Piecewise Acoustic Source Imaging with Unknown Speed of Sound Using a Level-Set Method

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.