Bubble Size Distribution Inversion from Multi-frequency Sound Speed and Attenuation Measurements

Passive acoustics has been identified as an important technique to determine the size distribution of bubbles created by underwater gas leakage. However, the performance of passive acoustic systems is subject to the signal-to-noise ratio (SNR) of bubble signals relative to background noise. This study aims to invert the bubble size distribution by actively transmitting multi-frequency acoustic probes and measuring the sound speed and attenuation variations. By exploiting the linearity within the effective compressibility of bubble-water mixture, three methods (global optimization, least squares, and constrained least squares) are proposed to solve the inversion problem. Simulation and experiment results confirm the validity of these methods, suggesting their potential as tools for quantifying underwater gas leakage.