Finite-difference time-domain analysis of ELF radio wave propagation in the spherical Earth–ionosphere waveguide and its validation based on analytical solutions

The finite-difference time-domain (FDTD) model of electromagnetic wave propagation in the Earth–ionosphere cavity was developed under assumption of an axisymmetric system, solving the reduced Maxwell equations in a 2D spherical coordinate system. The model was validated on different conductivity profiles for the electric and magnetic field components for various locations on Earth along the meridian. The characteristic electric and magnetic altitudes, phase velocity, and attenuation rate were calculated. We compared the results of numerical and analytical calculations and found good agreement between them. The undertaken FDTD modeling enables us to analyze the Schumann resonances and the propagation of individual lightning discharges occurring at various distances from the receiver. The developed model is particularly useful when analyzing ELF measurements