## Geomagnetic Coordinate Poles

The spherical harmonic mathematical computation for determining the reference fields is carried out in geographic, Earth-centered coordinates. The tabular values for the IGRF and DGRF coefficients can be grouped to represent the best-fitting dipole, quadrupole, octupole, and further multipole terms of the data-fitting process (Figure 3.8). This means that successive groups of terms produce field patterns just like those from an arrangement of electric charges at the corners of the multipole geometric arrangements.

The multipole terms have all been computed with respect to the Earth's spin axis and geographic center. Each one of the IGRF multipole patterns, shown in Figure 3.8, is symmetrical about the Earth's geographic center. The first three internal field g and h coefficients of the IGRF table (Figure 3.7) define the centered dipole terms. From these values we obtain a measure of the dipole field that allows us to compare its strength to other magnets and to see how our Earth's main field has been changing over the years—becoming rapidly smaller (Figure 3.9).

The dipole terms in the IGRF table are used to establish a Geomagnetic Coordinate System (Figure 3.3), a rearranged latitude and longitude pattern about the globe. This grid is spaced like the familiar geographic pattern, but uses the north and south magnetic dipole positions instead of the normal geographic spin-axis poles. The great circle of geomagnetic longitude that intersects the geographic north pole is labeled 180°. The symmetrically s

quadrupole octupole

FIGURE 3.8 ► Fields from these arrangements of magnetic poles form dipole, quadrupole, and octupole configurations that are represented by succeeding groups of g and h coefficients in the IGRF.

dipole quadrupole octupole

FIGURE 3.8 ► Fields from these arrangements of magnetic poles form dipole, quadrupole, and octupole configurations that are represented by succeeding groups of g and h coefficients in the IGRF.

1600 1700 1000 1900 2000

Year

FIGURE 3.9 ► The constant decrease of the Earth's dipole field strength is shown by the measurements that have been made since the time of Gilbert in 1600. Figure from M. Davis of NGDC/NOAA.

1600 1700 1000 1900 2000

Year

FIGURE 3.9 ► The constant decrease of the Earth's dipole field strength is shown by the measurements that have been made since the time of Gilbert in 1600. Figure from M. Davis of NGDC/NOAA.

located geomagnetic dipole field positions are presently offset about 11° from the geographic axis poles (Figure 3.3). Many geophysicists use the geomagnetic coordinate system to organize upper atmospheric and magnetospheric phenomena displays.

All the IGRF and DGRF field models show us that, on average, about 90% of the main (internal) field energy resides in these dipole terms. However, it should be remembered that this high percentage of dipole contribution to local field differs at each world location because of the varying sizes of the fields from the other multipole terms in the SHA fitting. We call the pole locations of the IGRF-dipole-term field the Geomagnetic Coordinate Poles—the second candidate for "Magnetic Poles".

Successive IGRF models show a westward magnetic pole drift at a rate that would cause them to circle the geographic poles in approximately 2000 to 3000 years. Note that if the representation of the dipolar part of the IGRF is subtracted from the model, the remainder (the nondipole field) shows patterns that, on average, drift westward slightly faster than the dipole fields. All these special features challenge the paleomagneticians' modeling and explanation of the deep internal current flows within the Earth (see Section 5.2.2, p. 128). Their research includes studies of the source differences for the dipole and multipole parts of the internal main field, interactions at the core-mantle boundary of the deep Earth, gravitational accretion at the Earth's solid inner core, and radioactive heating. The dipole field eccentricity contributes to their problem.

It is important to remember that the IGRF computation procedure of selecting the centered-Earth analysis axis is an arbitrary one, introduced by the researcher. To understand this fact, consider a situation in which the Earth has only a simple tilted dipole field that is offset from the Earth's center and there is no Earth-crust magnetization. If we analyzed our surface data about this dipole-field axis and center (rather than the spin axis and center), we would obtain essentially only the dipole coefficients of the spherical harmonic analysis—no others. If we instead analyze that hypothetical dipole about the Earth's spin axis and center, we would have a full set of multipole coefficients necessary to represent this simple tilted dipole field. Thus, a significant part of our IGRF multipole coefficients are introduced by our selection of an analysis position that is offset from the natural Earth dipole. The remaining parts of the IGRF low-order multipoles are thought to be due to the nondipole currents within the Earth's outer core (or at the core-mantle boundary) or due to fields from the Earth's magnetized crustal materials. Because of their short spacial dimensions, the high-order multipoles are considered to come only from crustal field sources or noise in the original data.

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