This work considers the inverse problem of localizing and characterizing multiple stationary pollution sources in surface waters or atmospheric media. This particular problem has been studied before and a uniqueness result was shown. In this paper, we revisit this work with the objective of providing a more complete study. In particular, an alternative uniqueness proof is conducted which is valid for more general pollution source structures. Additionally, a practical numerical identification method is developed and implemented. Finally, several numerical studies are performed which illustrate practical considerations as well as the effectiveness of the approach.