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Synthetic aperture radar (SAR) images acquired over the ocean frequently show sea wave-like patterns that have wavelengths well above those of ocean surface waves and that are sea surface signatures of oceanic internal waves (OIWs) or of atmospheric gravity waves (AGWs). However, it is often difficult to decide whether they result from the first or the second kind of waves, which has led many investigators to misinterpret SAR images of the sea surface. Based on solitary wave and radar imaging theories of AGWs and OIWs, we present criteria that help distinguish between them. However, there are cases where these criteria, which are based solely on the shape and structure of the features visible on the SAR images, yield ambiguous results. In these cases, one must resort to additional information on the generation of AGWs and OIWs, which are listed in this paper.