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Part I: Various image reconstruction algorithms used for subsurface targets are reviewed. It is shown how some approximate wavefield inversion techniques: Stripmap Synthetic Aperture Radar (SAR), Kirchhoff Migration (KM) and Frequency-Wavenumber (FK) migration are developed from various models for wavefield scattering. The similarities of these techniques are delineated both from a theoretical and practical perspective and it is shown that Stripmap SAR is, computationally, almost identical to FK migration. A plane wave interpretation of both Stripmap SAR and FK migration is used to show why they are so similar. The electromagnetic assumptions made in the image reconstruction algorithms are highlighted. In addition, it is shown that, theoretically, FK and KM are identical. Image reconstruction results for KM, Stripmap SAR and FK are shown for both synthetic and experimental Ground Penetrating Radar (GPR) data. Subjectively the reconstructed images show little difference, but computationally, Stripmap SAR (and therefore, FK migration) are much more efficient. Part II: A preliminary investigation into the use of the Singularity Expansion Method (SEM) for use in identifying landmines is completed using a Finite-Difference Time-Domain code to simulate a simplified GPR system. The Total Least Squares Matrix Pencil Method (TLS-MPM) is used to determine the complex poles from an arbitrary late-time signal. Both dielectric and metallic targets buried in lossless and lossy half-spaces are considered. Complex poles (resonances) of targets change significantly when the objects are buried in an external medium, and perturbation formulae for Perfect Electric Conductor (PEC) and dielectric targets are highlighted and used. These perturbation formulae are developed for homogenous surrounding media, and their utilization for the half-space (layered medium) GPR problem causes inaccuracies in their predictions. The results show that the decay rate (real part) of the complex poles is n

Part I: Various image reconstruction algorithms used for subsurface targets are reviewed. It is shown how some approximate wavefield inversion techniques: Stripmap Synthetic Aperture Radar (SAR), Kirchhoff Migration (KM) and Frequency-Wavenumber (FK) migration are developed from various models for wavefield scattering. The similarities of these techniques are delineated both from a theoretical and practical perspective and it is shown that Stripmap SAR is, computationally, almost identical to FK migration. A plane wave interpretation of both Stripmap SAR and FK migration is used to show why they are so similar. The electromagnetic assumptions made in the image reconstruction algorithms are highlighted. In addition, it is shown that, theoretically, FK and KM are identical. Image reconstruction results for KM, Stripmap SAR and FK are shown for both synthetic and experimental Ground Penetrating Radar (GPR) data. Subjectively the reconstructed images show little difference, but computationally, Stripmap SAR (and therefore, FK migration) are much more efficient. Part II: A preliminary investigation into the use of the Singularity Expansion Method (SEM) for use in identifying landmines is completed using a Finite-Difference Time-Domain code to simulate a simplified GPR system. The Total Least Squares Matrix Pencil Method (TLS-MPM) is used to determine the complex poles from an arbitrary late-time signal. Both dielectric and metallic targets buried in lossless and lossy half-spaces are considered. Complex poles (resonances) of targets change significantly when the objects are buried in an external medium, and perturbation formulae for Perfect Electric Conductor (PEC) and dielectric targets are highlighted and used. These perturbation formulae are developed for homogenous surrounding media, and their utilization for the half-space (layered medium) GPR problem causes inaccuracies in their predictions. The results show that the decay rate (real part) of the complex poles is n