Correspondence between sound propagation in discrete and continuous random media

Abstract

Wave propagation in random media is important in many applications such as sound propagation in a turbulent atmosphere and scattering by bubbles and microparticles in the ocean. Formulations for the statistical moments of the sound pressure field in continuous and discrete random media are usually done independently. In this presentation, it is demonstrated that the equations for the first two statistical moments in a continuous random medium have the same form as those for a discrete random medium if the scattering properties of the media are expressed in terms of the differential scattering cross section and total cross section. This analogy enables us to apply methods developed in wave propagation in continuous random media to discrete media, and vice versa. As an example, the existing theory of the interference of the direct and ground reflected waves in a turbulent atmosphere is used to study the effect of trees on the interference of these waves in a forest. The results obtained are compared with experimental data. The correspondence between wave propagation in discrete and continuous random media can also be used in other fields of physics.