Microlocal analysis of scattering data for nested conormal potentials

Working in the time domain, we show that the location of the singularities and the principal symbol of a potential that is conormal to nested submanifolds S2⊂S1⊂Rn, for n⩾3, can be recovered from the backscattering as well as from the restriction of the far-field pattern to more general determined sets of scattering data. This extends the work of Greenleaf and Uhlmann where the potentials considered are conormal to a single submanifold S⊂Rn. We utilize the microlocal analysis of the wave operator and multiplication by a nested conormal distribution in order to study their action on spaces of conormal-like distributions.