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Exploration of the terahertz (THz) portion of the electromagnetic spectrum has recently expanded due to advances in ultrafast optical laser systems. The application of THz imaging to detect explosive materials (and other chemical agents) is a promising potential application because of the unique spectral signatures found for many explosives in the THz band. However, since the wavelength of THz radiation is on the order of tens to hundreds of micrometers, the rough interface between materials and the granular nature of material mixtures (such as explosives) may cause frequency-dependent scattering, which could mask the spectral signature. Thus, to evaluate the effectiveness of THz imaging systems, it is necessary to characterize the combined volume and rough-surface scattering effects. Because of the complexity of the media and the requirement for broadband modeling, the finite-difference time-domain (FDTD) formulation is an ideal tool. In this paper, transmission measurements through granular media and reflection measurements from controlled rough surfaces are shown to be in good agreement with FDTD results. Methods for extracting the material spectral peaks from a limited number of measurements are presented and discussed.