Inverse problem of the wave equation and the Schwinger approximation

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.
• 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.