Optimization of migration method to locate buried object in lossy medium

We present an optimized frequency-wavenumber (F-K) migration method to localize buried objects such as landmines in lossy medium. F-K migration has been proposed to find the location of a buried object using ground penetrating radar (GPR) data. This approach makes use of a wave equation in the Fourier domain to back-propagate the received wavefield. For GPR applications however, standard F-K migration assumes that the ground surface is flat and the medium is loss-free which are not true in reality. When implemented in the Fourier domain, the wave equation becomes the Helmholtz equation. It is then straightforward to incorporate a complex index of refraction in the Helmholtz equation to describe wave phenomenon in lossy medium. We generalize F-K migration to the case of rough ground surface and lossy medium. In the framework of Tikhonov regularization, we develop an algorithm that optimally alters the wave propagation velocity and the complex index of refraction to take into account of the ground roughness and lossy medium. In the process of searching the optimal velocity and complex index of refraction, the algorithm is constrained to produce an image of minimum entropy. By minimizing the entropy of the resulting image, better results are obtained in terms of enhanced mainlobe, suppressed sidelobes, and reduced noise. We use examples from field data to demonstrate the performance of our method.