Mathematical Research Letters

Volume 17 (2010)

Number 5

Fourier integral operators with open umbrellas and seismic inversion for cusp caustics

Pages: 867 – 886



Raluca Felea (School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY 14623)

Allan Greenleaf (Department of Mathematics, University of Rochester, Rochester, NY 14627)


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.

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