An efficient sampling method for cross-borehole GPR imaging

This letter reformulates the recently proposed qualitative imaging technique, which is the near-field orthogonality sampling method (NOSM), for 2-D cross-borehole ground penetrating radar (GPR) applications. The NOSM employs the reduced scattered electric field as its indicator function. To derive a relationship between the scattered electric field and the indicator, an integral equation is defined, linking these two quantities to each other. The introduced integral equation is solved analytically for full aperture case. Furthermore, it is shown that the derived integral operator can work for limited aperture scenario. Thus, the NOSM can approximate positions of the targets even with a single-view-multistatic imaging configuration. Feasibility of the proposed method is tested with a specific cross-borehole GPR application, which is the oil shale survey in a limestone. Obtained results show that the proposed technique can distinguish multiple targets with a few numbers of measurements.