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Oil spills pose a significant threat to the maritime ecosystem. Identifying an oil spill is vital to assess its spread and drift to nearby coastal areas. Synthetic aperture radar (SAR) sensors are viable for mapping and monitoring marine oil spills. This study proposes a new technique that utilizes the dual-polarimetric Sentinel-1 SAR data. The method is based on projecting the <inline-formula><tex-math notation="LaTeX">$2 \times 2$</tex-math></inline-formula> covariance matrix onto distinct random realizations of the normalized scattering configuration. We then obtain the dual-polarimetric spectrum of the scattering-type parameter, <inline-formula><tex-math notation="LaTeX">$\theta _{\text{DP}}$</tex-math></inline-formula>. The <inline-formula><tex-math notation="LaTeX">$\theta _{\text{DP}}$</tex-math></inline-formula> spectrum is then used in the unsupervised K-means clustering technique to segment oil spills from the rest. The cluster findings are then compared to the accuracies obtained using the standard scattering-type parameters from the eigen-decomposition approach (VV, VH) intensities and Otsu thresholding of [<inline-formula><tex-math notation="LaTeX">$H$</tex-math></inline-formula> + <inline-formula><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula> + A] parameter. We demonstrate the proposed approach by clustering marine oil-spill extent over parts of India, Kuwait, the UAE, and the Mediterranean Sea obtained by Sentinel-1 SAR images. We observed that the clustering accuracy of the proposed technique outperforms the ones obtained from the channel (i.e., VV and VH) intensities, Otsu thresholding of [<inline-formula><tex-math notation="LaTeX">$H$</tex-math></inline-formula> + <inline-formula><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula> + A] parameter, and the eigen-decomposition-based method. The proposed approach improves the overall accuracy by <inline-formula><tex-math notation="LaTeX">$\approx\! 8\%$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">$\approx\!20\%$</tex-math></inline-formula>, respectively, over different study areas.