Geomagnetic spectrum of internal origin and lower mantle conductivity

For periods greater than approximately 4 years, Currie has previously argued that the magnetic continuum power spectrum S00(ƒ) observed at the earth's surface is primarily of internal origin and has shown that under simplifying assumptions it can be related to the poloidal spectrum Sii(ƒ) at the core-mantle boundary by the equation (S00(ƒ) = |Tn(ƒ)|2 Sii(ƒ), where the term |Tn(ƒ)|2 represents the mantle power transfer function, which, as a function of frequency ƒ, depends on harmonic degree n and the thickness and mean conductivity 〈σ〉 of the lower mantle. Analyses of data from eight widely distributed observatories show that, for periods between ∼4 and ∼33 years, the power spectra S00(ƒ) of Z and H components have a frequency dependence ƒα, where α ranges from −2 to −5, whereas, for the composite spectra, α = −2.9 ± 0.1 and α = −3.4 ± 0.1, respectively. The composite spectra are conjoined with the transfer function to yield estimates of the input composite spectrum Sii(ƒ) at the core-mantle boundary of the form Sii(ƒ) ∝ ƒa, where α depends critically on 〈σ〉. If there is exact correspondence, for periods considered here, between the highly idealized hydromagnetic turbulence power law recently obtained by Kraichnan and turbulence near the core-mantle boundary, then 〈σ〉 ≈ 2 × 10−9 emu; if there is no correspondence, a consensus agreement on the best value of 〈σ〉 would yield an estimate of the turbulence law in the uppermost part of the core for the periods considered.