However one key question is, “how do we know that the results of such an inversion are correct?” Let us undertake an example problem. We ask a computer to construct a time series of the hydrophone signal generated by a known bubble population using the models by Devin and Minnaert (mentioned earlier). We instruct the computer to use an emission amplitude weighting, which shows that for example bigger bubbles give out more sound than smaller bubbles, and bubbles close to the hydrophone contribute to the received signal more sound than those further away. We also ask the computer to add random noise, just as one would find in nature. Once we have told the computer how to construct an artificial hydrophone trace from a known bubble population, we tell it to generate a random population of bubbles: The computer knows what the population is, but we do not. Therefore we can undertake an inversion, estimate the bubble population from the sound signal, and then compare our estimation with the actual bubble population that the computer put in. The steps of this process of summarised below:

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