Permittivity and Conductivity Reconstruction by Full Waveform Inversion of GPR Data using the L-BFGS-B Algorithm

Full waveform inversion (FWI) of ground-penetrating radar data is an emerging technique for quantitative imaging of the near surface, mainly through the estimation of the dielectric permittivity (ε) and of the electric conductivity (σ). Recent studies already succeeded to provide high resolution cross-hole images by FWI using conjugate gradient algorithms. In this study, we present a frequency-domain FWI algorithm based on the L-BFGS-B optimization which takes into account the Hessian influence in the steepest-descent direction correcting for dimensionalities between parameters. We discuss the impact of the parametrization for the simultaneous reconstruction of ε and σ, showing that a robust criterion is provided by the ratio of the gradient norms in the directions of ε and σ: the relative amplitudes of the gradients of the chosen parameters greatly impact the conditioning of the inverse problem. We show that the sensitivity of the cost function to the selected parameters needs to be taken into account in the re-parametrization. An illustration is provided using an already published benchmark. It demonstrates the great efficiency of the L-BFGS-B optimization method to deal with non-linearities of the inverse problem.