{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T13:17:24Z","timestamp":1773839844333,"version":"3.50.1"},"reference-count":47,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2022,10,27]],"date-time":"2022-10-27T00:00:00Z","timestamp":1666828800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Nature Science Foundation of China","award":["62201003"],"award-info":[{"award-number":["62201003"]}]},{"name":"National Nature Science Foundation of China","award":["62271001"],"award-info":[{"award-number":["62271001"]}]},{"name":"National Nature Science Foundation of China","award":["61901274"],"award-info":[{"award-number":["61901274"]}]},{"name":"National Nature Science Foundation of China","award":["U20A20164"],"award-info":[{"award-number":["U20A20164"]}]},{"name":"National Nature Science Foundation of China","award":["61901001"],"award-info":[{"award-number":["61901001"]}]},{"name":"National Nature Science Foundation of China","award":["JCYJ20190808141818890"],"award-info":[{"award-number":["JCYJ20190808141818890"]}]},{"name":"National Nature Science Foundation of China","award":["2020A1515011475"],"award-info":[{"award-number":["2020A1515011475"]}]},{"name":"Shenzhen Science and Technology Innovation Committee","award":["62201003"],"award-info":[{"award-number":["62201003"]}]},{"name":"Shenzhen Science and Technology Innovation Committee","award":["62271001"],"award-info":[{"award-number":["62271001"]}]},{"name":"Shenzhen Science and Technology Innovation Committee","award":["61901274"],"award-info":[{"award-number":["61901274"]}]},{"name":"Shenzhen Science and Technology Innovation Committee","award":["U20A20164"],"award-info":[{"award-number":["U20A20164"]}]},{"name":"Shenzhen Science and Technology Innovation Committee","award":["61901001"],"award-info":[{"award-number":["61901001"]}]},{"name":"Shenzhen Science and Technology Innovation Committee","award":["JCYJ20190808141818890"],"award-info":[{"award-number":["JCYJ20190808141818890"]}]},{"name":"Shenzhen Science and Technology Innovation Committee","award":["2020A1515011475"],"award-info":[{"award-number":["2020A1515011475"]}]},{"name":"Guangdong Natural Science Foundation","award":["62201003"],"award-info":[{"award-number":["62201003"]}]},{"name":"Guangdong Natural Science Foundation","award":["62271001"],"award-info":[{"award-number":["62271001"]}]},{"name":"Guangdong Natural Science Foundation","award":["61901274"],"award-info":[{"award-number":["61901274"]}]},{"name":"Guangdong Natural Science Foundation","award":["U20A20164"],"award-info":[{"award-number":["U20A20164"]}]},{"name":"Guangdong Natural Science Foundation","award":["61901001"],"award-info":[{"award-number":["61901001"]}]},{"name":"Guangdong Natural Science Foundation","award":["JCYJ20190808141818890"],"award-info":[{"award-number":["JCYJ20190808141818890"]}]},{"name":"Guangdong Natural Science Foundation","award":["2020A1515011475"],"award-info":[{"award-number":["2020A1515011475"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Ground penetrating radar (GPR) forward modeling is one of the core geophysical research topics and also the primary task of simulating ground penetrating radar system. It is a process of simulating the propagation laws and characteristics of electromagnetic waves in simulated space when the distribution of internal parameters in the exploration region is known. And the finite-difference-time-domain (FDTD) method has the characteristics of simulating the space-time transient evolution of electromagnetic wave, whose numerical method is simple and easy to program, so it has become one of the most extensively utilized methods in GPR forward modeling. It is generally known that the conventional FDTD approach requires finer uniform Yee cell all the time to produce satisfactory accuracies from numerical simulations of the GPR. However, the smaller temporal incremental has to be adopted due to the lower spatial incremental, which would dramatically weaken the advantage of the FDTD method. To solve this issue, the subgridding-technique-based hybrid local-one-dimensional FDTD (LOD-FDTD) is applied in this work to modeling the classical GPR scenarios. In this method, the unconditional-stable LOD-FDTD is employed in the fine-grid domain, while the traditional FDTD is used in the coarse-grid domain, which could avoid the oversampling problem in the local domain if the uniform fine-grid scheme is adopted. Meanwhile due to the unconditional stability of the LOD-FDTD, the larger time step, derived from the coarse grid which satisfies the Courant-Friedrichs-Lewy (CFL) stability condition, could be utilized in the whole domain so that the long-time interpolation process could be circumvented. Additionally, the proposed approach could be arbitrarily adjusted by means of different ratio of both coarse- and fine-grid, and hence it holds much higher generality. As compared with the auxiliary differential equation (ADE) technique, the Z-transform method is integrated into FDTD methods for modeling multi-pole Debye-based dispersive media in this method, resulting in more direct numerical implementations and fewer computing steps. Finally, three different classical GPR problems are carried out to validate accuracies and efficiencies of the proposed method.<\/jats:p>","DOI":"10.3390\/rs14215393","type":"journal-article","created":{"date-parts":[[2022,10,27]],"date-time":"2022-10-27T22:36:17Z","timestamp":1666910177000},"page":"5393","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Efficacious GPR Implementations of Z-Transform-Based Hybrid LOD-FDTD with Subgridding Scheme: Theoretical Formalism and Numerical Study"],"prefix":"10.3390","volume":"14","author":[{"given":"Guoda","family":"Xie","sequence":"first","affiliation":[{"name":"Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, Anhui University, Hefei 230601, China"},{"name":"Information Materials and Intelligent Sensing Laboratory of Anhui Province, Anhui University, Hefei 230601, China"},{"name":"Laboratory of Target Recognition and Feature Extraction, Lu\u2019an 237000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ziheng","family":"Song","sequence":"additional","affiliation":[{"name":"Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, Anhui University, Hefei 230601, China"},{"name":"Information Materials and Intelligent Sensing Laboratory of Anhui Province, Anhui University, Hefei 230601, China"},{"name":"Laboratory of Target Recognition and Feature Extraction, Lu\u2019an 237000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2175-3282","authenticated-orcid":false,"given":"Guilin","family":"Hou","sequence":"additional","affiliation":[{"name":"Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, Anhui University, Hefei 230601, China"},{"name":"Information Materials and Intelligent Sensing Laboratory of Anhui Province, Anhui University, Hefei 230601, China"},{"name":"Laboratory of Target Recognition and Feature Extraction, Lu\u2019an 237000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ming","family":"Fang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, Anhui University, Hefei 230601, China"},{"name":"Information Materials and Intelligent Sensing Laboratory of Anhui Province, Anhui University, Hefei 230601, China"},{"name":"Laboratory of Target Recognition and Feature Extraction, Lu\u2019an 237000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Naixing","family":"Feng","sequence":"additional","affiliation":[{"name":"Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, Anhui University, Hefei 230601, China"},{"name":"Information Materials and Intelligent Sensing Laboratory of Anhui Province, Anhui University, Hefei 230601, China"},{"name":"Laboratory of Target Recognition and Feature Extraction, Lu\u2019an 237000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhixiang","family":"Huang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, Anhui University, Hefei 230601, China"},{"name":"Information Materials and Intelligent Sensing Laboratory of Anhui Province, Anhui University, Hefei 230601, China"},{"name":"Laboratory of Target Recognition and Feature Extraction, Lu\u2019an 237000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"7671","DOI":"10.1109\/TGRS.2019.2915676","article-title":"Modeling of multilayered media Green\u2019s functions with rough interfaces","volume":"57","author":"Jonard","year":"2019","journal-title":"IEEE Trans. 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