2D full waveform inversion of GPR surface data: Permittivity and conductivity imaging

In this study, we present a frequency-domain full waveform inversion (FWI) algorithm of ground-penetrating radar (GPR) data for the simultaneous reconstruction of the dielectric permittivity and electrical conductivity of the investigated material. The inverse problem is formulated as a quasi-Newton optimization scheme, where the influence of the Hessian is approximated by the L-BFGS-B algorithm. Numerical tests on a cross-shaped benchmark from the literature demonstrate the need for an ad hoc scaling between the relative permittivity ε_r and a relative conductivity σ_r through a reference conductivity σ_o We study the behavior of the inversion with respect to this reference conductivity and to the frequency sampling approach (simultaneous vs. sequential inversion), showing that i) the inversion process should be governed by the permittivity update to respect the natural sensitivity of the cost function and provide a reliable kinematic background soon the early iterations, ii) the value of σ_o should be tuned to find a compromise between resolution and noise in the final image of conductivity. We apply our scaling approach in a realistic synthetic example, illustrating that the quasi-Newton method based on the L-BFGS-B algorithm is able to reconstruct both permittivity and conductivity from multi-offset data acquired with a surface-to-surface acquisition configuration.