Comparison of resolution functions of 3-D multi-component with 3-D single-component imaging algorithms for ground penetrating radar data

Abstract

For electromagnetic imaging the vectorial character of the emitted eld and the radiation characteristics of the source and the receiver play an important role. The scalar imaging algorithms, such as Synthetic Aperture Radar (SAR) and the Gazdag phase shift, are commonly used to image GPR data, but are originally developed for the imaging of scalar seismic re ections and thus do not take into account the vectorial character and the radiation characteristics of the source and receiver antennas. An analytical discussion is presented about the imaging of a point scatterer present in a homogeneous space using a zero-o set con guration. For a single frequency component this results in a resolution function. Due to the closed-form expressions for the forward and inverse wave eld extrapolators, closed-form expressions are obtained for these resolution functions. Both scalar inverse wave eld extrapolators do not represent the point scatterer adequately and motivate the introduction of modi ed scalar inverse wave eld extrapolators. Still, the modi ed SAR and Gazdag extrapolators do not result in a circular symmetric resolution function, which is the expected representation of a point scatterer. To obtain a stable inverse wave eld extrapolator based on the electromagnetic scattering formalism, it is necessary to combine two orthogonal components of the measured scattered electric eld, which leads to a multi-component imaging algorithm. The multicomponent imaging algorithm results in a circular symmetric resolution function, which represents the point scatterer adequately. For two homogeneous halfspaces it is not feasible to carry out a similar analytical approach. However, in numerical sense the same procedure can be carried out, which has the important bene t that also the o set between the source and receiver can be taken into account. Numerical results are presented for two homogeneous halfspaces and imaging results of experiments are presented, which take into account the vectorial character of the measured electric eld, the o set between the source and receiver and the presence of a dielectric homogeneous halfspace.