We numerically investigate the propagation of radar type short pulses from a horizontal dipole in the presence of some simple models of inhomogeneous ground with a flat surface. We use 3-dimensional (3-D) pseudospectral time domain (PSTD) and 2-D finite difference time domain forward modeling to determine the range and azimuth dependence of electric field components and to simulate events in a moveout profile. The models are: (i) a uniform half space with either high or low conductivity; (ii) a vertical dielectric wedge; (iii) a surface thin layer with a monocline wedge overlaid on the dielectric half space. Our homogeneous results agree with the analytical solutions, and more clearly show the significant vertical electric field component, which occurs for all models. The incorporation of an anomalous dielectric quadrant does not affect the air wave and only complicates ground wave propagation near the boundary. Modeling of a monocline dielectric wedge shows predictable subsurface reflections and refractions, some of which are highly dispersive events, depending on the direction of propagation. We present two field examples that appear to demonstrate some of our findings. We conclude that air waves make suitable references for moveout profiles regardless of dielectric complications, and that our results provide some insight into the interpretation of unique events seen in moveout profiles.