  The electromagnetic induction equation (Helmholtz equation) for the
electrically conducting Earth is generalised to the inclusion of a spatially
fluctuating internal conductivity spectrum that is superimposed on a
one-dimensional large-scale conductivity reference-profile which depends solely
on the vertical coordinate z>0. This large-scale profile is assumed to be
known. The distribution of the fluctuations is allowed to be arbitrary. The
conductivity-fluctuation generalised Helmholtz equation depends on the spectral
density of the fluctuations as function of the vertical and horizontal
coordinates. Application to the inverse geomagnetic/magneto-telluric problem is
discussed. We show analytically that the inverse problem yields the
conductivity fluctuation spectrum. The relation between the spectral density
and the obtained conductivity profile is given.
