Corrections to Foldy’s effective medium theory for propagation in bubble clouds and other collections of very small scatterers

Propagation through underwater bubble clouds is often discussed in terms of Foldy’s effective medium theory of wave propagation through a random collection of a large number of point scatterers. This paper is concerned with corrections to that theory. This work was motivated by a paper of Ye and Ding, who provided the next term after Foldy’s in an expansion in powers of Foldy’s term for the effective wave number squared. When Foldy’s term is not small, truncation after Ye and Ding’s term overestimates the correction. A correction is derived which includes Ye and Ding’s, but is much smaller than theirs when Foldy’s term is large. The correction amounts to replacing the scattering amplitude in Foldy’s expression with an effective scattering amplitude that differs from the original scattering amplitude by having the scattering loss calculated in the effective medium.