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2.7.6 Geomagnetism

The Earth’s magnetic field corresponds approximately to that of a dipole situated at the centre of the Earth with its axis inclined at an angle of about 11° to the axis of rotation. There are, however, appreciable temporal and spatial departures from this simple model. According to presently accepted theories, the smooth geomagnetic or ‘normal’ field and its slow secular change are ascribed to fluid motions in the Earth’s electrically conducting core. The influence of magnetic constituents of crustal rocks superposes on the normal field anomalies whose magnitude can, in extreme cases, be comparable to that of the normal field.

In addition, changes on the Sun and of its position relative to the Earth cause erratic and often rapid fluctuations in the magnetic field (magnetic storms) occasionally exceeding one-tenth of the normal field value, as well as smaller and more regular diurnal and seasonal variations.

The geomagnetic field at any point is usually defined by three of seven elements: five intensity components, H (parallel to the Earth's surface), Z (vertically downwards), F or T (total, scalar), X (geographic north) and Y (geographic east); and two angles, D (declination or variation, D = arctan Y/X) and I (inclination or dip, I = arctan Z/H).

The main geomagnetic field, due to internal sources, at points on or above the Earth's surface may be represented by the following series:

X =  (gnm cos mλ + hnm sin mλ)(a/r)n + 2 dPnm(θ) , dθ Y =  (gnm sin mλ − hnm cos mλ)(a/r)n + 2m cosec θPnm(θ), Z = −  (gnm cos mλ + hnm sin mλ)(a/r)n + 2(n+1) Pnm(θ),

where a is the Earth's mean radius, λ is east longitude, r is radial distance from the Earth’s centre and P_n^m(θ) is an associated Legendre function of the colatitude or north polar distance, θ, of degree n and order m. The set of numerical coefficients (g_n^m, h_n^m), usually expressed in units of nT, constitute a spherical harmonic model of the geomagnetic field.

The associated Legendre functions used in geomagnetism are of the Schmidt quasi-normalized form. They are such that the mean square value of P_n^m cos mλ or P_n^m sin mλ taken over a sphere is (2n + 1)⁻¹ and may be derived from the relation:

Pnm(c) =		δm(n − m)!(1 − c2)m		1/2	dm	Pn(c)
		(n + m)!			dcm

where

   c = cos θ

   δ_m = 1 for m = 0; 2 for m 1

and

   P_n(c) is the Legendre polynomial of degree n.

The International Geomagnetic Reference Field (IGRF) is a set of 21 spherical harmonic models: 20 describing the main geomagnetic field at epochs from 1900 to 1995, inclusive, five years apart and one for the (predicted) annual rate of secular variation for the interval 1995 to 2000. The main-field models extend to m = n = 10 (120 coefficients each) and the secular variation model is truncated at m = n = 8 (80 coefficients). Field component values for dates differing from the epochs of the main-field models are derived, for dates before 1995, by linear interpolation and, for dates after 1995, by using the secular variation model to up-date the 1995 main-field model. For further details see R. A. Langel (1992).

(Click the Images to view Larger Images)

Figures 1 and 2 show contours of the declination and of the secular variation of the declination, respectively, at 1995 derived from the IGRF. A Fortran subroutine for synthesizing field component values from a spherical harmonic model is described by S. R. C. Malin and D. R. Barraclough (1981).

More detailed world magnetic charts are published by the Hydrographic Office of the Ministry of Defence and are obtainable from Admiralty Chart Agents. The latest charts for all elements are for epoch 1995.

Magnetic elements for London at different epochs

Values from 1850 onwards are for Greenwich. For 1580 the D observation was by Borough and the I value is Norman's observation made about 1576.

    * Maximum. ^† Minimum.

Geomagnetic data 1990

The following table contains the mean values of D, H and Z observed during the year 1990 and their annual rates of change for a selection of permanent magnetic observatories.

    ^† Sign conventions: positive values of latitude are north; of longitude, and of D and its annual change are east; and of Z and its annual change are downwards.

References

R. A. Langel (1992) J. Geomagn. Geoelectr. 44, 679–707.
S. R. C. Malin and D. R. Barraclough (1981) Computers and Geosciences 7, 401–405.

D.R.Barraclough

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