An approximated imaging approach for GPR surveys with antennas far from the interface

GPR systems for remote surveys, i.e. working with antennas not in contact with the medium under test, are becoming more and more widespread. This kind of systems entails several advantages but complicate the imaging in a not negligible way. Indeed, the wave propagation cannot be properly modeled anymore as occurring into a homogeneous medium and the presence of the air-medium interface has to be taken into account in order to obtain accurate images of the scenario under test. This paper deals with an approximate imaging approach, wherein an equivalent wavenumber is introduced to describe the underlining scattering phenomenon by using a ray based model. By doing so and exploiting the Born Approximation, the imaging is faced as the solution of a linear inverse scattering problem formulated by computing the Green's function and the incident field into the spatial domain. Numerical results are provided to test the effectiveness of the proposed approach.