Illuminating the Electrical Conductivity of the Lowermost Mantle from Below

jault, dominique;

The magnetic field that originates in the earth’s core is transformed across the electrically conducting mantle before being observed, at the earth’s surface or above. Assuming that the conductivity depends only on radius, it has been customary to treat the mantle as a linear
time-invariant filter for the core magnetic field, with properties (as a function of the frequency ω) specified by the transfer function (ω). An high-frequency approximation to (ω), which is derived from a three terms WKBJ expansion with ω −1/2 as small parameter, is found here
to reproduce adequately, for low harmonic degrees and/or thin conducting layers, the exact solution, which is evaluated numerically. It is contrasted with the low-frequency estimation of , which consists in a perturbation procedure and in writing (ω) as a series in powers
of ω (ω → 0). The low-frequency theory is applied to the magnetic variations produced by the geostrophic core flows with about 6 yr period as the phase of these flows is independently determined from their effect on the length of the day. Apart from that, the low-frequency approximation overestimates the screening by the mantle of high-frequency signals, especially the low harmonic degree ones. In practice, the attenuating factor defined from the O(ω2) term
in the expansion of as ω→0 cannot be retrieved from analyses of geomagnetic time-series. Application of the mantle filter theory hinges on our knowledge about the time spectrum of the magnetic field at the core surface. The low-frequency theory had been previously applied
to observatory series on the assumption that geomagnetic jerks occurring in the core are rare and isolated events. Rather than following up these earlier studies, I note that the spectral density function for the second time derivative of the main magnetic field coefficients is approximately independent of ω in a frequency range for which the mantle has undoubtedly negligible influence. In the absence of any other information, this scaling law is extrapolated
to higher frequencies.