  Let $\mR$ be the restriction of the spherical Radon transform to the set of
spheres centered on a hypersurface $\mS$. We study the inversion of $\mR$ by a
closed-form formula. We approach the problem by studying an oscillatory
integral, which depends on the observation surface $\mS$ as a parameter. We
then derive various microlocal analytic properties of the associated
closed-form inversion formula.
