Characterizing the underwater environment can be approached directly by taking measurements, or by inversion where geoacoustic properties of the environment are derived from the way sound interacts with it. Single-element time-reversal mirror was proposed as a physics-motivated, data processing technique, utilizing inputs from either a controlled source or noise interferometry. Once completed, the same technique can be used to detect and track quiet underwater targets, maximizing naval application by allowing surreptitious monitoring, especially in denied areas, with single receivers that are easier to deploy than arrays. Solving the inverse problem with this technique results in ambiguous solutions, however. When a single metric of spatial focus is used, multiple combinations of geoacoustic parameters are able to meet the criteria set. In this work, we propose and evaluate additional metrics, based on temporal focus expected from the time-reversal mirror process, to evaluate the different combinations and arrive at the unique solution, with parameters that match the environment. Using numerical simulations, in the cases examined, this was achieved with a subset of the proposed metrics, thereafter applied in a specific sequence, to arrive at the unique solution. Having completed analysis via numerical simulations, our recipe of metrics is ready to be assessed with real-world data.