Is the non-dipole magnetic field random?

Statistical modelling of the Earth's magnetic field B has a long history (see e.g. McDonald 1957; Gubbins 1982; McLeod 1986; Constable & Parker 1988). In particular, the spherical harmonic coefficients of scalar fields derived from B can be treated as Gaussian random variables (Constable & Parker 1988). In this paper, we give examples of highly organized fields whose spherical harmonic coefficients pass tests for independent Gaussian random variables. The fact that coefficients at some depth may be usefully summarized as independent samples from a normal distribution need not imply that there really is some physical, random process at that depth. In fact, the field can be extremely structured and still be regarded for some purposes as random. In this paper we examined the radial magnetic field B_r produced by the core, but the results apply to any scalar field on the core–mantle boundary (CMB) which determines B outside the CMB.