  We consider compact smooth Riemmanian manifolds with boundary of dimension
greater than or equal to two. For the initial-boundary value problem for the
wave equation with a lower order term $q(t,x)$, we can recover the X-ray
transform of time dependent potentials $q(t,x)$ from the dynamical
Dirichlet-to-Neumann map in a stable way. We derive H\"older stability
estimates for the X-ray transform of $q(t,x)$ which do not require measurements
on the entirety of the boundary. The essential technique involved is the
Gaussian beam Ansatz, and the proofs are done with the minimal assumptions on
the geometry for the Ansatz to be well-defined.
