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The structure of a common land mine typically exhibits many types of geometric symmetries. These structural symmetries translate into symmetries of the bistatic scattering response of a mine target. A bistatic radar array can therefore be constructed that identifies the presence of these symmetries, and thus can distinguish mines from other asymmetric subsurface objects, such as rocks. To fully exploit this phenomenon, a mathematical description of the types of geometric symmetries exhibited by mines, as well as the resulting effect on bistatic scattering, is required. Geometric symmetry can be described mathematically in terms of group theory. An object that is invariant under ever operation (e.g. reflection, rotation) ofa finite symmetry group is said to posses the symmetry ofthat group. In this paper, this concept is extended to bistatic measurements, such that invariant bistatic measurements can be identified for each mine type. For example, from a single bistatic observation of a square mine, fifteen other bistatic observations of that mine can be determined. The bistatic scattering response is therefore determined to be invariant over a group of order 16. By contrast, the scattering response ofan asymmetric object is invariant over a group oforder two. As a result, the proper collection of bistatic observations can provide a powerful method for classifying subsurface objects as either symmetric (e.g., mines) or asymmetric (e.g., rocks). This paper demonstrates how group theory can be used construct the necessary bistatic array processing to accurately determine different types of target symmetries at arbitrary subsurface locations. This processing is applied to an array of bistatic GPR measurements, and the results demonstrate the efficacy of this idea in identifying symmetric subsurface objects.
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