2D frequency-domain full-waveform inversion of GPR data: Permittivity and conductivity imaging

Full waveform inversion of Ground Penetrating Radar data is a promising and challenging technique. As both dielectric permittivity and electrical conductivity should be recovered, the associated inverse problem is intrinsically multi-parameter. It requires to properly account for the influence of the Hessian matrix to mitigate the trade-offs between constitutive parameters. Recently, a first step in this direction was performed with the l-BFGS quasi-Newton method, which is based on an approximation of the inverse Hessian computed from previous gradient estimations. We propose to go further in solving locally the Newton equation related to the optimization workflow. For this purpose, we implement the truncated Newton method where the computation of the gradient and Hessian-vector products are respectively based on first-order and second-order adjoint state methods. On a synthetic case study, using the TE mode with borehole and surface acquisitions, we compare our results with those obtained using the l-BFGS method and we show an improvement in the precision of reconstructed parameters. A better decoupling between the two parameters is obtained with the truncated Newton method.