Inverse problems for the wave equation with a single coincident source-receiver pair

We prove uniqueness for inverse problems for the operator ∂ 2 t − ∆ x − q(x) for data coming from a single coincident source-receiver pair. We prove uniqueness when q 1 ≥ q 2 or when q is a product of an unknown spherically symmetric function and a known function of the angular variables but the source receiver pair is NOT at the center