### ASA 127th Meeting M.I.T. 1994 June 6-10

## 5pUW15. Application of isoperimetric inequalities to the problem of
acoustic scattering from irregularly shaped objects.

**David R. Palmer
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*NOAA/AOML, 4301 Rickenbacker Cswy., Miami, FL 33149
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It is of general interest to determine the extent that acoustic remote
sensing can estimate physical properties of particulates suspended in the
ocean. One question that can be asked is how well the concentration of
particulates can be determined from measurements of the backscattered acoustic
intensity. When it applies, Rayleigh scattering theory provides the
relationship between the concentration and the intensity. The assumption is
always made in application of the theory that the individual scatterers can be
regarded as spheres. While this assumption is intuitively reasonable, it is
desirable to have error estimates. In this work, bounds are derived for the
error that can occur in mass-concentration estimates due to the
spherical-scatterer assumption. These bounds are obtained by using the theory
of isoperimetric inequalities and are rigorous; depending only on the validity
of Rayleigh scattering theory. The formalism is applied to the problem of
estimating the concentration of particulates in black smoker hydrothermal
plumes. These particulates consist of several different metallic sulfides
having different size distributions. It is found that the spherical-scatterer
assumption results in over-estimating the total mass concentration by at most a
factor of 5 and under-estimating it by at most a factor of 0.7.