After World War II, a renewed spirit of international cooperation in geophysics brought about a rapid growth of the International Association of Geomagnetism and Aeronomy (IAGA; pronounced "eye-yah-gah"). As part of a special IAGA working group, scientists from the principal navigation nations periodically analyze the collected global geomagnetic field records to determine an International Geomagnetic Reference Field (IGRF). This is a model of the Earth's main field that can be represented by a short table of values

called Gauss coefficients. The work is revisited every five years to accommodate the gradual changing main-field behavior.

Also, when additional recovered data become available, that group of ge-omagneticians regularly reanalyze past IGRF field models to construct retrospective corrections. The revised final table of values is called the Definitive Geomagnetic Reference Field (DGRF). To prepare the model fields, the scientists use a special mathematical technique, spherical harmonic analysis (SHA), which was devised in the early nineteenth century by Carl Friedreich Gauss (Figure 1.8) of Germany.

The SHA global analysis of the field uses all the reliable magnetic measurements around the Earth, intelligently adjusted to a common date, called the analysis epoch. Each observatory measurement is a summation of the magnetic field sources arising from locations both exterior and interior to the Earth at the measuring site. Field values from the irregular distribution of world observatories are connected in a way that allows an interpolated representation for all latitudes and longitudes. The SHA analysis method fits that representation of the magnetic field with the harmonic series of spherical oscillations (Figure 3.6).

Because the magnetic measurements surround the Earth (inside this surface is a volume that contains all the internal field contributions), the mathematical methods used in the SHA analysis permits the researcher to separate the field sources above (external to) the Earth from those within (internal to)

FIGURE 3.6 ► For modeling the Earth's field, a large set of spherical harmonic functions (examples of four are shown) are adjusted in magnitude so that, when all are added together, a smooth and compact representation for the global surface magnetic field measurements can be computed. The number of oscillations that appear in these figures along circles of latitude and longitude are determined from the harmonic indices, n and m. Display program from P. McFadden of AGSO.

FIGURE 3.6 ► For modeling the Earth's field, a large set of spherical harmonic functions (examples of four are shown) are adjusted in magnitude so that, when all are added together, a smooth and compact representation for the global surface magnetic field measurements can be computed. The number of oscillations that appear in these figures along circles of latitude and longitude are determined from the harmonic indices, n and m. Display program from P. McFadden of AGSO.

the Earth. External field sources are discarded when determining the main field because ionospheric and space currents are unimportant for understanding the fields from deep in the Earth's interior. The IGRF table (Figure 3.7) represents the main field of internal sources indexed for paired SHA coefficients, g and h, which are Gauss coefficient multipliers for the Earth's field

g/h |
n |
m |
DGRF |
DGRF |
DGRF |
DGRF |
DGRF |
DGRF |
DGRF |
IGRF | |

1960 |
1965 |
1970 |
1975 |
1980 |
1985 |
1990 |
1995 |
SV (nT/yr) | |||

g |
1 |
0 |
-30421 |
-30334 |
-30220 |
-30100 |
-29992 |
-29873 |
-29775 |
-29682 |
17.6 |

g |
1 |
1 |
-2169 |
-2119 |
-2068 |
-2013 |
-1956 |
-1905 |
-1848 |
-1789 |
13.0 |

h |
1 |
1 |
5791 |
5776 |
5737 |
5675 |
5604 |
5500 |
5406 |
5318 |
-18.3 |

g |
2 |
0 |
-1555 |
-1662 |
-1781 |
-1902 |
-1997 |
-2072 |
-2131 |
-2197 |
-13.2 |

g |
2 |
1 |
3002 |
2997 |
3000 |
3010 |
3027 |
3044 |
3059 |
3074 |
3.7 |

h |
2 |
1 |
-1967 |
-2016 |
-2047 |
-2067 |
-2129 |
-2197 |
-2279 |
-2356 |
-15.0 |

g |
2 |
2 |
1590 |
1594 |
1611 |
1632 |
1663 |
1687 |
1686 |
1685 |
-0.8 |

h |
2 |
2 |
206 |
114 |
25 |
-68 |
-200 |
-306 |
-373 |
-425 |
-8.8 |

g |
3 |
0 |
1302 |
1297 |
1287 |
1276 |
1281 |
1296 |
1314 |
1329 |
1.5 |

g |
3 |
1 |
-1992 |
-2038 |
-2091 |
-2144 |
-2180 |
-2208 |
-2239 |
-2268 |
-6.4 |

h |
3 |
1 |
-414 |
-404 |
-366 |
-333 |
-336 |
-310 |
-284 |
-263 |
4.1 |

g |
3 |
2 |
1289 |
1292 |
1278 |
1260 |
1251 |
1247 |
1248 |
1249 |
-0.2 |

h |
3 |
2 |
224 |
240 |
251 |
262 |
271 |
284 |
293 |
302 |
2.2 |

g |
3 |
3 |
878 |
856 |
838 |
830 |
833 |
829 |
802 |
769 |
-8.1 |

h |
3 |
3 |
-130 |
-165 |
-196 |
-223 |
-252 |
-297 |
-352 |
-406 |
-12.1 |

g |
4 |
0 |
957 |
957 |
952 |
946 |
938 |
936 |
939 |
941 |
0.8 |

g |
4 |
1 |
800 |
804 |
800 |
791 |
782 |
780 |
780 |
782 |
0.9 |

h |
4 |
1 |
135 |
148 |
167 |
191 |
212 |
232 |
247 |
262 |
1.8 |

g |
4 |
2 |
504 |
479 |
461 |
438 |
398 |
361 |
325 |
291 |
-6.9 |

h |
4 |
2 |
-278 |
-269 |
-266 |
-265 |
-257 |
-249 |
-240 |
-232 |
1.2 |

g |
4 |
3 |
-394 |
-390 |
-395 |
-405 |
-419 |
-424 |
-423 |
-421 |
0.5 |

h |
4 |
3 |
3 |
13 |
26 |
39 |
53 |
69 |
84 |
98 |
2.7 |

g |
4 |
4 |
269 |
252 |
234 |
216 |
199 |
170 |
141 |
116 |
-4.6 |

It |
4 |
4 |
-255 |
-269 |
-279 |
-288 |
-297 |
-297 |
-299 |
-301 |
-1.0 |

FIGURE 3.7 ► A portion of the table of the IGRF and DGRF values that model the Earth's main field every five years. The numbers (Gauss coefficients), are indexed as types g and h, with associated pairs of superscripts and subscripts that go from 0 to 12, matching the n and m spherical harmonics (see Figure 3.6). The SV (secular variation) column gives the estimated change per year for projecting the last IGRF coefficient values into future years. Only approximately one-third of the full table length is displayed here. The full table can be found at the website http://www.ngdc.noaa.gov/seg/potfld/ geomag.html.

computation and are identified with the spherical harmonics, m and n, depicted in Figure 3.6. With this table and special formulae, scientists can compute, for the given epoch, a best representation of the main magnetic field strength and direction at any location on Earth and the field's extension into nearby space. The total field map shown in Figure 2.21 was created from year 2000 IGRF tabular values.

Internal field models have been established back to 1945; less accurate, special analyses have been carried out back to 1600. From a full IGRF or DGRF table, scientists can compute two magnetic pole positions (north and south) where the angle of the internal field (dip) is vertical to the Earth's surface. We call these IGRF Field Poles—an initial candidate for our designation of "Magnetic Poles". These poles are determined from a global field, but still suffer from the problem that our pole concept refers to a position for just the magnetic dipole part. As we shall see below, the full IGRF analysis fits features other than a dipole in its modeling.

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