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This paper examines the statistics of the phase and magnitude of multilook synthetic aperture radar (SAR) interferograms toward deployment of along-track interferometry (ATI) for slow ground moving-target indication (GMTI). While the known probability density function (pdf) of the interferogram's phase (derived under the assumption of Gaussian backscatter) is shown to agree almost perfectly for a wide variety of backscatter conditions, the corresponding magnitude's pdf tends to deviate strongly in most cases. Motivated by this discrepancy, a novel distribution is derived for the interferogram's magnitude. This pdf, called the polynomial or p-distribution, matches the real data much more accurately, particularly for heterogeneous composite terrain. For extremely heterogeneous terrain, such as urban areas, both pdfs for interferometric phase and magnitude fail and are extended. Based on these statistics, a completely automatic detection scheme with constant false-alarm rates (CFARs) for slow moving targets is proposed. All involved parameters required to determine the detection thresholds are estimated from the sample data. It is demonstrated, on the basis of experimental airborne SAR data, that this detector is capable of detecting slow moving vehicles within severe ground clutter.