Simultaneous GPR Reconstruction of Electrical Conductivity and Permittivity

International audienceGround-penetrating radar (GPR) is a non-invasive prospecting technique based on the electromagnetic waves sampling of the near surface. Building quantitative images through these waves requires the reconstruction of both electrical permittivity and conductivity. This multi-parameter reconstruction is performed through the minimization of a misfit function measuring the discrepancy between observed and synthetic data. The minimization is achieved with a local descent method based on the Newton equation. Both the gradient and the product of the Hessian matrix with a model vector are necessary for avoiding any trade-off between parameter classes, especially when high contrasts are encountered by electromagnetic waves. This presentation is devoted to the design of these two key ingredients needed when updating the model, based on efficient first- and second-order adjoint methods. We formulate the problem in the frequency domain and we show that we need two forward modeling for the gradient and two additional forward modeling for the product of the Hessian matrix and a model vector. Our formulation is such that these quantities are obtained through solution fields, regardless of the numerical scheme used to obtain them