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 Pnm(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 (gnm, hnm), 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
Pnm cos
mλ or Pnm 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
δm = 1 for
m = 0; 2 for m
1
and
Pn(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.
|
Epoch |
Declination |
Inclination |
H/μT |
Z/μT |
| |
deg |
min |
deg |
min |
|
|
|
|
|
|
|
|
|
1580 |
11 |
19 E |
71 |
50 |
— |
— |
|
1665 |
0 |
0 |
— |
— |
— |
|
1673 |
— |
73 |
47 |
— |
— |
|
1719 |
11 |
30 W |
— |
— |
— |
|
1720 |
— |
75 |
14* |
— |
— |
|
1816 |
24 |
28 W* |
— |
— |
— |
|
1818 |
— |
70 |
35 |
— |
— |
|
1850 |
22 |
24 W |
68 |
47 |
— |
— |
|
1875 |
19 |
21 W |
67 |
42 |
17.97 |
43.83 |
|
1907 |
16 |
0 W |
66 |
56 |
18.55* |
43.57 |
|
1913 |
15 |
15 W |
66 |
50† |
18.53 |
43.32 |
|
1929 |
12 |
23 W |
66 |
54 |
18.38 |
43.06† |
|
1937 |
11 |
1 W |
66 |
59 |
18.34† |
43.17 |
|
1946 |
9 |
37 W |
67 |
2* |
18.39 |
43.37 |
|
1975 |
6 |
39 W |
66 |
27 |
19.16 |
43.98 |
|
|
|
|
|
|
|
|
* 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.
|
Observatory |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Resolute Bay . |
+ 74.7 |
−94.9 |
− 48.7 |
+ 79 |
1 068 |
+ 30 |
58 248 |
− 30 |
|
Bjørnøya . . |
+ 74.5 |
19.2 |
+ 4.3 |
+ 5 |
9 027 |
− 23 |
52 875 |
− 1 |
|
Point Barrow . |
+ 71.3 |
−156.8 |
+ 25.0 |
− 9 |
9 504 |
− 32 |
56 270 |
− 6 |
|
Tromsø . . . |
+ 69.7 |
18.9 |
+ 1.5 |
+ 5 |
11 146 |
− 18 |
51 624 |
+ 6 |
|
College . . . |
+ 64.9 |
−147.8 |
+ 26.9 |
− 11 |
12 751 |
− 24 |
55 333 |
− 6 |
|
Lerwick (UK) . |
+ 60.1 |
−1.2 |
− 6.4 |
+ 8 |
14 898 |
− 4 |
48 001 |
+ 17 |
|
Magadan . . |
+ 60.1 |
151.0 |
−13.5 |
− 2 |
17 714 |
− 20 |
52 610 |
+ 24 |
|
Moscow . . . |
+ 55.5 |
37.3 |
+ 8.2 |
+ 1 |
17 207 |
+ 13 |
48 773 |
+ 5 |
|
Eskdalemuir (UK) |
+ 55.3 |
−3.2 |
− 6.9 |
+ 7 |
17 314 |
+ 2 |
45 950 |
+ 16 |
|
Irkutsk . . . |
+ 52.2 |
104.4 |
− 2.2 |
+ 2 |
19 282 |
− 26 |
56 999 |
+ 13 |
|
Hartland (UK) |
+ 51.0 |
−4.5 |
− 6.2 |
+ 8 |
19 395 |
+ 8 |
43 896 |
+ 14 |
|
Memambetsu . |
+ 43.9 |
144.2 |
− 8.6 |
− 2 |
26 341 |
− 18 |
41 641 |
+ 42 |
|
Coimbra . . . |
+ 40.2 |
−8.4 |
− 6.1 |
+ 6 |
25 071 |
+ 10 |
36 284 |
− 12 |
|
Fredericksburg |
+ 38.2 |
− 77.4 |
− 9.5 |
− 6 |
20 660 |
+ 17 |
50 223 |
− 105 |
|
Kakioka . . . |
+ 36.2 |
140.2 |
− 6.8 |
− 2 |
30 136 |
− 10 |
34 953 |
+ 43 |
|
Tucson . . . |
+ 32.2 |
− 110.8 |
+ 11.8 |
− 1 |
25 342 |
− 32 |
42 505 |
− 45 |
|
Quetta . . . |
+ 30.2 |
67.0 |
+ 1.5 |
+ 1 |
32 510 |
− 5 |
33 550 |
− 15 |
|
Honolulu
. . |
+ 21.3 |
− 158.0 |
+ 11.0 |
− 4 |
27 574 |
− 13 |
22 048 |
− 26 |
|
Alibag . . . |
+ 18.6 |
72.9 |
− 0.5 |
+ 1 |
37 982 |
− 10 |
17 982 |
+ 3 |
|
San
Juan . . |
+ 18.1 |
− 66.2 |
− 10.9 |
− 8 |
27 195 |
− 6 |
29 585 |
− 146 |
|
Guam
. . . |
+ 13.6 |
144.9 |
+ 1.8 |
−1 |
35 863 |
+ 3 |
7 269 |
+ 20 |
|
Bangui . . . |
+ 4.4 |
18.6 |
− 2.0 |
+ 5 |
32 028 |
− 6 |
− 9 294 |
− 16 |
|
Pamatai . . . |
− 17.6 |
−149.6 |
+ 11.3 |
0 |
30 980 |
− 34 |
− 18 926 |
− 2 |
|
Vassouras . . |
− 22.4 |
− 43.6 |
− 20.3 |
− 5 |
20 332 |
− 91 |
− 12 167 |
− 89 |
|
Hartebeesthoek |
− 25.9 |
27.7 |
− 16.0 |
− 4 |
12 879 |
− 16 |
− 26 148 |
+ 74 |
|
Gnangara . . |
− 31.8 |
116.0 |
− 3.1 |
+ 3 |
23 195 |
−
2 |
− 53 802 |
+ 13 |
|
Hermanus . . |
− 34.4 |
19.2 |
− 23.4 |
− 3 |
10 932 |
− 35 |
− 24 849 |
+ 92 |
|
Canberra . . |
− 35.3 |
149.4 |
+ 12.5 |
+ 1 |
23 653 |
−
6 |
− 53 663 |
+ 17 |
|
Kerguelen . . |
− 49.4 |
70.3 |
− 53.0 |
−10 |
18 603 |
− 32 |
− 44 708 |
− 4 |
|
Macquarie Island |
− 54.5 |
159.0 |
+ 29.7 |
+ 5 |
12 577 |
−
4 |
− 63 519 |
+ 32 |
|
Mawson . . |
− 67.6 |
62.9 |
− 64.4 |
− 8 |
18 492 |
+ 14 |
− 46 015 |
+ 71 |
|
|
|
|
|
|
|
|
|
|
† 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.
|
|
|
Lat. |
Long. |
|
|
North magnetic dip-pole
(1995) |
+ 78.7° |
104.8°W |
|
|
South magnetic dip-pole
(1995) |
− 64.6° |
138.6°E |
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
|