A note on two expressions for the spatial power spectrum of the geomagnetic field

The spatial power spectrum of the geomagnetic field is usually assumed to be exponential in the spherical harmonic degree (n). An equally valid assumption, however, is that the spectrum at the surface of the Earth's core has a power-law dependence on n. Some implications of these two assumptions are discussed, noting that, in the first case, a value for the core radius can be derived from the slope of the spectrum and, in the second, that the spectrum for radii greater than the radius of the core is a mixture of the exponential and power-law types.