### ASA 124th Meeting New Orleans 1992 October

## 2pAO12. New theory/algorithms for bubble density measurement using inverse
acoustic scattering techniques.

**Ramani Duraiswami
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*DYNAFLOW, Inc., 7210 Pindell School Rd., Fulton, MD 20759
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Acoustical techniques have long been used to estimate the bubble density
function. The conventional technique assumes isolated (non-interacting)
scatterers, and results in a Fredholm integral equation of the first kind
relating the bubble density and the measured scattering is obtained. These
ill-posed equations are numerically challenging to solve, especially when the
data---obtained from experiments---inevitably contain noise/error. Usually
these equations are solved by assuming resonant scattering, or by accounting
approximately for off-resonance scattering. Additionally the conventional model
used for the bubble scattering, does not properly account for thermal losses in
the bubble oscillations. In the present work, a multiphase model for sound
propagation through bubbly liquids (due to Caflisch et al.) is combined with
Prosperetti's model for bubble oscillations, to develop two new equations for
determining the bubble population function from measured phase-velocity and
attenuation data. The new theory/equations address perceived drawbacks in the
conventional technique. The equations are evaluated for their potential for
determining the bubble population, by testing them with analytical data with
varying artificial noise. Numerical algorithms using new regularization
techniques are developed. [Work supported by NSF.]