Mathematical Research Letters
Volume 17 (2010)
Fourier integral operators with open umbrellas and seismic inversion for cusp caustics
Pages: 867 – 886
The composition of Fourier integral operators (FIOs) need not in general be an FIO. Motivated by the problem of linearized seismic inversion in the presence of cusp caustics for the background sound speed, we consider FIOs whose canonical relations have certain two-sided cusp degeneracies, and show that the resulting compositions have wave-front relations in the union of the diagonal and an open umbrella, the simplest type of singular Lagrangian manifold.