| Ground Penetrating Radar (GPR) is a proven method of characterizing the shallow subsurface. Most interpretations using GPR have relied upon raw data records or records that have been processed with seismic data processing techniques. To aid in the interpretation of GPR reflection sections, a regularized pseudo-inverse algorithm is described based on Geophysical Diffraction. Tomography (GDT) from multifrequency multi-monostatic GPR measurements. The algorithm is based on the first Born approximation for vector electromagnetic (EM) scattering. Fully analytical reconstruction results are obtained by using a regulaxized pseudo-inverse operator. In contrast to existing matrix-based methods, which numerically calculate the pseudo-inverse, our calculations are based on continuous operators. The main advantage of our method is the computational efficiency. While the existing, analytical, GDT techniques, known as Filtered Backpropagation (FBProp), require a lossless background, the algorithm described here allows either a lossless background medium or an attenuating background. Since radar wavelengths are often times on the same order as the depth and size of underground object of interest, the evanescent components are included in our algorithm to enhance the image resolution. The quality of the images and limitations of some simplifying assumptions are investigated for two-dimensional and three-dimensional algorithms using both simulated and experimental data. It is found that our inversion formula yields good image quality and is not substantially limited by the necessary simplifying assumptions. |
