A word of caution is however called for. In the last example the agreement between the input bubble population and that retrieved from the inversion must be interpreted in the following light. The inversion was carried out using the very same models that were used to created the artificial data. Hence the same limited physics applied in both creating the problem and in solving it.
In the real world, there will be a mismatch if the model used by the inversion does not contain all the relevant physics present in the real world phenomenon used to generate the acoustic data. This will tend to degrade the accuracy of the result of obtained by the inversion.
The models of Devin and Minnaert assume free-field conditions. In almost all instances where bubbles are entrained, there will be reverberation (from for example the gas/liquid interface from which the bubbles were entrained). Incorporation of this reverberation into the models is not simple. For details see:
Leighton T G, Ramble D G, Phelps A D, Morfey C L and Harris P P, Acoustic detection of gas bubbles in a pipe, Acta Acustica, 84, 1998, 801-814.
Leighton T G, White P R, Morfey CL, Clarke J W L, Heald G J, Dumbrell H A and Holland K R,
The effect of reverberation on the damping of bubbles
. Journal of the Acoustical Society of America, 112(4), 2002, 1366-1376.Consider for example of the bubbles were entrained under breaking waves in the surf zone, as shown in the picture.To apply the theory in the above references, we must consider a bubble in a region of ocean which is simplified, as shown on the next slide.
Click here for the homepage of the Centre for Ultrasonics and Underwater Acoustics