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

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Abstract

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)].

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Authors and Affiliations

  1. School of of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY, 14623, USA

    Raluca Felea

  2. Department of Mathematics, University of Rochester, Rochester, NY, 14627, USA

    Allan Greenleaf

  3. Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada

    Malabika Pramanik

Authors
  1. Raluca Felea
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  2. Allan Greenleaf
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  3. Malabika Pramanik
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Corresponding author

Correspondence to Allan Greenleaf.

Additional information

A. Greenleaf was partially supported by NSF grants DMS-0138167 and DMS-0551894.

M. Pramanik was partially supported by an NSERC Discovery grant.

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Felea, R., Greenleaf, A. & Pramanik, M. An FIO calculus for marine seismic imaging, II: Sobolev estimates. Math. Ann. 352, 293–337 (2012). https://doi.org/10.1007/s00208-011-0644-5

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  • DOI: https://doi.org/10.1007/s00208-011-0644-5

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