On the magnetic sounding of planetary interiors

Two ways have been suggested for using the magnetic field of a planet to estimate the radius of its electrically conducting core, assumed spherical and concentric with the planet's surface. In the frozen flux method, the core radius is assumed to have the value r(FF), for which the integrated unsigned radial magnetic flux, from the sphere of that radius, is most nearly constant in time. In the flat spectrum method, the core radius is assumed to have the value r(FS) for which the power spectrum of the field, defined as the mean square energy density in the lth spherical harmonic component of the field at that radius, is most nearly independent of l. These two methods are here applied to a new geodynamo integration that is a continuation of a recently published simulation (see Glatzmaier and Roberts, 1995a, Phys, Earth Planet. Inter., 91: 63-75; Glatzmaier and Roberts, 1995b, Nature, 377: 203-209) and which, like the Earth, maintains a more strongly dipole dominated magnetic field. The rate of change of the unsigned flux was averaged over two different 300 year intervals at a number of radii, r, from the geocenter, The resulting functions of r were found to have zeros at r(FF) of approximately 3550 km and 3477 km, respectively. This demonstrates how sensitive this method is to the time interval selected for the computation. Even if, as is often done when the flat spectrum method is applied to the Earth, the centered dipole (l = 1) is excluded, the spectrum of our model could not be made convincingly flat; but a radius r(FS) at which it is most flat can be defined. The value of r(FS) is, however, very sensitive to the number of spherical harmonics retained in the spectrum and to a lesser extent is time dependent. On the basis of these studies, and impressed by the lack of a sound physical justification for the flat spectrum method, we conclude that that method provides a less certain way of estimating the radius of a planetary core than does the frozen flux approximation, and that even the latter should be employed with caution.