Editing Earth's magnetic field (section)

==== Radial dependence ====
Spherical harmonic analysis can be used to distinguish internal from external sources if measurements are available at more than one height (for example, ground observatories and satellites). In that case, each term with coefficient {{math|<var>g<sub>m</sub></var><sup>ℓ</sup>}} or {{math|<var>h<sub>m</sub></var><sup>ℓ</sup>}} can be split into two terms: one that decreases with radius as {{math|1/<var>r</var><sup>ℓ+1</sup>}} and one that ''increases'' with radius as {{math|<var>r</var><sup>ℓ</sup>}}. The increasing terms fit the external sources (currents in the ionosphere and magnetosphere). However, averaged over a few years the external contributions average to zero.<ref name="MMMch2" />

The remaining terms predict that the potential of a dipole source ({{math|ℓ{{=}}1}}) drops off as {{math|1/<var>r</var><sup>2</sup>}}. The magnetic field, being a derivative of the potential, drops off as {{math|1/<var>r</var><sup>3</sup>}}. Quadrupole terms drop off as {{math|1/<var>r</var><sup>4</sup>}}, and higher order terms drop off increasingly rapidly with the radius. The radius of the outer core is about half of the radius of the Earth. If the field at the core-mantle boundary is fit to spherical harmonics, the dipole part is smaller by a factor of about 8 at the surface, the quadrupole part by a factor of 16, and so on. Thus, only the components with large wavelengths can be noticeable at the surface. From a variety of arguments, it is usually assumed that only terms up to degree {{math|14}} or less have their origin in the core. These have wavelengths of about {{cvt|2000|km}} or less. Smaller features are attributed to crustal anomalies.<ref name="MMMch2" />