Accurate antenna models in ground penetrating radar diffraction tomography

Linear inversion schemes based on the concept of diffraction tomography have proven successful for ground penetrating radar (GPR) imaging. In many GPR surveys, the antennas of the GPR are located close to the air-soil interface and, therefore, it is important to incorporate the presence of this interface in the inversion scheme (see Hansen, T.B. and Meincke Johansen, P., IEEE Trans. Geoscience and Remote Sensing, vol.38, p.496-506, 2000). Hansen and Meincke Johansen modeled the antennas as ideal (Hertzian) electric dipoles. Since practical GPR antennas are not ideal, it is of interest to investigate the validity of this model. We extend that formulation to hold for arbitrary antennas. For simplicity, the 2.5D case is considered, that is, it is assumed that the scattering object in the soil is invariant in one direction, which, for instance, is the case for a pipe. The arbitrary antennas are modeled by their plane-wave receiving and transmitting spectra. We find these spectra numerically for a resistively loaded dipole using the method of moments. Also, we illustrate, through a numerical example, the importance of taking into account the correct antenna pattern in GPR diffraction tomography.