Measurement of bulk electrical properties using GPR with a variable reflector","volume":"23","author":"Redman","year":"2018","journal-title":"J. Environ. Eng. Geophys."},{"key":"ref_25","unstructured":"B\u00f6ttcher, C.J.F. (1952). Theory Electric Polarisation, Elsevier Publishing Company."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Sihvola, A.H. (1999). Electromagnetic Mixing Formulas and Applications, IET Digital Library.","DOI":"10.1049\/PBEW047E"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"19","DOI":"10.3141\/2152-03","article-title":"In-place hot-mix asphalt density estimation using ground-penetrating radar","volume":"2152","author":"Leng","year":"2010","journal-title":"Transp. Res. Rec."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1109\/PROC.1974.9388","article-title":"High dielectric constant microwave probes for sensing soil moisture","volume":"62","author":"Birchak","year":"1974","journal-title":"Proc. IEEE"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1080\/14786449208620364","article-title":"LVI. On the influence of obstacles arranged in rectangular order upon the properties of a medium","volume":"34","author":"Rayleigh","year":"1892","journal-title":"Lond. Edinb. Dublin Philos. Mag. J. Sci."},{"key":"ref_30","unstructured":"B\u00f6ttcher, C.J.F., van Belle, O.C., Bordewijk, P., and Rip, A. (1978). Theor. electr. Polarization, Elsevier Science Ltd."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Brown, W.F., Franz, W., and Forsbergh, P. (1956). Dielectrics\/Dielektrika. Handbuch der Physik, Springer.","DOI":"10.1007\/978-3-642-45841-5"},{"key":"ref_32","first-page":"83","article-title":"Physik, 40, 817 (1913)","volume":"3","author":"Wagner","year":"1914","journal-title":"Arch. Elektroteeh"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"636","DOI":"10.1002\/andp.19354160705","article-title":"Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizit\u00e4tskonstanten und Leitf\u00e4higkeiten der Mischk\u00f6rper aus isotropen Substanzen","volume":"416","author":"Bruggeman","year":"1935","journal-title":"Annalen der physik"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"574","DOI":"10.1029\/WR016i003p00574","article-title":"Electromagnetic determination of soil water content: Measurements in coaxial transmission lines","volume":"16","author":"Topp","year":"1980","journal-title":"Water Resour. Res."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/j.cpc.2016.08.020","article-title":"gprMax: Open source software to simulate electromagnetic wave propagation for Ground Penetrating Radar","volume":"209","author":"Warren","year":"2016","journal-title":"Comput. Phys. Commun."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1016\/j.cpc.2018.11.007","article-title":"A CUDA-based GPU engine for gprMax: Open source FDTD electromagnetic simulation software","volume":"237","author":"Warren","year":"2019","journal-title":"Comput. Phys. Commun."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Taflove, A., and Hagness, S.C. (2005). Computational Electromagnetics: The Finite-Difference Time-Domain Method, Artech House Publishers. [3rd ed.].","DOI":"10.1002\/0471654507.eme123"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1109\/TAP.1966.1138693","article-title":"Numerical solution of initial boundary value problems involving Maxwell\u2019s equations in isotropic media","volume":"14","author":"Yee","year":"1966","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Sadiku, M.N. (2000). Numerical Techniques in Electromagnetics, CRC press.","DOI":"10.1201\/9781420058277"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"5","DOI":"10.3997\/1873-0604.2006014","article-title":"A review of practical numerical modelling methods for the advanced interpretation of ground-penetrating radar in near-surface environments","volume":"5","author":"Cassidy","year":"2007","journal-title":"Near Sur. Geophys."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1016\/j.jappgeo.2008.09.009","article-title":"The application of finite-difference time-domain modelling for the assessment of GPR in magnetically lossy materials","volume":"67","author":"Cassidy","year":"2009","journal-title":"J. Appl. Geophys."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1109\/JSTARS.2015.2468597","article-title":"A realistic FDTD numerical modeling framework of ground penetrating radar for landmine detection","volume":"9","author":"Giannakis","year":"2016","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1983","DOI":"10.1109\/TAP.2004.832501","article-title":"Modeling and investigation of a geometrically complex UWB GPR antenna using FDTD","volume":"52","author":"Lee","year":"2004","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1163\/156939306775777224","article-title":"Modeling and investigation of planar parabolic dipoles for GPR applications: A comparison with bow-tie using FDTD","volume":"20","author":"Uduwawala","year":"2006","journal-title":"J. Electomagn. Waves Appl."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1768","DOI":"10.1109\/TGRS.2018.2869027","article-title":"Realistic FDTD GPR antenna models optimized using a novel linear\/nonlinear Full-Waveform Inversion","volume":"57","author":"Giannakis","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1109\/36.481890","article-title":"A fully three-dimensional simulation of a ground-penetrating radar: FDTD theory compared with experiment","volume":"34","author":"Bourgeois","year":"1996","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_47","unstructured":"Klysz, G., Balayssac, J., Laurens, S., and Ferrieres, X. (2004, January 21\u201324). Numerical FDTD simulation of the direct wave propagation of a GPR coupled antenna. Proceedings of the Tenth International Conference on Grounds Penetrating Radar, Delft, The Netherlands."},{"key":"ref_48","unstructured":"Caratelli, D., Yarovoy, A., and Ligthart, L.P. (2009, January 23\u201327). Accurate FDTD modelling of resistively-loaded bow-tie antennas for GPR applications. Proceedings of the 2009 3rd European Conference on Antennas and Propagation, Berlin, Germany."},{"key":"ref_49","unstructured":"Bourgeois, J., and Smith, G. (1997, January 13\u201318). A complete electromagnetic simulation of a ground penetrating radar for mine detection: Theory and experiment. Proceedings of the IEEE Antennas and Propagation Society International Symposium 1997, Montreal, QC, Canada."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/S0926-9851(02)00241-0","article-title":"Near-field dipole radiation dynamics through FDTD modeling","volume":"52","author":"Radzevicius","year":"2003","journal-title":"J. Appl. Geophys."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/j.jappgeo.2013.08.001","article-title":"Characterizing the energy distribution around GPR antennas","volume":"99","author":"Diamanti","year":"2013","journal-title":"J. Appl. Geophys."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"K23","DOI":"10.1190\/1.1926574","article-title":"Resistively loaded antennas for ground-penetrating radar: A modeling approach","volume":"70","author":"Lampe","year":"2005","journal-title":"Geophysics"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"1318","DOI":"10.1109\/TAP.2004.827510","article-title":"Numerical modeling of ultrawide-band dielectric horn antennas using FDTD","volume":"52","author":"Venkatarayalu","year":"2004","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Turk, A.S., Sahinkaya, D.A., Sezgin, M., and Nazli, H. (2007, January 27\u201329). Investigation of convenient antenna designs for ultra-wide band GPR systems. Proceedings of the 2007 4th International Workshop on, Advanced Ground Penetrating Radar, Aula Magna Partenope, Italy.","DOI":"10.1109\/AGPR.2007.386550"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"G37","DOI":"10.1190\/1.3548506","article-title":"Creating finite-difference time-domain models of commercial ground-penetrating radar antennas using Taguchi\u2019s optimization method","volume":"76","author":"Warren","year":"2011","journal-title":"Geophysics"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/S0926-9851(98)00009-3","article-title":"Dielectric permittivity of concrete between 50 MHz and 1 GHz and GPR measurements for building materials evaluation","volume":"40","author":"Robert","year":"1998","journal-title":"J. Appl. Geophys."},{"key":"ref_57","first-page":"78","article-title":"Analysis of total chloride content in concrete","volume":"3","year":"2015","journal-title":"Case Stu. Constr. Mater."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"827","DOI":"10.1007\/BF02481655","article-title":"Non-destructive evaluation of concrete moisture by GPR: Experimental study and direct modeling","volume":"38","author":"Laurens","year":"2005","journal-title":"Mater. Struct."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1016\/j.cemconres.2017.04.006","article-title":"Transport properties of concrete after drying-wetting regimes to elucidate the effects of moisture content, hysteresis and microcracking","volume":"98","author":"Wu","year":"2017","journal-title":"Cem. Concr. Res."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1680\/adcr.1998.10.4.187","article-title":"The permittivity and conductivity of concretes at ground-penetrating radar frequencies","volume":"10","author":"Shaw","year":"1998","journal-title":"Adv. Cem. Res."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1016\/S0963-8695(01)00009-3","article-title":"Dielectric properties of concrete and their influence on radar testing","volume":"34","author":"Soutsos","year":"2001","journal-title":"NDT e Int."},{"key":"ref_62","doi-asserted-by":"crossref","unstructured":"Terrasse, G., Nicolas, J.M., Trouv\u00e9, E., and Drouet, \u00c9. (September, January 29). Automatic localization of gas pipes from GPR imagery. Proceedings of the 2016 24th European Signal Processing Conference (EUSIPCO), Budapest, Hungary.","DOI":"10.1109\/EUSIPCO.2016.7760678"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1007\/s11220-006-0024-5","article-title":"A review of GPR for landmine detection","volume":"7","author":"Daniels","year":"2006","journal-title":"Sens. Imaging Int. J."},{"key":"ref_64","unstructured":"Brown, E. Density of asphalt concrete-how much is needed? In Proceedings of the 69th Annual Meeting of the TransportationResearch Board, Washington, DC, USA, 8\u20139 January 1990."},{"key":"ref_65","unstructured":"Yelf, R. (2004, January 21\u201324). Where is true time zero?. Proceedings of the Tenth International Conference on Grounds Penetrating Radar, Delft, The Netherlands."},{"key":"ref_66","unstructured":"Zadhoush, H. (2020). Numerical modelling of ground penetrating radar for optimisation of the time-zero adjustment and complex refractive index model. [Ph.D. Thesis, The University of Edinburgh]."},{"key":"ref_67","doi-asserted-by":"crossref","unstructured":"Warren, C., and Giannopoulos, A. (2012, January 4\u20138). Investigation of the directivity of a commercial ground-penetrating radar antenna using a finite-difference time-domain antenna model. Proceedings of the 2012 14th International Conference on Ground Penetrating Radar (GPR), Shanghai, China.","DOI":"10.1109\/ICGPR.2012.6254865"},{"key":"ref_68","first-page":"8","article-title":"Paraview: An end-user tool for large data visualization","volume":"717","author":"Ahrens","year":"2005","journal-title":"Vis. Handb."},{"key":"ref_69","doi-asserted-by":"crossref","unstructured":"Lachowicz, J., and Rucka, M. (2017, January 28\u201330). A concept of heterogeneous numerical model of concrete for GPR simulations. Proceedings of the 2017 9th International Workshop on Advanced Ground Penetrating Radar (IWAGPR), Edinburgh, UK.","DOI":"10.1109\/IWAGPR.2017.7996032"},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/j.cemconres.2009.09.012","article-title":"Influence of aggregate size and volume fraction on shrinkage induced micro-cracking of concrete and mortar","volume":"40","author":"Grassl","year":"2010","journal-title":"Cem. Concr. Res."},{"key":"ref_71","first-page":"425","article-title":"Aggregate stability and size distribution","volume":"5","author":"Kemper","year":"1986","journal-title":"Methods Soil Anal. Part I Phys. Mineral. Methods"},{"key":"ref_72","unstructured":"Jury, W.A., and Horton, R. (2004). Soil Physics, John Wiley & Sons."},{"key":"ref_73","doi-asserted-by":"crossref","unstructured":"Ukaegbu, I.K., Gamage, K.A., and Aspinall, M.D. (2019). Nonintrusive Depth Estimation of Buried Radioactive Wastes Using Ground Penetrating Radar and a Gamma Ray Detector. Remote Sens., 11.","DOI":"10.3390\/rs11020141"},{"key":"ref_74","first-page":"2267","article-title":"Calibration of time domain reflectometry for water content measurement using a composite dielectric approach","volume":"26","author":"Roth","year":"1990","journal-title":"Water Resour. Res."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1006\/jaer.1998.0338","article-title":"Soil water content measurement with a high-frequency capacitance sensor","volume":"71","author":"Gardner","year":"1998","journal-title":"J. Agric. Eng. Res."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1109\/TGRS.1985.289498","article-title":"Microwave dielectric behavior of wet soil-Part II: Dielectric mixing models","volume":"GE-23","author":"Dobson","year":"1985","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"803","DOI":"10.1109\/36.387598","article-title":"Dielectric properties of soils in the 0.3-1.3-GHz range","volume":"33","author":"Peplinski","year":"1995","journal-title":"IEEE Trans. Geosci. Remote Sens."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/4\/723\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:24:54Z","timestamp":1760160294000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/4\/723"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,16]]},"references-count":77,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2021,2]]}},"alternative-id":["rs13040723"],"URL":"https:\/\/doi.org\/10.3390\/rs13040723","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,2,16]]}}}