Efficient Near-Field Imaging for Single-Borehole Radar With Widely Separated Transceivers

In this paper, the formulation of Stolt migration is modified for impulse borehole radar near-field imaging in the subsurface scenarios where the transceiver is widely separated with respect to the detection range. The proposed approach consists of the following aspects. First, the locations of the transmitter and receiver in the survey are regarded as independent sample dimensions, and the original sample set is converted to an enlarged virtual sample set. The frequency-wavenumber spectrum (FWS) of the virtual sample set is available via multidimensional fast Fourier transform (FFT). Then, the relation between the angular frequency and wavenumbers of the transmitter and receiver is derived in the frame of the virtual sample set, which provides the basis for the interpolation in angular frequency and weighting process of FWS. By applying multidimensional inverse FFT (IFFT) to the interpolated and weighted FWS of the virtual sample set, the energy of target responses will focus in some profile of the IFFT result, the position of which is related with the separation between the transmitter and receiver. Finally, the desired target space can be extracted from the IFFT result. The improved Stolt migration technique is compared with the conventional Stolt migration algorithm, back-projection method, and Kirchhoff migration algorithm on synthetic data and validated by single-borehole radar experiment in the subsurface scenario. The results show that the developed Stolt migration is superior to the conventional methods in cross-range resolution, computational cost, and the ability to reconstruct locations and shapes of targets.