Hyperbola fitting for characterising cylindrical targets in GPR data using deep learning permittivity predictions

Hyperbola fitting, although commonly used for the interpretation of GPR data, is an ill-posed problem, where many different combinations of medium velocity, target depth and radius can lead to similar hyperbolic signatures. Without any a priori information, these parameters cannot be accurately estimated through hyperbola fitting. In this paper, a hyperbola fitting scheme for characterising cylindrical targets in GPR data with a priori knowledge of the medium velocity is presented. The medium velocity is obtained through permittivity predictions from a neural network scheme which was trained using realistic synthetic data generated utilising a 3D accurate model of a real GPR transducer. Fixing the velocity, estimates of depth and radius of targets can be obtained through optimisation by fitting a hyperbolic curve to the data in an automatic approach. The scheme was tested with both numerical and real data showing that an accurate estimate of the target depth can be obtained, whereas the radius could not be estimated accurately. This shows that even with known medium velocity, radius cannot be estimated reliably since small changes in the radius do not alter significantly the resultant hyperbolic response, in addition to other uncertainties regarding the real data that influence the radius estimation.