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Archive for Rational Mechanics and Analysis

, Volume 231, Issue 1, pp 409–464 | Cite as

Scattering Control for the Wave Equation with Unknown Wave Speed

  • Peter Caday
  • Maarten V. de Hoop
  • Vitaly Katsnelson
  • Gunther UhlmannEmail author
Article

Abstract

Consider the acoustic wave equation with unknown wave speed c, not necessarily smooth. We propose and study an iterative control procedure that erases the history of a wave field up to a given depth in a medium, without any knowledge of c. In the context of seismic or ultrasound imaging, this can be viewed as removing multiple reflections from normal-directed wavefronts.

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Notes

Acknowledgements

P.C. and V.K. were supported by the Simons Foundation under the MATH + X program. M.V.dH. was partially supported by the Simons Foundation under the MATH + X program, the National Science Foundation under Grant DMS-1559587, and by the members of the Geo-Mathematical Group at Rice University. G.U. is Walker Family Endowed Professor of Mathematics at the University of Washington, and was partially supported by the National Science Foundation, a Si-Yuan Professorship at Hong Kong University of Science and Technology, and a FiDiPro Professorship at the Academy of Finland.

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Conflict of interest

The authors declare that they have no conflict of interest regarding this work.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Peter Caday
    • 1
  • Maarten V. de Hoop
    • 1
    • 2
  • Vitaly Katsnelson
    • 1
  • Gunther Uhlmann
    • 3
    • 4
    Email author
  1. 1.Department of Computational and Applied MathematicsRice UniversityHoustonUSA
  2. 2.Department of Earth, Environmental, and Planetary SciencesRice UniversityHoustonUSA
  3. 3.Department of MathematicsUniversity of WashingtonSeattleUSA
  4. 4.Institute for Advanced StudyHong Kong University of Science and TechnologyClear Water BayHong Kong

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