The geomagnetic/magneto-telluric induction problem with spatial conductivity fluctuations

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. \\

@article{id2161,
  author = {Treumann, R. A. and Baumjohann, W.},
  journal = {ArXiv},
  language = {en},
  note = {13 pages, 2 figures},
  number = {1701.07272},
  pages = {1-13},
  title = {The geomagnetic/magneto-telluric induction problem with spatial conductivity fluctuations},
  url = {http://arxiv.org/abs/1701.07272},
  volume = {arXiv:},
  year = {2017},
}

%O Journal Article
%A Treumann, R. A.
%A Baumjohann, W.
%J ArXiv
%G en
%O 13 pages, 2 figures
%N 1701.07272
%P 1-13
%T The geomagnetic/magneto-telluric induction problem with spatial conductivity fluctuations
%U http://arxiv.org/abs/1701.07272
%V arXiv:
%D 2017