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. Refer to PDF file for exact formula.)

Publication Date



This is the pre-print of an article published by Taylor & Francis in Communications in Partial Differential Equations on 11 Jan 2008, available online: https://doi.org/10.1080/03605300701318716

Also archived at: arXiv:math.AP/0605774 v1 31 May 2006

The second author was partially supported by NSF grant DMS-0138167.

Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works in February 2014.

Document Type


Department, Program, or Center

School of Mathematical Sciences (COS)


RIT – Main Campus