The ‘inversion’ we would now like to undertake would be to
obtain the bubble population size distributions from the acoustic information.
In fact, in the last slide we just did this in a qualitative way by comparing
the relative natural frequencies of any bubbles we can identify.However we may wish to do this in a quantitative way, when the
exponentially decaying sinusoids generated by various bubbles might overlap or
be hidden in noise (and so not be as readily identifiable as on the last
slide). To do this we need a model of how the bubble generates the sound. That
model is a lightly damped harmonic oscillator,because we have seen from the previous slides that the bubbles produce
a pressure emission which to first order
resembles the
exponentially decaying sinusoid that is characteristic of the lightly damped
oscillator. To summarise in note form:
Inversion: Obtaining bubble population size distributions
from the acoustic information