Multiple Scattering of a Pulse from a Random Collection of Volume Scatterers

Abstract

The first systematic treatment of multiple scattering based on the wave equation was made by L. L. Foldy [“The Multiple Scattering of Waves,” Phys. Rev. 67, 107–119 (1945)]. Foldy's unique contribution was the introduction of the concept of “configurational” averaging of relevant physical quantities by defining a joint probability distribution for the occurrence of a particular scatterer configuration. Although there has been a considerable amount of work done since Foldy's paper, it seems to have been done only for the scattering of monochromatic radiation. In this paper, Foldy's work is extended to include the scattering of pulses (time-limited signals). The theory is applied to the case where the random collection of volume scatterers represents a dense school of fish (or equivalently, a collection of air bubbles). The scattering properties used for a single fish are those reported by D. E. Weston [“Sound Propagation in the Presence of Bladder Fish,” AD No. 806078 (Sept. 1966)]. Consequently, the theory takes into account dispersion and absorption in the scattering volume. The ensemble average of the scattered pulse is determined as a function of time.