Solving a two-dimensional telegraph equation with anisotropic parameters

We solve a two-dimensional telegraph equation with anisotropic parameters, which models the propagation of electromagnetic waves in the Earth–ionosphere waveguide, in the frequency range 0.1 − 30 Hz. The results are generalized to allow for the Earth’s sphericity and the horizontal inhomogeneity of the waveguide. It is shown that the resonance character of reflection from the ionosphere at frequencies below 10 Hz becomes pronounced for the horizontal magnetic-field components and for the vertical electric-field component of a horizontal dipole. In the case of low solar activity under nighttime conditions, the oscillations in the frequency dependences of the field components are much more pronounced compared with the case of high solar activity. © 2002 Plenum Publishing Corporation.