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Inversion of the geomagnetic secular variation: uniqueness and feasibility Johnson, Ian Mayhew

Abstract

The inversion problem of the geomagnetic secular variation, that is the recovery of the electrical conductivity distribution of the earth's lower mantle from the attenuation of the magnetic field across the lower mantle, is shown to have a unique solution. This implies that the electrical conductivity is uniquely determined by the spatial and time history of the magnetic field at the base of the mantle. The derivation of the inversion method is based on the inverse Sturm-Liouville theory of I. M. Gel'fand and B. M. Levitan. Numerical experiments on the theory with synthetic electrical conductivity profiles indicate a computationally stable inversion method. The resolving power of the inversion is shown to have a predictable dependence on the extent of the attenuation information. The attenuation properties required for the inversion are shown to be recoverable from the spatial deconvolution of two autocorrelation functions which are expressions of the statistical characteristics of the magnetic field components at the boundary of the core and the mantle.

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