Unique determination of the damping coefficient in the wave equation using point source and receiver data

In this article, an inverse problem of determining the damping coefficient appearing in a wave equation is studied. We prove that the time-derivative perturbation of wave operator in three space dimension can be recovered uniquely from the data coming from a single coincident source-receiver pair. Since the problem under consideration is under-determined, so some extra assumption on the coefficient is required to prove the uniqueness.