Equations of the electromagnetic field in dispersive media

The frequency/time dispersion of the electric properties of rocks is intensively investigated in geo-electromagnetics. In particular, the strong disperson effects in transient geo-electromagnetics, like non-monotonous transient response, sign reversals etc., have been considered by many authors. The aim of this paper is to describe the electromagnetic field in dispersive media in the most general form. The validility of replacing constant parameters with frequency/time variable ones is the subject to analysis as well. It is emphasized first of all that Maxwell’s equations written in canonical form are universal ones to describe the electromagnetic (EM) field both in non-dispersive and dispersive media, provided material correlations are presented by Duhamel integrals. It is shown that in the time domain additional conduction and displacement currents appear due to changes of conductivity and permittivity parameters with time. Methods of changing constant parameters with time variable ones are principally not correct in time domain and correct in frequency domain. It is shown, however, that separate analysis of dispersion of conductivity or permittivity is impossible. EM field defined by the complex admittivity including both frequency dependent conductivity and permittivity is to be analyzed.

@unpublished{id1382,
  author = {Kamenetsky, Felix M.},
  language = {en},
  title = {Equations of the electromagnetic field in dispersive media},
  url = {http://www.geophysik.lmu.de/{\textasciitilde}kamen/EqDispIntnet09.pdf},
  year = {2009},
}

%O Unpublished Work
%A Kamenetsky, Felix M.
%G en
%T Equations of the electromagnetic field in dispersive media
%U http://www.geophysik.lmu.de/~kamen/EqDispIntnet09.pdf
%D 2009