Rayleigh scattering from nonspherical particles

A comprehensive framework is developed for calculating the intensity received by a monostatic sonar system due to backscattering from a cloud of nonspherical particles suspended in the ocean. The cloud can consist of different types of particles having arbitrary shapes, volume distributions, and orientations, as well as an overall mass density that varies spatially within the cloud. In the Rayleigh region it is possible to average over particle orientation exactly. The averaged backscattered intensity depends on particle shape through the eigenvalues of a tensor that can, in principle, be determined by solving a boundary value problem for a harmonic function. Since the solution to this boundary value problem is out of reach practically, bounds are obtained on the eigenvalues using the theory of isoperimetric inequalities. Bounds can thereby be obtained on the backscattered intensity that are independent of particle shape. These bounds form the basis for obtaining estimates of the error that is made by assuming the particles in the cloud scatter sound as if they were spherical. A number of examples and applications are considered, the most important of which is the feasibility of a sonar to image black smoker hydrothermal plumes. The reassuring result that the spherical particle assumption is likely to lead to feasibility criteria that underestimate the performance of a sonar is obtained. The isoperimetric bounds are combined with the principle of maximum entropy, applied to the distribution of particle shapes, to obtain a new expression for the square of the amplitude for backscattering at wave number k0 from a particle of volume V, specific bulk modulus e and specific density h: Φ2=(k20V/4π)2[(e−1)/e+(h2−1)/2h]2. This amplitude is obtained by averaging over particle orientation and particle shape and is to be compared to the corresponding quantity for a sphere Φ2sp=(k20V/4π)2[(e−1)/e +(3(h−1))/(2h+1)]2. The use of the new expression is preferred in situations where it is known the particle shapes are quite variable and irregular and where 1.0≤h≤2.5. In all the examples considered it is found the error that results from assuming the particles scatter sound as if they were spherical is small. This is comforting and consistent with one’s intuition that in the Rayleigh region the scattered sound should be somewhat insensitive to the shape of the scatterer.