Model-Based Quantitative Cross-Borehole GPR Imaging via Virtual Experiments

In this paper, we present a new model-based linear inversion approach for cross-borehole ground penetrating radar quantitative imaging. The approach is reliable and computationally effective as it consists of the cascade solution of two linear inverse problems. The first problem yields a qualitative image of the targets (i.e., their location and approximate shape) and the information needed to cast a set of virtual experiments wherein a linear scattering model that implicitly depends on unknown targets holds true. By relying on such a model, it is possible to achieve, via linear inversion, a quantitative estimate of the targets' electric permittivity and conductivity in a much broader range of cases as compared with traditional approximations, such as the Born approximation. The quantitative imaging capabilities of the proposed method are enhanced by means of an original strategy, in which the features of virtual experiments are exploited to counteract the data reduction caused by the aspect limitation of the measurement configuration. Results against simulated data are reported to show the capability to successfully image nonweak scatters.