A model for electromagnetic propagation in the lithosphere

The propagation properties of a crystal waveguide are derived using a model where dielectric constant and couductivity increase with depth according to a simple algebraic relation. The model is more realistic and consistent with currently available geological information and with reasonable extrapolations of crustal properties than are previously treated models. The mathematical analysis, moreover, is straightforward and rigorous, leading to an explicit analytical solution in the form of a mode expansion, the individual terms of which can be written in closed form. Numerical evaluation of the model leads to a total attenuation rate (for the dominant mode) of 0.256 dB km for a frequency of 1 kHz. A geologically critical attribute of the model is a positive temperature gradient with depth as the principal controlling influence on the electric profile. A temperature gradient lower than the one used in constructing the model would significantly reduce the attenuation rate.