, Volume 352, Issue 2, pp 293-337
Date: 04 Feb 2011

An FIO calculus for marine seismic imaging, II: Sobolev estimates

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We establish sharp L 2-Sobolev estimates for classes of pseudodifferential operators with singular symbols [Guillemin and Uhlmann (Duke Math J 48:251–267, 1981), Melrose and Uhlmann (Commun Pure Appl Math 32:483–519, 1979)] whose non-pseudodifferential (Fourier integral operator) parts exhibit two-sided fold singularities. The operators considered include both singular integral operators along curves in \({\mathbb R^2}\) with simple inflection points and normal operators arising in linearized seismic imaging in the presence of fold caustics [Felea (Comm PDE 30:1717–1740, 2005), Felea and Greenleaf (Comm PDE 33:45–77, 2008), Nolan (SIAM J Appl Math 61:659–672, 2000)].

A. Greenleaf was partially supported by NSF grants DMS-0138167 and DMS-0551894.
M. Pramanik was partially supported by an NSERC Discovery grant.