Qualitative model of spatio-temporal radiation pattern of GPR antenna

In our recent work, a simple qualitative model of a dipole GPR antenna radiation pattern has been developed. Replacing the real resistively-loaded dipole by an infinite line current source stretched along the ground-air interface reduces derivation to a 2D boundary value problem for a scalar wave equation which admits an exact analytical solution. Using the complex variable technique we express the Green function in terms of elementary functions and obtain the spatio-temporal radiation pattern for an arbitrary current pulse form by Duhamel integral. In spite of this simplification, the constructed solution describes quite well the ultra-wideband (UWB) pulse emitted by a realistic GPR antenna. These analytical results are useful for the interpretation of GPR raw data by giving a full description of the pulse amplitude and waveform dependence on the radiation angle. Moreover, an inverse problem can be solved: to find the unknown antenna current pulse from the signal measured in the air half-space. Two cases are considered: the surface wave and the aerial wave propagating upwards. This information gives the possibility to deconvolve the subsurface probing data thus increasing the GPR resolution.