{"id":916,"date":"2023-08-16T11:48:47","date_gmt":"2023-08-16T15:48:47","guid":{"rendered":"https:\/\/wpstaging.whoi.edu\/site\/deeptow\/?page_id=916"},"modified":"2023-10-25T15:34:43","modified_gmt":"2023-10-25T19:34:43","slug":"the-eccentric-dipole-model","status":"publish","type":"page","link":"https:\/\/website.whoi.edu\/deeptow\/the-eccentric-dipole-model\/","title":{"rendered":"The Eccentric Dipole Model"},"content":{"rendered":"\n\n\t<h1>The Eccentric Dipole Model<\/h1>\n\t<p>The Eccentric Dipole (ED) model of Earth&#8217;s magnetic field is an attempt to get a better approximation Earth&#8217;s geomagnetic pole locations compared to the simple dipole (i.e. bar magnet) approximation of the\u00a0<a href=\"https:\/\/website.whoi.edu\/deeptow\/the-centered-dipole-model\/\">centered dipole approach<\/a>. The eccentric dipole approximation acknowledges that the field is slightly offset from the Earth&#8217;s spin axis although it retains a dipolar character. The eccentric dipole model uses the first 8 terms of the\u00a0<a href=\"https:\/\/website.whoi.edu\/deeptow\/geomagnetic-reference-field\/\">spherical harmonic expansion<\/a>\u00a0(i.e. the Gauss coefficients up to degree 2) of the International Geomagnetic Reference Field (IGRF). These are the g<sub>1<\/sub><sup>0<\/sup>, g<sub>1<\/sub><sup>1<\/sup>, h<sub>1<\/sub><sup>1<\/sup>, g<sub>2<\/sub><sup>0<\/sup>, g<sub>2<\/sub><sup>1<\/sup>, h<sub>2<\/sub><sup>1<\/sup>, g<sub>2<\/sub><sup>2<\/sup>, h<sub>2<\/sub><sup>2<\/sup>\u00a0terms. Two different types of poles can be calculated: an eccentric dipole axial pole which is where the axis of the dipole intersects the Earth&#8217;s surface and\u00a0<a href=\"https:\/\/website.whoi.edu\/deeptow\/wp-content\/uploads\/sites\/66\/2023\/08\/northpole_eddip-scaled.jpg\">an eccentric dipole &#8216;dip&#8217; pole<\/a>\u00a0where the field is vertical at Earth&#8217;s surface. See Fraser-Smith, (1987) for a full explanation. See also background information on spherical harmonics on\u00a0<a href=\"https:\/\/www.spenvis.oma.be\/help\/background\/magfield\/cd.html\">the Space Environment Information System\u00a0<\/a>operated by the European Space Agency.<\/p>\n\t\t\t\t<a href=\"https:\/\/website.whoi.edu\/deeptow\/wp-content\/uploads\/sites\/66\/2023\/08\/northpole_ed-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\/northpole_ed-scaled.jpg\" alt=\"Geomagnetic Eccentric Axial Dipole North Pole\" height=\"1978\" width=\"2560\" title=\"northpole_ed\" \/>\n\t\t\t\t<\/a>\n\t<p>The following table lists the calculated Eccentric Dipole (ED) axial pole and dip pole locations for the North Magnetic Pole (NMP). Epochs 1600 through 1800 are from Barraclough (1974) the remainder are calculated from the DGRF\/IGRF models.<\/p>\n\n<table id=\"tablepress-4\" class=\"tablepress tablepress-id-4 tablepress-responsive\">\n<thead>\n<tr class=\"row-1 odd\">\n\t<th class=\"column-1\">      <\/th><th class=\"column-2\"><h3>ED Axial Pole<\/h3><\/th><th class=\"column-3\"><\/th><th class=\"column-4\"><h3>ED Dip Pole<\/h3><\/th><th class=\"column-5\"><\/th>\n<\/tr>\n<\/thead>\n<tbody class=\"row-hover\">\n<tr class=\"row-2 even\">\n\t<td class=\"column-1\"><strong>Year<\/strong><\/td><td class=\"column-2\"><strong>\tED Axial Latitude (\u00b0N)<\/strong><\/td><td class=\"column-3\"><strong>ED Axial Longitude (\u00b0E)<\/strong><\/td><td class=\"column-4\"><strong>ED Dip Latitude (\u00b0N)<\/strong><\/td><td class=\"column-5\"><strong>ED Dip Longitude (\u00b0E)<\/strong><\/td>\n<\/tr>\n<tr class=\"row-3 odd\">\n\t<td class=\"column-1\"> 1600 <\/td><td class=\"column-2\">83.2<\/td><td class=\"column-3\">301.2<\/td><td class=\"column-4\">82.3<\/td><td class=\"column-5\">267.2<\/td>\n<\/tr>\n<tr class=\"row-4 even\">\n\t<td class=\"column-1\"> 1700 <\/td><td class=\"column-2\">81.9<\/td><td class=\"column-3\">296.5<\/td><td class=\"column-4\">80.6<\/td><td class=\"column-5\">263.3<\/td>\n<\/tr>\n<tr class=\"row-5 odd\">\n\t<td class=\"column-1\"> 1800 <\/td><td class=\"column-2\">79.2<\/td><td class=\"column-3\">291.0<\/td><td class=\"column-4\">78.5<\/td><td class=\"column-5\">268.7<\/td>\n<\/tr>\n<tr class=\"row-6 even\">\n\t<td class=\"column-1\"> 1900 <\/td><td class=\"column-2\">80.06<\/td><td class=\"column-3\">277.76<\/td><td class=\"column-4\">81.07<\/td><td class=\"column-5\">241.07<\/td>\n<\/tr>\n<tr class=\"row-7 odd\">\n\t<td class=\"column-1\"> 1950 <\/td><td class=\"column-2\">80.90<\/td><td class=\"column-3\">275.85<\/td><td class=\"column-4\">82.39<\/td><td class=\"column-5\">224.31<\/td>\n<\/tr>\n<tr class=\"row-8 even\">\n\t<td class=\"column-1\"> 1960 <\/td><td class=\"column-2\">81.17<\/td><td class=\"column-3\">274.67<\/td><td class=\"column-4\">82.64<\/td><td class=\"column-5\">218.93<\/td>\n<\/tr>\n<tr class=\"row-9 odd\">\n\t<td class=\"column-1\"> 1970 <\/td><td class=\"column-2\">81.40<\/td><td class=\"column-3\">273.18<\/td><td class=\"column-4\">82.70<\/td><td class=\"column-5\">214.25<\/td>\n<\/tr>\n<tr class=\"row-10 even\">\n\t<td class=\"column-1\"> 1975 <\/td><td class=\"column-2\">81.56<\/td><td class=\"column-3\">272.26<\/td><td class=\"column-4\">82.67<\/td><td class=\"column-5\">211.67<\/td>\n<\/tr>\n<tr class=\"row-11 odd\">\n\t<td class=\"column-1\"> 1980 <\/td><td class=\"column-2\">81.78<\/td><td class=\"column-3\">271.19<\/td><td class=\"column-4\">82.65<\/td><td class=\"column-5\">208.11<\/td>\n<\/tr>\n<tr class=\"row-12 even\">\n\t<td class=\"column-1\"> 1985 <\/td><td class=\"column-2\">82.05<\/td><td class=\"column-3\">270.20<\/td><td class=\"column-4\">82.65<\/td><td class=\"column-5\">204.24<\/td>\n<\/tr>\n<tr class=\"row-13 odd\">\n\t<td class=\"column-1\"> 1990 <\/td><td class=\"column-2\">82.31<\/td><td class=\"column-3\">269.16<\/td><td class=\"column-4\">82.65<\/td><td class=\"column-5\">200.33<\/td>\n<\/tr>\n<tr class=\"row-14 even\">\n\t<td class=\"column-1\"> 1995 <\/td><td class=\"column-2\">82.60<\/td><td class=\"column-3\">268.02<\/td><td class=\"column-4\">82.64<\/td><td class=\"column-5\">200.91<\/td>\n<\/tr>\n<tr class=\"row-15 odd\">\n\t<td class=\"column-1\"> 2000 <\/td><td class=\"column-2\">82.96<\/td><td class=\"column-3\">266.97<\/td><td class=\"column-4\">82.68<\/td><td class=\"column-5\">205.53<\/td>\n<\/tr>\n<tr class=\"row-16 even\">\n\t<td class=\"column-1\"> 2005 <\/td><td class=\"column-2\">83.30<\/td><td class=\"column-3\">265.93<\/td><td class=\"column-4\">82.71<\/td><td class=\"column-5\">209.75<\/td>\n<\/tr>\n<tr class=\"row-17 odd\">\n\t<td class=\"column-1\"> 2010 <\/td><td class=\"column-2\">83.67<\/td><td class=\"column-3\">264.37<\/td><td class=\"column-4\">82.66<\/td><td class=\"column-5\">213.84<\/td>\n<\/tr>\n<tr class=\"row-18 even\">\n\t<td class=\"column-1\"> 2015 <\/td><td class=\"column-2\">84.09<\/td><td class=\"column-3\">262.43<\/td><td class=\"column-4\">82.52<\/td><td class=\"column-5\">218.56<\/td>\n<\/tr>\n<tr class=\"row-19 odd\">\n\t<td class=\"column-1\"> 2020 <\/td><td class=\"column-2\">84.17<\/td><td class=\"column-3\">262.01<\/td><td class=\"column-4\">82.48<\/td><td class=\"column-5\">219.38<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-4 from cache -->\n<p>Like the\u00a0<a href=\"https:\/\/website.whoi.edu\/deeptow\/the-centered-dipole-model\/\">Centered Dipole (CD) model<\/a>, the Eccentric Dipole (CD) model of the\u00a0<a href=\"https:\/\/website.whoi.edu\/deeptow\/primer-on-marine-magnetism\/\">geomagnetic field<\/a>\u00a0is only an approximation of the geomagnetic field using a limited number of the coefficients in the\u00a0<a href=\"https:\/\/website.whoi.edu\/deeptow\/geomagnetic-reference-field\/\">spherical harmonic expansion<\/a>\u00a0of the IGRF model. However, these dipole models do give a general sense of the time averaged behavior of the field. It is possible to use all of the Gauss coefficients of the spherical harmonic expansion to define the field and pole locations.<\/p>\n<h4>References<\/h4>\n<p>Barraclough, D.R., Spherical harmonic analyses of the geomagnetic field for eight epochs between 1600 and 1910,\u00a0<i>Geophys. J. R. Astron. Soc.<\/i>, 36, 497-513, 1974.<\/p>\n<p>Fraser-Smith, A.C., Centered and Eccentric Geomagnetic Dipoles and their poles, 1600-1985,\u00a0<i>Rev. Geophys.<\/i>, 25, 1-16, 1986.<\/p>\n\n","protected":false},"excerpt":{"rendered":"<p>The Eccentric Dipole Model The Eccentric Dipole (ED) model of Earth&#8217;s magnetic field is an attempt to get a better approximation Earth&#8217;s geomagnetic pole locations compared to the simple dipole (i.e. bar magnet) approximation of the\u00a0centered dipole approach. The eccentric dipole approximation acknowledges that the field is slightly offset from the Earth&#8217;s spin axis although&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\/916"}],"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=916"}],"version-history":[{"count":3,"href":"https:\/\/website.whoi.edu\/deeptow\/wp-json\/wp\/v2\/pages\/916\/revisions"}],"predecessor-version":[{"id":940,"href":"https:\/\/website.whoi.edu\/deeptow\/wp-json\/wp\/v2\/pages\/916\/revisions\/940"}],"wp:attachment":[{"href":"https:\/\/website.whoi.edu\/deeptow\/wp-json\/wp\/v2\/media?parent=916"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}