Summary: We analyse further inverse problems related to synthetic aperture radar imaging considered by C. J. Nolan and M. Cheney [Inverse Probl. 18, No. 1, 221–235 (2002; Zbl 0991.35110)]. Under a nonzero curvature assumption, it is proved that the forward operator \(F\) is associated with a two-sided fold, \(C\). To reconstruct the singularities in the wave speed, we form the normal operator \(F*F\). In our work [Commun. Partial Differ. Equations 30, No. 10–12, 1717–1740 (2005; Zbl 1087.35101)] and [C. J. Nolan, SIAM J. Appl. Math. 61, No. 2, 659–672 (2000; Zbl 0966.35005)], it was shown that \(F*F \in I^{2m,0}(\Delta , C_{1})\), where \(C_{1}\) is another two-sided fold. In this case, the artefact on \(C_{1}\) has the same strength as the initial singularities on \(\Delta \) and cannot be removed. By working away from the fold points, we construct recursively operators \(Q_{i}\) which, when applied to \(F*F\), migrate the primary artefact. One part is lower order, has less strength and is smoother than the image to be reconstructed. The other part is as strong as the original artefact, but is spatially separated from the scene.