Estimating the Size of Scatterers in GPR Data Sets by Means of a Novel Post-Tracking Diffraction Analysis

We developed an algorithm that automatically estimates the size of scatterers by translating and refitting their respective hyperbolic diffractions. Given a spherical scatterer, its radius rigidly moves the resulting diffraction towards earlier arrival times, compared to the diffraction produced by a point-scatterer located at the same position. We can thus estimate the radius by reversing this effect, that is by rigidly moving the analyzed diffraction forwards until it can be linearized through a change in coordinates, as it would be with a point-scatterer. Furthermore, we can more accurately estimate the EM velocity above the scatterer, which would otherwise be overestimated. The applied time shift is measured from the first break of the recorded diffraction, and it is then combined with the obtained EM velocity to recover the scatterer radius. The proposed procedure can be sensitive to significant deviations from the theoretical hyperbolic shape. Such distortions can be caused by elongated scatterers, rapid lateral EM velocity variations, signal interference, random and coherent noise, erroneous trace positioning, as well as excessively low temporal and spatial sampling rates. We apply the algorithm to both synthetic and real GPR profiles, showing an overall good performance, and further discuss its applicability to lower-quality data sets.