Towards 3D full-wave inversion for GPR

Full-wave inversion (FWI) for GPR is an imaging approach in which one tries to determine the parameters describing the subsurface (such as permittivity and permeability) which would best reproduce the observed data, via a non-linear least-squares optimisation problem. The approach can account for multiple-scattering and multi-path information in the data, and results in quantitative information about the subsurface. The method is now well studied for seismic imaging, as well as for GPR imaging in 2D. However, taking a 2D imaging approach limits the applicability and accuracy of FWI whenever significant 3D effects have been observed, such as out-of-plane scattering. We present a theoretical approach to FWI for GPR in 3D, which utilises Total Variation regularisation and a novel Hessian approximation, as well as a coupled finite-element boundary-integral solver for Maxwell's equations to simulate the GPR forward problem. We test the algorithm with a numerical experiment into the reconstruction of a domain containing nearby targets buried in a cluttered, stochastically varying, background soil medium.