{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:05:44Z","timestamp":1760148344898,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,4,23]],"date-time":"2023-04-23T00:00:00Z","timestamp":1682208000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&amp;D Program of China","award":["2022YFF0706200","XDA14050300","41874088"],"award-info":[{"award-number":["2022YFF0706200","XDA14050300","41874088"]}]},{"name":"Strategic Priority Research Program of the Chinese Academy of Sciences","award":["2022YFF0706200","XDA14050300","41874088"],"award-info":[{"award-number":["2022YFF0706200","XDA14050300","41874088"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2022YFF0706200","XDA14050300","41874088"],"award-info":[{"award-number":["2022YFF0706200","XDA14050300","41874088"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The controlled source extremely low frequency (CSELF) method bears the potential for deep resource exploitation utilizing the skywave. The \u201cSkywave\u201d denotes the electromagnetic wave propagating through the waveguide formed by the Earth and ionosphere. It has a considerable penetration depth into the lithosphere due to its low-frequency band. Previous research on extremely low-frequency electromagnetic fields with the coupled lithosphere, atmosphere, and planar ionosphere models ignored the effect of the Earth\u2019s curvature. Thus, we aimed to present the exact formulas for horizontal electric dipoles (HED) in a spherical \u201cEarth-ionosphere\u201d model. These new formulas consider the Earth\u2019s curvature as a multilayer medium rather than a homogeneous underground. We introduce three techniques: function combination pairs, addition and subtraction terms, and Pad\u00e9 approximants, to handle slow convergence in numerical calculation. In the spherical waveguide, electromagnetic fields are mutually interfered with and produce oscillations, which is different from the planar model. The influence of Earth\u2019s curvature cannot be neglected with the increase in source\u2013receiver distance, though it is negligible within 3000 km. Furthermore, it is worth noting that apparent resistivity \u03c1\u03b8\u03c6 enters the waveguide area earlier than \u03c1\u03c6\u03b8. This method can be used as Green\u2019s function to simulate the electromagnetic field of actual antennas and 3-D models.<\/jats:p>","DOI":"10.3390\/rs15092235","type":"journal-article","created":{"date-parts":[[2023,4,24]],"date-time":"2023-04-24T02:06:11Z","timestamp":1682301971000},"page":"2235","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Electromagnetic Field of a HED in the Spherical \u201cEarth-Ionosphere\u201d Model and Its Application in Geophysics"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0306-6825","authenticated-orcid":false,"given":"Ya","family":"Gao","sequence":"first","affiliation":[{"name":"CAS Engineering Laboratory for Deep Resources Equipment and Technology, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8055-6225","authenticated-orcid":false,"given":"Qing-Yun","family":"Di","sequence":"additional","affiliation":[{"name":"CAS Engineering Laboratory for Deep Resources Equipment and Technology, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China"},{"name":"Innovation Academy for Earth Science, Chinese Academy of Sciences, Beijing 100029, China"},{"name":"College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0368-0238","authenticated-orcid":false,"given":"Chang-Min","family":"Fu","sequence":"additional","affiliation":[{"name":"CAS Engineering Laboratory for Deep Resources Equipment and Technology, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China"},{"name":"Innovation Academy for Earth Science, Chinese Academy of Sciences, Beijing 100029, China"},{"name":"College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"given":"Yi-Lang","family":"Zhang","sequence":"additional","affiliation":[{"name":"CAS Engineering Laboratory for Deep Resources Equipment and Technology, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China"},{"name":"Innovation Academy for Earth Science, Chinese Academy of Sciences, Beijing 100029, China"},{"name":"College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing 100049, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"401","DOI":"10.6028\/jres.065D.051","article-title":"On the theory of mixed-path ground-wave propagation on a spherical earth","volume":"65","author":"Wait","year":"1961","journal-title":"J. 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