Methane is the second most abundant greenhouse gas after carbon dioxide. Anthropogenic sources are the dominant emitters of methane. The poor spatial resolution of satellite imagery, high interclass similarity, the multi-scalar nature of features, and the dominance of background limit the performance of the previous approaches. Further, the reliance on high-resolution imagery limits the cost-effective global application of the works introduced in the literature. To resolve this, the present work proposes a novel method for methane source classification based on open-source multi-spectral satellite imagery of Sentinel-1 and 2. The work utilizes deep dual-scale convolutions with scaled dot product self-attention calculated across the 15 composite bands of Sentinel-1 and 2 data. The incorporation of non-RGB bands along with the RGB bands further enables the model to learn the spectral differences essential for the classification. The experimental results witness the superior performance of the developed method against other considered state-of-the-art methods.