Reflection imaging of layered media without using low frequencies

We study the reconstruction of a layered medium from reflection data when the source pulse does not have low frequencies. We do the analysis in the Born approximation and in the frequency domain. We determine the frequency range which can stably be recovered. We employ stable analytic continuation to extend this frequency range down to zero. We give an explicit condition on the depth, the lowest wave number and the aperture that implies the possibility of stable reconstruction and demonstrate by a numerical example what can be achieved.