RUSSIAN JOURNAL OF EARTH SCIENCES VOL. 10, ES4003, doi:10.2205/2007ES000258, 2008
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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 |
[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
X,
Y
of the horizontal components of the main field,
X
=X/ cosj,
Y
=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%.
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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 |
[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.
Citation: 2008), Chart-making of the Earth's main magnetic field, Russ. J. Earth Sci., 10, ES4003, doi:10.2205/2007ES000258.
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