RUSSIAN JOURNAL OF EARTH SCIENCES VOL. 10, ES4003, doi:10.2205/2007ES000258, 2008

Analysis of Data of the Earth's Magnetic Field

2007ES000258-fig05
Figure 5
[15]  The calculations were made in reference points through the Internet with the help of the web program of the British Geological Survey (BGS - http://www.bgs.ac.uk/) for 1995, 2000 and 2005, the reference points were the same for all these years, their number was 1768. Each point contained a latitude, a longitude and three components - X, Y, Z of the vector of strength of the main field (axis X is directed along the geographical meridian to the north, axis Y - along the parallel to the east, axis Z - downwards), module of the horizontal component of the main field |H|, angle of declination D (between vector H of the horizontal component and geographic meridian) and angle of inclination I (between vector F of the full strength and vector H ). The system of reference points on the chart was irregular, with extension at magnetic poles with the purpose of more accurate determination of location of these poles. Values |H| in reference points were interpolated in matrix |H| with the resolution of 1o of latitude and 1o of longitude (63525 elements in the matrix), at that the algorithm of interpolation of the program "Analytical GIS Eco'' [Shary et al., 2005] didn't alter the values in reference points. Isolines |H| were generated according to this matrix, corresponding to values |H|, equal to 500, 1000, 2000, 4000,..., 40,000 nT (value |H| changed from 0 to 41,380 nT). Relating to the necessity of the correct account of the matrix borders isolines |H| were calculated to 87o N. The magnetic poles were determined by equation |H| = 0. Full strength of the main field |F| altered from 22,870 to 67,140 nT. Isolines |F| are shown in Figure 5.

[16]  Figure 5 shows that both in 1995 and 2005 there were three maxima and one minimum |F|. The proximity of maxima |F| to the magnetic poles is explained by the prevailing role of the main magnetic dipole, and these extrema's deviation from magnetic poles is related to the non-dipole component of the main field. The latter is also related to the presence of the maximum |F| on the territory of Russia and of the minimum in South America.

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Figure 6
[17]  Analogically the magnetic equator was obtained ( |Z| =0) according to the matrix of values of the vertical component of the main field Z . Value Z in the points of the matrix grid changed in 1995 from -67,157 to +60,703 nT, in 2005 - from -67,080 to 60,800 nT. The izolines of horizontal component |H| of the main field and magnetic equator for 1995, 2000 and 2005 are shown correspondingly in Figures 6a and 6b. It is clear from them that |H| has 4 extrema. The two of them (the minima) are magnetic poles, approximately corresponding to the main magnetic dipole of the Earth. In these minima |H|=0. Another local minimum is located in the south of Africa, with |H| = 10,410 nT, and a local minimum is located near Singapore, with |H| = 41,380 nT. These last extrema are related to the non-dipole field. The North magnetic pole for 1995 and 2000 at the ocean level has coordinates 81o N, 110o W, and the South magnetic pole for 1995 and 2000 at the ocean level - 65oS, 138oE.

[18]  Magnetic meridians were constructed the following way. From each point of the matrix grid along the horizontal components of the main magnetic field X and Y small segments were laid off towards the direction of horizontal component H of the main geomagnetic field. It was done by the special program (The program was developed by P. Shary.) according to two matrices, of the eastern and western components of the main geomagnetic field.

[19]  Since in the geographical projection (In a geographical projection the chart is represented by a rectangle with longitude and latitude laid off on its axis.) these hatches have considerably changed direction in comparison to equiangular projection (retaining angles and distances the same as on a sphere, different to a geographical projection), then the values of the horizontal component of the main geomagnetic field were transformed by stretching along axis x in 1/ cosj times (here j is a latitude ranging from -90o to +90o), that gave new values Xprime, Yprime of the horizontal components of the main field, Xprime=X/ cosj, Yprime=Y according to which the angles of hatches were calculated. This method of transformation of hatches is approximate (the exact solution is considerably more complicated), but it is sufficiently precise for the scale 1:25,000,000. The sampling comparisons in the equiangular Gauss-Kruger projection (where angles aren't distorted) have shown that the difference between the exact values and the values obtained by this method didn't exceed 0.5%.

2007ES000258-fig07
Figure 7
[20]  The hatches of the transformed directions of the horizontal component of the main field in the area of local minimum |H| near the southern end of Africa are shown in Figure 7.

[21]  It is noteworthy that the hatches of the transformed directions demonstrate on the chart the correct visually apprehended values of angles with geographic meridians only in equiangular projection, because only in these projections the angles on the chart and on the reference-ellipsoid do correspond to each other.

[22]  At the geographical equator 18 points were marked in equal intervals (in 20o longitude), and a magnetic meridian was drawn through each of them. The last one is a smooth curve, due to the fact that potential V in the above-mentioned IGRF formula is infinitely differentiated. A tangent to this curve is the most close to the calculated transformed directions of hatches in the closest to magnetic meridian grid points of the matrix.

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Figure 8
[23]  Each magnetic meridian from a given point r of the geographical equator was drawn like a smooth curve, consisting of several sections; a tangent to this curve in each point is directed along the hatches (i.e. along the declination of the main geomagnetic field). Magnetic meridians are coming out of the South magnetic pole ending in the North. In areas free from external sources of the field (where the impact of magnetic anomalies of the Earth's crust is irrelevant) a compass is directed towards a magnetic meridian (Figure 8).

[24]  Figure 8 also shows the magnetic equator. The chosen 18 magnetic meridians intersect with the geographical equator in each 20o of longitude. A magnetic meridian, corresponding to longitude -180o correlates with the one for longitude +180o, because it's the same. Some magnetic meridians, for example directed from the South pole along a geographical meridian to the south, are continued in the other hemisphere. In such cases in order to avoid artifacts in a browser (for example, in geographic information systems) a magnetic meridian is represented by numerical data as several sections of an integral curve - for the northern and southern hemispheres, or when a magnetic meridian intersects with the geographic meridian of 180o.

[25]  It is worth mentioning that magnetic meridians demonstrate on the chart the correct visually apprehended values of angles with geographic meridians given in equiangular projections.


RJES

Citation: Zhalkovsky, Ye. A. (2008), Chart-making of the Earth's main magnetic field, Russ. J. Earth Sci., 10, ES4003, doi:10.2205/2007ES000258.

Copyright 2008 by the Russian Journal of Earth Sciences

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