By Ronald T. Merrill

Our wisdom of the Earth's box has constructed over many centuries. ordinarily, the various facets of geomagnetism, reminiscent of archeomagnetish, paleomagnetish, and the advanced arithmetic of dynamo idea, were studied in isolation from one another. The Magnetic box of the Earth attracts jointly those significant strains of inquiry into an built-in framework to focus on their interrelationships and supply a extra finished figuring out of the geomagnetic box and its software to investigations of our planet's deep inside. Thereticians and observationalists will welcome the volume's special approach.

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**Additional info for The Magnetic Field of the Earth: Paleomagnetism, the Core, and the Deep Mantle**

**Sample text**

4 Determination of the Gauss Coefficients In principle, the number of measurements on the Earth's surface required to obtain the Gauss coefficients up to / = TV is straightforward. As aheady noted, go is zero because there are no magnetic monopoles. Then for / = 1 there are two gf terms, gf and g\; for / = 2 there are 3 terms, gl,g\,^r\dgl; and for / = A^ there are TV + 1 terms. Therefore, the total number of terms gf to degree N is 2 + (A^ + 1)" N= . 17) Following a similar procedure for the hj" terms (note that all hf terms vanish), one finds that the total number of terms h"' to degree A'^ is 1 + A^ N .

The expansion to too high a degree produces an unstable model. Thus, in general, it is better to fit a model in which the harmonic series is simply truncated above some degree, rather than including some high-degree harmonics and excluding some low-degree harmonics. 1 that ground-based magnetic observations are poorly distributed, so these problems occur in spherical harmonic modeling of the Earth's magnetic field. Clearly it is desirable to use those orthogonal functions that are most efficient for the problem at hand.

VxB=0). Thus one can define a scalar potential vj/^ for the magnetic induction such that B = -Vv|/^. 14), but without the \iQ when (gf\h^) are in nanotesla (this is the common practice for lAGA publications relating to the International Geomagnetic Reference Field (IGRF); see also Langel, 1987). Schmidt (1939) also developed general formulas for a spheroidal body; however, for the Earth, with polar radius some 21 km smaller than the equatorial radius, the coefficients are only slightly modified by Schmidt's refinement (see Vestine, 1967).