RUSSIAN JOURNAL OF EARTH SCIENCES VOL. 10, ES4003, doi:10.2205/2007ES000258, 2008
[10] The International Association of Geomagnetism and Aeronomy (IAGA) deals with preparing the IGRF data. These data are presented by decomposition by spherical harmonics by converting vectors of full strength to coefficients of potential of the main geomagnetic field by formula
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where R - average radius of Earth (6371.2 km), r, q, l - geocentric spherical coordinates ( r - distance from the center of Earth, q - 90o-latitude, l - Greenwich longtitude), gnm(t), hnm(t) - Gauss coefficients for time t, Pnm( cosq) - the seminormed by Schmidt associated Legendre functions with grade n and order m. Potential V beyond the Earth's scale satisfies the Laplas equation DV=0 and in the written form corresponds to the absence of electric currents outside the scale of Earth [Sharma, 1989]. The spherical harmonics are functions Ynm(q, l) in the form of Pnm( cosq) cos(ml) and Pnm( cosq) sin(ml); it was proved related to them that they are single-valued and continuous on the surface of a single sphere [Stigan, 1979]. The coefficients are functions of time and for the IGRF they are taken as changing at constant speed during an epoch. The table of coefficients from 1900 to 2005 in the form of an Excel file is available in the Internet (http://www.ngdc.noaa.gov/IAGA/vmod/). The biggest contribution to V is given by the member with coefficient g10, proportionate to cosq/r2 and describes the field of the central magnetic dipole, directed along the axis of Earth's rotation. The adding of two other members (proportionate to P11, or sinq ) entails tilting of the dipole axis, and the next senior members shift it at a distance of ~300 km from the Earth's center.
[11] In July 2003 the IAGA has completed its work of the new 9th IGRF generation. If the previous (for the epochs before 2000) generations were based on N = 10 (120 Gauss coefficients), then for 2000 and 2005 N = 13 (195 coefficients) and the Gauss coefficients are given already not with an accuracy to 1 nT, but 0.1 nT. For calculating velocity of change of the main field the same formula is used at N =8 (80 coefficients). According to the data for 1995, 2000 and 2005 we performed calculations for 0 latitude, converting from the geocentric to geodetic system of coordinates, based on reference-ellipsoid WGS-84 with semi-axis lengths a = 6378,137 km, b = 6356,752 km.
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[13] The three components of the main field vector F are designated by X, Y, Z. Component X is directed to the geographical North, Y - to the East, Z - to the center of Earth. H is the horizontal component of the main field vector. Angle D is called the field declination, angle I - inclination.
[14] The geomagnetic poles reflect only the main dipole of the main geomagnetic field; contrary to magnetic poles, they don't correspond to the reduction of horizontal component to zero. In practice (in navigation etc) magnetic, and not geomagnetic poles are used. The magnetic equator is also shown, that doesn't concur with the geographic one and isn't a circle.
Citation: 2008), Chart-making of the Earth's main magnetic field, Russ. J. Earth Sci., 10, ES4003, doi:10.2205/2007ES000258.
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