The study of the acoustic emission of underwater gas bubbles is a subject of both theoretical and applied interest, since it finds an important application in the development of acoustic monitoring tools for detection and quantification of underwater gas leakages. An underlying physical model is essential in the study of such emissions, but is not enough: also some statistical procedure must be applied in order to deal with all uncertainties (including those caused by background noise). In this paper, we take a probabilistic (Bayesian) methodology which is well known in the statistical signal analysis communitiy, and apply it to the problem of estimating the radii of air bubbles in water. We introduce the bubblegram, a feature extraction technique graphically similar to the traditional spectrogram but tailored to respond only to pulse structures that correspond to a given physical model. We investigate the performance of the bubblegram and our model in general using laboratory generated data.

水下气泡声发射的研究是一个具有理论和应用兴趣的主题，因为它在开发用于检测和量化水下气体泄漏的声学监测工具中具有重要的应用价值。在此类排放的研究中，基础物理模型是必不可少的，但还不够：还必须应用一些统计程序来处理所有不确定性（包括由背景噪声引起的不确定性）。在本文中，我们采用统计信号分析界众所周知的概率（贝叶斯）方法，并将其应用于估计水中气泡半径的问题。我们介绍气泡图，一种在图形上类似于传统频谱图的特征提取技术，但专门用于响应与给定物理模型相对应的脉冲结构。我们一般使用实验室生成的数据来研究气泡图和我们的模型的性能。