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This study reconstructs acoustic sources from wave equation data without knowing sound speed. Algorithms uniquely determine source shape or amplitudes, validated in 2D and 3D numerical experiments.

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Area of Science:

  • Acoustics
  • Inverse Problems
  • Computational Mathematics

Background:

  • Inverse problems involve determining unknown parameters from measurements.
  • Acoustic source reconstruction is crucial in various fields, including geophysics and medical imaging.
  • Existing methods often require knowledge of the wave speed or multiple measurements.

Purpose of the Study:

  • To develop methods for reconstructing piecewise constant passive acoustic sources from limited data.
  • To address the challenge of unknown sound speed in acoustic inversion.
  • To uniquely determine source shape and amplitudes under different prior assumptions.

Main Methods:

  • Utilizing the acoustic wave equation for source inversion.
  • Developing a level set algorithm for shape reconstruction when amplitudes are known.
  • Employing a least-squares fitting algorithm for amplitude recovery when singularities are known.
  • Bridging low-frequency source inversion with gravimetry inverse problems.

Main Results:

  • Proved unique determination of source shape when amplitudes are known.
  • Demonstrated unique determination of source amplitudes when singularities are known.
  • Validated proposed algorithms through numerical experiments in two and three dimensions.
  • Quantitatively evaluated the performance and accuracy of the reconstruction algorithms.

Conclusions:

  • The study successfully reconstructs acoustic sources without prior knowledge of sound speed.
  • The developed algorithms offer robust solutions for both shape and amplitude determination.
  • The findings have implications for advancing acoustic source inversion techniques and related fields.