Linear GPR inversion for lossy soil and a planar air--soil interface

A three-dimensional (3-D) inversion scheme for fixed-offset ground penetrating radar (GPR) is derived that takes into account the loss in the soil and the planar air--soil interface. The forward model of this inversion scheme is based upon the first Born approximation and the dyadic Green function for a two-layer medium. The forward model is inverted using the Tikhonov-regularized pseudo-inverse operator. This involves two steps: filtering and backpropagation. The filtering is carried out by numerically solving Fredholm integral equations of the first kind and the back-propagation is performed using fast Fourier transforms (FFTs). Numerical results are provided to illustrate the performance of the inversion scheme. Index Terms--Diffraction tomography, ground penetrating radar (GPR), inverse scattering, pseudo-inverse operator.