{"id":930,"date":"2023-08-17T08:22:26","date_gmt":"2023-08-17T12:22:26","guid":{"rendered":"https:\/\/wpstaging.whoi.edu\/site\/deeptow\/?page_id=930"},"modified":"2023-10-25T15:34:04","modified_gmt":"2023-10-25T19:34:04","slug":"geomagnetic-reference-field","status":"publish","type":"page","link":"https:\/\/website.whoi.edu\/deeptow\/geomagnetic-reference-field\/","title":{"rendered":"Geomagnetic Reference Field"},"content":{"rendered":"\n\n\t<h1>Geomagnetic Reference Field<\/h1>\n<p>Earth&#8217;s magnetic field can be approximated by a series expansion of orthogonal spherical harmonics. This expansion is an infinite series in terms of coefficients g<sub>n<\/sub><sup>m<\/sup>\u00a0and h<sub>n<\/sub><sup>m<\/sup>\u00a0where m varies from 0 to n and n varies from 1 to infinity. Typically, the series is truncated at n = 10 or more recently n = 12 (i.e. 12 terms). In the spherical coordinate system, the expansion of Earth&#8217;s magnetic field in terms of the magnetic potential, V in spherical harmonics can be written as:<\/p>\n\t\t\t\t<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/website.whoi.edu\/deeptow\/wp-content\/uploads\/sites\/66\/2023\/08\/igrf.gif\" alt=\"Equation\" height=\"50\" width=\"427\" title=\"igrf\" \/>\n\t<p>where R<sub>E<\/sub>\u00a0is the mean radius of the Earth (6371.2 km) and P<sub>n<\/sub><sup>m<\/sup>\u00a0(cos\u00a0<i>\u03b8<\/i>) are the Schmidt quasi-normalized associated Legendre functions where\u00a0<i>\u03b8<\/i>\u00a0is the colatitude (90-latitude) and\u00a0<i>\u03c6<\/i>\u00a0is the longitude. Schmidt (1934) introduced the following normalization constant for the associated Legendre function\u00a0<b>P<sub>n<\/sub><sup>m<\/sup>(x)<\/b>:<\/p>\n\t\t\t\t<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/website.whoi.edu\/deeptow\/wp-content\/uploads\/sites\/66\/2023\/08\/leg1.gif\" alt=\"Equation 2\" height=\"95\" width=\"251\" title=\"leg1\" \/>\n\t<p>The associated Legendre function becomes:<\/p>\n\t\t\t\t<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/website.whoi.edu\/deeptow\/wp-content\/uploads\/sites\/66\/2023\/08\/leg2.jpg\" alt=\"Equation 3\" height=\"105\" width=\"431\" title=\"leg2\" \/>\n\t\n\t\t\t\t<a href=\"https:\/\/website.whoi.edu\/deeptow\/wp-content\/uploads\/sites\/66\/2023\/08\/fld2005c.jpg\" target=\"_self\" rel=\"noopener\">\n\t\t\t\t<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/website.whoi.edu\/deeptow\/wp-content\/uploads\/sites\/66\/2023\/08\/fld2005c.jpg\" alt=\"Geomagnetic field intensity for epoch 2005\" height=\"1275\" width=\"1650\" title=\"fld2005c\" \/>\n\t\t\t\t<\/a>\n\t\t\t\t<a href=\"https:\/\/website.whoi.edu\/deeptow\/wp-content\/uploads\/sites\/66\/2023\/08\/inc2005c-scaled.jpg\" target=\"_self\" rel=\"noopener\">\n\t\t\t\t<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/website.whoi.edu\/deeptow\/wp-content\/uploads\/sites\/66\/2023\/08\/inc2005c-scaled.jpg\" alt=\"Geomagnetic field direction (inclination or angle from vertical) for epoch 2005.\" height=\"1978\" width=\"2560\" title=\"inc2005c\" \/>\n\t\t\t\t<\/a>\n\t\t\t\t<a href=\"https:\/\/website.whoi.edu\/deeptow\/wp-content\/uploads\/sites\/66\/2023\/08\/dec2005c-1-scaled.jpg\" target=\"_self\" rel=\"noopener\">\n\t\t\t\t<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/website.whoi.edu\/deeptow\/wp-content\/uploads\/sites\/66\/2023\/08\/dec2005c-1-scaled.jpg\" alt=\"Declination 2005\" height=\"1978\" width=\"2560\" title=\"dec2005c (1)\" \/>\n\t\t\t\t<\/a>\n\t<h4>References<\/h4>\n<p>Cain, J. C., S. J. Hendricks, R. A. Langel, and W. V. Hudson, A proposed model for the international geomagnetic reference field-1965, J. Geomag. Geoelectr., 19, 335-355, 1967.<\/p>\n<p>Campbell, W., Introduction to geomagnetic fields, Cambridge University Press, Cambridge, 1997.<\/p>\n<p>Chapman, S. and J. Bartels, Geomagnetism, 2 vols., pp 1049, Oxford University Press, London, 1940.<\/p>\n<p>Langel, R. A., Main Field, Chapter Four in Geomagnetism, ed. J. A. Jacobs, Academic Press, London, 1987.<\/p>\n<p>Maus, S. et al., The 10th generation International Geomagnetic Reference Field, Geophys J. Int., 161, 561-565, 2005.<\/p>\n<p>Peddie, N. W., International Geomagnetic Reference Field: The Third Generation, J. Geomag. Geoelectr., 34, pp. 309-326, 1985.<\/p>\n<p>Schmidt, A., Der magnetische mittlepunkt de erde und seine Bedeutung, Gerlands Beitr. Geophys., 41, 346-358, 1934.<\/p>\n\n","protected":false},"excerpt":{"rendered":"<p>Geomagnetic Reference Field Earth&#8217;s magnetic field can be approximated by a series expansion of orthogonal spherical harmonics. This expansion is an infinite series in terms of coefficients gnm\u00a0and hnm\u00a0where m varies from 0 to n and n varies from 1 to infinity. Typically, the series is truncated at n = 10 or more recently n&hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_relevanssi_hide_post":"","_relevanssi_hide_content":"","_relevanssi_pin_for_all":"","_relevanssi_pin_keywords":"","_relevanssi_unpin_keywords":"","_relevanssi_related_keywords":"","_relevanssi_related_include_ids":"","_relevanssi_related_exclude_ids":"","_relevanssi_related_no_append":"","_relevanssi_related_not_related":"","_relevanssi_related_posts":"","_relevanssi_noindex_reason":""},"_links":{"self":[{"href":"https:\/\/website.whoi.edu\/deeptow\/wp-json\/wp\/v2\/pages\/930"}],"collection":[{"href":"https:\/\/website.whoi.edu\/deeptow\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/website.whoi.edu\/deeptow\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/website.whoi.edu\/deeptow\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/website.whoi.edu\/deeptow\/wp-json\/wp\/v2\/comments?post=930"}],"version-history":[{"count":3,"href":"https:\/\/website.whoi.edu\/deeptow\/wp-json\/wp\/v2\/pages\/930\/revisions"}],"predecessor-version":[{"id":1079,"href":"https:\/\/website.whoi.edu\/deeptow\/wp-json\/wp\/v2\/pages\/930\/revisions\/1079"}],"wp:attachment":[{"href":"https:\/\/website.whoi.edu\/deeptow\/wp-json\/wp\/v2\/media?parent=930"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}