David R. Palmer
NOAA/AOML, 4301 Rickenbacker Cswy., Miami, FL 33149
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.