Efficient Stolt Migration for Large Nonuniform Single Borehole Radar Surveys

In this paper, the formulation of Stolt migration is modified for impulse borehole radar imaging in large nonuniform subsurface scenarios. By applying the nonuniform fast Fourier transform (FFT) to the acquisition of the frequency-wavenumber spectrum (FWS), the efficiency of Stolt migration for nonuniform surveys is improved. First, each nonuniform exponent basis in Fourier transform is approximated with a weighted summation of several uniform exponent bases. Then, the nonuniform samples with the same uniform exponent basis are accumulated to generate a larger virtual uniform sample set. The FWS of nonuniform samples is approximated with the virtual sample set by FFT. Finally, angular frequency interpolation and inverse FFT are performed over a sample FWS to reconstruct the reflectivity map of the imaging area. The selection of approximation parameters is discussed to make a tradeoff between approximation error and computational cost. The improved Stolt migration technique is compared with the conventional backprojection method and the Kirchhoff migration method on synthetic data and validated by a single borehole radar experiment in a subsurface scenario. The results show that the developed Stolt migration is superior to the conventional methods in terms of computational cost, cross-range resolution, and the ability to reconstruct the targets.