  We simulate EM pulse propagation along the nonuniform earth surface using so
called time-domain parabolic equation. To solve it by finite differences, we
introduce a time-domain analog of the impedance boundary condition and a
nonlocal BC of transparency reducing open computational domain to a strip of
finite width. Numerical examples demonstrate influence of soil conductivity on
the wide-band pulse waveform. For a high-frequency modulated EM pulse, we
develop an asymptotic approach based on the ray structure of the monochromatic
wave field at carrier frequency. This radically diminishes the computation
costs and allows for pulsed wave field calculation in vast domains measured by
tens of thousands wavelengths.
