An FIO calculus for marine seismic imaging: folds and cross caps

Details An FIO calculus for marine seismic imaging: folds and cross caps An FIO calculus for marine seismic imaging: folds and cross caps

2006-05-31

arxiv.org/abs/math/0605774v2

Mathematics

Analysis of PDEs

Revised; 35 pages; to appear in Comm. in P.D.E

Scientific paper

We consider a linearized inverse problem, arising in offshore seismic exploration, for an isotropic wave equation with sound speed assumed to be a small, singular perturbation of a smooth background. Under an assumption of at most fold caustics for the background, we identify the geometry of the canonical relation underlying the linearization, F, which is a Fourier integral operator, and establish a composition calculus sufficient to describe the normal operator F^*F. The resulting artifacts are 1/2 derivative smoother than in the case of a single-source seismic experiment.

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