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Inverse problem of the wave equation and the Schwinger approximation

Hooshyar1, Lam, Razavy

  • 1University of Texas at Dallas, Programs in Mathematical Sciences, Richardson 75083-0688, USA.

The Journal of the Acoustical Society of America
|January 21, 2000
PubMed
Summary

A novel Schwinger variational method enhances acoustic wave profile inversion for spherical inhomogeneities. This stable, accurate technique improves upon the Born approximation, even at high frequencies.

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Area of Science:

  • Acoustics and wave propagation
  • Inverse problems and computational physics

Background:

  • Profile inversion is crucial for characterizing media with acoustic wave propagation.
  • Existing methods like the Born approximation have limitations, especially at high frequencies.
  • Spherical inhomogeneities present unique challenges in wave inversion.

Purpose of the Study:

  • To introduce a new, stable, and accurate profile inversion method for acoustic waves.
  • To adapt the Schwinger variational method for acoustic wave equations, enabling high-frequency analysis.
  • To compare the new method's performance against the Born approximation.

Main Methods:

  • Transformed the acoustic wave equation into a Schrodinger equation.
  • Applied the Schwinger variational method for profile inversion.

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  • Utilized an exactly solvable analytical example for illustration.
  • Conducted numerical simulations with synthetic data, including noisy datasets.

    • Main Results:

    • The new method demonstrates stability and superior accuracy compared to the Born approximation.
    • The transformed Schrodinger equation allows application of both methods at high frequencies.
    • Numerical examples validate the method's effectiveness and stability under various conditions.
    • Analytical and numerical results confirm the method's robustness.

    Conclusions:

    • The presented Schwinger variational method offers a significant advancement in acoustic wave profile inversion.
    • The method is robust, accurate, and stable, outperforming the Born approximation.
    • This approach is suitable for analyzing acoustic waves in media with spherical inhomogeneities, even at high frequencies.