It is often convenient to represent the geomagnetic field H by the sum of terms Hnm, each being derived from a scalar potential Vnm by ((1))where each Vnm is a spherical harmonic ((2)) In what follows we use 〈X〉 to denote the average value of X over the surface of the sphere r = a, ((3))
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F. J. Lowes (1966) studied this question.