Stable determination of X-ray transforms of time dependent potentials from partial boundary data

We consider compact smooth Riemannian manifolds with boundary of dimension greater than two. We show that for wave equations, boundary data on the manifold are enough to determine time dependent and time independent lower order source terms in a variety of geometric settings. The main technique is the use of the Gaussian beam Ansatz. We briefly discuss the relationship of the work to recent progress on the Calderon problem.