Knee model: Comparison between heuristic and rigorous solutions for the Schumann resonance problem
Rapid development of computers allows for application of the direct numerical solution of the global electromagnetic resonance problem in the Earth-ionosphere cavity. Direct numerical solutions exploit the cavity models with the given conductivity profile of atmosphere such as exponential or the kne...
Gespeichert in:
| Veröffentlicht in: | Journal of atmospheric and solar-terrestrial physics 2015-12, Vol.135, p.85-91 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 91 |
|---|---|
| container_issue | |
| container_start_page | 85 |
| container_title | Journal of atmospheric and solar-terrestrial physics |
| container_volume | 135 |
| creator | Galuk, Yu.P. Nickolaenko, A.P. Hayakawa, M. |
| description | Rapid development of computers allows for application of the direct numerical solution of the global electromagnetic resonance problem in the Earth-ionosphere cavity. Direct numerical solutions exploit the cavity models with the given conductivity profile of atmosphere such as exponential or the knee profiles. These profiles are usually derived from the knee model by Mushtak and Williams (2002) developed for obtaining the realistic ELF propagation constant. It is usually forgotten that profiles of the knee model are only a convenient approximate interpretation for the heuristic relations used in computations. We demonstrate that the rigorous full wave solution of the electromagnetic problem for such profiles deviates from that obtained in the knee model. Therefore the direct numerical solutions must also depart from the heuristic one. We evaluate deviations of the heuristic knee model data from those pertinent to equivalent profile of atmospheric conductivity.
•Schumann resonances and ELF waves in the Earth-ionosphere cavity.•Knee profiles of the ionosphere and ELF propagation constant.•A comparison between heuristic and rigorous solutions for the Schumann resonance. |
| doi_str_mv | 10.1016/j.jastp.2015.10.008 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_1778016743</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S1364682615300699</els_id><sourcerecordid>1778016743</sourcerecordid><originalsourceid>FETCH-LOGICAL-c435t-7e0d62d6f0d35722046f235249dc20b5b3f14c062e03a00f91248738d44aebb03</originalsourceid><addsrcrecordid>eNqNkEtP3DAUhaOKSoUpv6AbL9lkev2I46nEAo2gRYzEou3acuybjqPEHuyEin9fD9M1YnWvjs65j6-qvlBYU6Dy67AeTJ4Pawa0KcoaQH2ozqlqNzVVTJyVnktRS8Xkp-oi5wEAWqbkedU9BEQyRYfjN7KN08Ekn2MgHc5_EQPZ41KE2VtigiPJ_4kpLpnkOC6zjyGTPiYy75H8tPtlMiGQhCVvgkVySLEbcfpcfezNmPHyf11Vv-9uf21_1LvH7_fbm11tBW_mukVwkjnZg-NNyxgI2TPeMLFxlkHXdLynwoJkCNwA9BvKhGq5ckIY7Drgq-rqNLfsfVowz3ry2eI4moDlZk3bVhVYreDvsDaUUcG4KlZ-stoUc07Y60Pyk0kvmoI-wteDfoWvj_CPYoFfUtenFJaHnz0mna3HAsX5hHbWLvo38_8AT0iOvA</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1751214238</pqid></control><display><type>article</type><title>Knee model: Comparison between heuristic and rigorous solutions for the Schumann resonance problem</title><source>Elsevier ScienceDirect Journals</source><creator>Galuk, Yu.P. ; Nickolaenko, A.P. ; Hayakawa, M.</creator><creatorcontrib>Galuk, Yu.P. ; Nickolaenko, A.P. ; Hayakawa, M.</creatorcontrib><description>Rapid development of computers allows for application of the direct numerical solution of the global electromagnetic resonance problem in the Earth-ionosphere cavity. Direct numerical solutions exploit the cavity models with the given conductivity profile of atmosphere such as exponential or the knee profiles. These profiles are usually derived from the knee model by Mushtak and Williams (2002) developed for obtaining the realistic ELF propagation constant. It is usually forgotten that profiles of the knee model are only a convenient approximate interpretation for the heuristic relations used in computations. We demonstrate that the rigorous full wave solution of the electromagnetic problem for such profiles deviates from that obtained in the knee model. Therefore the direct numerical solutions must also depart from the heuristic one. We evaluate deviations of the heuristic knee model data from those pertinent to equivalent profile of atmospheric conductivity.
•Schumann resonances and ELF waves in the Earth-ionosphere cavity.•Knee profiles of the ionosphere and ELF propagation constant.•A comparison between heuristic and rigorous solutions for the Schumann resonance.</description><identifier>ISSN: 1364-6826</identifier><identifier>EISSN: 1879-1824</identifier><identifier>DOI: 10.1016/j.jastp.2015.10.008</identifier><language>eng</language><publisher>Elsevier Ltd</publisher><subject>Approximation ; Conductivity profile ; Constants ; Deviation ; Full wave solution ; Global electromagnetic resonance ; Heuristic ; Holes ; Knee model ; Knees ; Mathematical models ; Schumann resonances</subject><ispartof>Journal of atmospheric and solar-terrestrial physics, 2015-12, Vol.135, p.85-91</ispartof><rights>2015</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c435t-7e0d62d6f0d35722046f235249dc20b5b3f14c062e03a00f91248738d44aebb03</citedby><cites>FETCH-LOGICAL-c435t-7e0d62d6f0d35722046f235249dc20b5b3f14c062e03a00f91248738d44aebb03</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S1364682615300699$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3537,27903,27904,65308</link.rule.ids></links><search><creatorcontrib>Galuk, Yu.P.</creatorcontrib><creatorcontrib>Nickolaenko, A.P.</creatorcontrib><creatorcontrib>Hayakawa, M.</creatorcontrib><title>Knee model: Comparison between heuristic and rigorous solutions for the Schumann resonance problem</title><title>Journal of atmospheric and solar-terrestrial physics</title><description>Rapid development of computers allows for application of the direct numerical solution of the global electromagnetic resonance problem in the Earth-ionosphere cavity. Direct numerical solutions exploit the cavity models with the given conductivity profile of atmosphere such as exponential or the knee profiles. These profiles are usually derived from the knee model by Mushtak and Williams (2002) developed for obtaining the realistic ELF propagation constant. It is usually forgotten that profiles of the knee model are only a convenient approximate interpretation for the heuristic relations used in computations. We demonstrate that the rigorous full wave solution of the electromagnetic problem for such profiles deviates from that obtained in the knee model. Therefore the direct numerical solutions must also depart from the heuristic one. We evaluate deviations of the heuristic knee model data from those pertinent to equivalent profile of atmospheric conductivity.
•Schumann resonances and ELF waves in the Earth-ionosphere cavity.•Knee profiles of the ionosphere and ELF propagation constant.•A comparison between heuristic and rigorous solutions for the Schumann resonance.</description><subject>Approximation</subject><subject>Conductivity profile</subject><subject>Constants</subject><subject>Deviation</subject><subject>Full wave solution</subject><subject>Global electromagnetic resonance</subject><subject>Heuristic</subject><subject>Holes</subject><subject>Knee model</subject><subject>Knees</subject><subject>Mathematical models</subject><subject>Schumann resonances</subject><issn>1364-6826</issn><issn>1879-1824</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><recordid>eNqNkEtP3DAUhaOKSoUpv6AbL9lkev2I46nEAo2gRYzEou3acuybjqPEHuyEin9fD9M1YnWvjs65j6-qvlBYU6Dy67AeTJ4Pawa0KcoaQH2ozqlqNzVVTJyVnktRS8Xkp-oi5wEAWqbkedU9BEQyRYfjN7KN08Ekn2MgHc5_EQPZ41KE2VtigiPJ_4kpLpnkOC6zjyGTPiYy75H8tPtlMiGQhCVvgkVySLEbcfpcfezNmPHyf11Vv-9uf21_1LvH7_fbm11tBW_mukVwkjnZg-NNyxgI2TPeMLFxlkHXdLynwoJkCNwA9BvKhGq5ckIY7Drgq-rqNLfsfVowz3ry2eI4moDlZk3bVhVYreDvsDaUUcG4KlZ-stoUc07Y60Pyk0kvmoI-wteDfoWvj_CPYoFfUtenFJaHnz0mna3HAsX5hHbWLvo38_8AT0iOvA</recordid><startdate>201512</startdate><enddate>201512</enddate><creator>Galuk, Yu.P.</creator><creator>Nickolaenko, A.P.</creator><creator>Hayakawa, M.</creator><general>Elsevier Ltd</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7TG</scope><scope>KL.</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope></search><sort><creationdate>201512</creationdate><title>Knee model: Comparison between heuristic and rigorous solutions for the Schumann resonance problem</title><author>Galuk, Yu.P. ; Nickolaenko, A.P. ; Hayakawa, M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c435t-7e0d62d6f0d35722046f235249dc20b5b3f14c062e03a00f91248738d44aebb03</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Approximation</topic><topic>Conductivity profile</topic><topic>Constants</topic><topic>Deviation</topic><topic>Full wave solution</topic><topic>Global electromagnetic resonance</topic><topic>Heuristic</topic><topic>Holes</topic><topic>Knee model</topic><topic>Knees</topic><topic>Mathematical models</topic><topic>Schumann resonances</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Galuk, Yu.P.</creatorcontrib><creatorcontrib>Nickolaenko, A.P.</creatorcontrib><creatorcontrib>Hayakawa, M.</creatorcontrib><collection>CrossRef</collection><collection>Meteorological & Geoastrophysical Abstracts</collection><collection>Meteorological & Geoastrophysical Abstracts - Academic</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Journal of atmospheric and solar-terrestrial physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Galuk, Yu.P.</au><au>Nickolaenko, A.P.</au><au>Hayakawa, M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Knee model: Comparison between heuristic and rigorous solutions for the Schumann resonance problem</atitle><jtitle>Journal of atmospheric and solar-terrestrial physics</jtitle><date>2015-12</date><risdate>2015</risdate><volume>135</volume><spage>85</spage><epage>91</epage><pages>85-91</pages><issn>1364-6826</issn><eissn>1879-1824</eissn><abstract>Rapid development of computers allows for application of the direct numerical solution of the global electromagnetic resonance problem in the Earth-ionosphere cavity. Direct numerical solutions exploit the cavity models with the given conductivity profile of atmosphere such as exponential or the knee profiles. These profiles are usually derived from the knee model by Mushtak and Williams (2002) developed for obtaining the realistic ELF propagation constant. It is usually forgotten that profiles of the knee model are only a convenient approximate interpretation for the heuristic relations used in computations. We demonstrate that the rigorous full wave solution of the electromagnetic problem for such profiles deviates from that obtained in the knee model. Therefore the direct numerical solutions must also depart from the heuristic one. We evaluate deviations of the heuristic knee model data from those pertinent to equivalent profile of atmospheric conductivity.
•Schumann resonances and ELF waves in the Earth-ionosphere cavity.•Knee profiles of the ionosphere and ELF propagation constant.•A comparison between heuristic and rigorous solutions for the Schumann resonance.</abstract><pub>Elsevier Ltd</pub><doi>10.1016/j.jastp.2015.10.008</doi><tpages>7</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1364-6826 |
| ispartof | Journal of atmospheric and solar-terrestrial physics, 2015-12, Vol.135, p.85-91 |
| issn | 1364-6826 1879-1824 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1778016743 |
| source | Elsevier ScienceDirect Journals |
| subjects | Approximation Conductivity profile Constants Deviation Full wave solution Global electromagnetic resonance Heuristic Holes Knee model Knees Mathematical models Schumann resonances |
| title | Knee model: Comparison between heuristic and rigorous solutions for the Schumann resonance problem |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-28T08%3A02%3A34IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Knee%20model:%20Comparison%20between%20heuristic%20and%20rigorous%20solutions%20for%20the%20Schumann%20resonance%20problem&rft.jtitle=Journal%20of%20atmospheric%20and%20solar-terrestrial%20physics&rft.au=Galuk,%20Yu.P.&rft.date=2015-12&rft.volume=135&rft.spage=85&rft.epage=91&rft.pages=85-91&rft.issn=1364-6826&rft.eissn=1879-1824&rft_id=info:doi/10.1016/j.jastp.2015.10.008&rft_dat=%3Cproquest_cross%3E1778016743%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1751214238&rft_id=info:pmid/&rft_els_id=S1364682615300699&rfr_iscdi=true |