Secular‐invariant relationships among internal geomagnetic field coefficients

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Abstract
Some features of the secular variation of the geomagnetic field are examined. Contours encircling constant magnetic flux (third adiabatic invariant), corresponding to a “shell” of field lines in secular motion, reveal a general westward drift that is longitude and latitude dependent (with minima in the north Pacific and south Atlantic areas). Some invariant relationships appear among the field coefficients in the tilted, centered dipole (geomagnetic) coordinate system. The quadrupole phases ϕ2¹ and ϕ2², with a westward drift of 0.38 degrees per year, seem to bear a constant phase difference of 45° physically this corresponds to a n=2, m=1 current system that is tilted with respect to the geomagnetic equator. The octupole phases, particularly ϕ3², appear to be locked to the earth's rotation vector (no drift at all in the tilted dipole system). In our present epoch, the energy contained in the quadrupole and octupole field outside the core is increasing at a rate roughly equal to that of decrease of main dipole field energy. The hexadecapole terms show a mixture of westward and eastward drifts. On the average, the total hexadecapole current system does not reveal any notable drift in the original (geographic) frame of reference.

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