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Oil spillages on a sea's or an ocean's surface are a threat to marine and coastal ecosystems. They are mainly caused by ship accidents, illegal discharge of oil from ships during cleaning and oil seepage from natural reservoirs. Synthetic-Aperture Radar (SAR) has proved to be a useful tool for analyzing oil spills, because it operates in all-day, all-weather conditions. An oil spill can typically be seen as a dark stretch in SAR images and can often be detected through visual inspection. The major challenge is to differentiate oil spills from look-alikes, i.e., low-wind areas, algae blooms and grease ice, etc., that have a dark signature similar to that of an oil spill. It has been noted over time that oil spill events in Pakistan's territorial waters often remain undetected until the oil reaches the coastal regions or it is located by concerned authorities during patrolling. A formal remote sensing-based operational framework for oil spills detection in Pakistan's Exclusive Economic Zone (EEZ) in the Arabian Sea is urgently needed. In this paper, we report the use of an encoder–decoder-based convolutional neural network trained on an annotated dataset comprising selected oil spill events verified by the European Maritime Safety Agency (EMSA). The dataset encompasses multiple classes, viz., sea surface, oil spill, look-alikes, ships and land. We processed Sentinel-1 acquisitions over the EEZ from January 2017 to December 2023, and we thereby prepared a repository of SAR images for the aforementioned duration. This repository contained images that had been vetted by SAR experts, to trace and confirm oil spills. We tested the repository using the trained model, and, to our surprise, we detected 92 previously unreported oil spill events within those seven years. In 2020, our model detected 26 oil spills in the EEZ, which corresponds to the highest number of spills detected in a single year; whereas in 2023, our model detected 10 oil spill events. In terms of the total surface area covered by the spills, the worst year was 2021, with a cumulative 395 sq. km covered in oil or an oil-like substance. On the whole, these are alarming figures. [ABSTRACT FROM AUTHOR]