## 1 Introduction  
The oil and gas industry has had deleterious ecological impacts on the waters of the Gulf of Mexico, which has experienced two very large offshore spillage episodes releasing tons of crude petroleum in this tropical marine environment (Figure 1): the Ixtoc-1 discharge off the Mexican coast in 1979 [1; 2; 3; 4; 5; 6], and the Deepwater Horizon event off the U.S. coast in 2010 [7; 8; 9]. These two accidents are recognized as the largest peacetime oil-related environmental incidents [10; 11; 12]. The Gulf also contains a large number of oil seepage sites [13; 14; 15; 16]. Among these, is the world's largest active natural oil leak at the sea floor, the Cantarell Oil Seep [17; 18] in Campeche Bay (Figure 1). The use of satellite sensors to identify the sea-surface expression of oil slicks (oil seeps and oil spills) has been extensively studied by the ocean remote sensing scientific community, e.g., [14; 15; 16; 17; 18; 19]. Together with mathematical simulations and field studies [20; 21], satellites are able to provide means for effective surveillance and tracking of oil slicks, as well as to assist in guiding clean-up operations along shorelines [7; 8; 22]. Spaceborne microwave synthetic aperture radars (SAR) are well-suited for detecting oil slicks [23]. SAR faces two major challenges when it comes to discerning oil slicks: first, the separation of regions in which the return radar backscatter is smoothened from the chaotic rough sea clutter [18; 24; 25; 26]; and second, the separation of the non-unique oil (slicks) signature from radar false targets (e.g., low wind, rain cells, etc.) [27; 28]. A third challenge has emerged as a recent subject matter: the separation of oil (seeps) from oil (spills)--i.e., the discrimination of the slick category: seeps vs. spills [29; 30; 31; 32; 33; 34]. This innovative seep-spill differentiation process contributes in various ways to ocean remote sensing, to offshore fossil fuel operational activities, to environmental preservation and cleanup, to the operation of fisheries, and to marine and coastal policy-making in general. The slick category discrimination provides the scientific community opportunities to put forth a set of systemic structural recommendations, or solutions, linking the petroleum industry with political, economic, social, and ecological issues--for instance, in oil-related management practices or in environmental monitoring strategy responses. The presently available and upcoming C-band SAR satellite constellation missions (e.g., Sentinel-1 of the Copernicus Programme [35; 36; 37] and RADARSAT Constellation Mission [38; 39]), along with the existing free open-source SAR processing toolboxes (e.g., SNAP [40] and POLSARPRO [41]), can provide academic centers, environmental agencies, nongovernmental organizations, and the petroleum industry itself with the required support to build libraries with the category of oil slicks in the vicinities of offshore oil and gas facilities. The scrutiny of these oil-slick category records is of great interest not only from the political-economic perspective (i.e., discovery of new exploration frontiers based on the identification of oil seeps observed in the surface of the ocean coming from active petroleum systems), but is also relevant from the social-ecological viewpoint (i.e., it can assist in reducing headline uproar inquires with reliable timely information with the detection of oil spills using more efficient environmental surveillance techniques). Figure 1: The location of Campeche Bay (dotted box). The position of the Cantarell Oil Seep (dot), kxtoc-1 platform (+), and the Deepwater Horizon well (x) are also shown. Courtesy of [PERSON] (LabSAR/LAMCE/PEC/COPPE/UFRJ). Our objective in this paper is to use a simple, but mathematically robust multivariate data analysis technique (i.e., build an algorithm based on linear discriminant analysis (LDA) applied to SAR-derived measurements) to seek improvements in slick category differentiation.