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The problem of subsurface target detection has been studied. Modifications of a damped exponential model has been applied for reducing the clutter due to a rough boundary. Utilizing numerical simulations, a sensitivity analysis is performed to investigate the features of detection of low-contrast targets. The dependence of the received signal on the properties of an inhomogeneous medium, rough surface and the locations of the objects has been studied. The calculations have been performed for randomly buried objects. It has been found that it is possible to significantly improve the ratio between the scattered signal from subsurface objects and the scattering from a rough boundary.