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Two Dimensional Velocity Inversion for Acoustic Waves with Incomplete Information

  • A. J. Hermans
Part of the Progress in Scientific Computing book series (PSC, volume 2)

Abstract

We consider a two-dimensional inverse problem. The index of refraction or propagation speed of a medium is known, in some localized region up to small perturbations. Our objective is to construct these small perturbations from observation of the scattered field generated by a known incident field. It follows that in the ideal case the observations have to be collected along a closed curve surrounding the finite support of the perturbations. We shall present a method to solve the incomplete problem, where the data collection took place along a part of the closed curve.

Keywords

Helmholtz Equation Scattered Field Fredholm Integral Equation Incident Field Finite Support 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    J.K. Cohen and N. Bleistein: An inverse method for determining small variations in propagation speed. SLAM J. Appl. Math. Vol. 32, 1977.Google Scholar
  2. [2]
    H. Schomberg: Nonlinear image reconstruction from projections of ultrasonic travel times and electric current densities. Proc. of the conference on Mathematical aspects of computerized tomography, ed. G.T. Herman and F. Natterer, Springer, 1980.Google Scholar
  3. [3]
    F. Stenger: An algorithm for ultrasonic tomography based on inversion of the Helmholtz equation.Google Scholar

Copyright information

© Birkhäuser Boston 1983

Authors and Affiliations

  • A. J. Hermans

There are no affiliations available

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