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 = ∂2 t − x and multiplication by a nested conormal distribution in order to study their action on spaces of conormal-like distributions. Crown Copyright © 2011 Published by Elsevier Inc. All rights reserved