Correspondence between sound propagation in discrete and continuous random media with application to forest acoustics

Ostashev, Vladimir E.; Wilson, D. Keith; Muhlestein, Michael B. and Attenborough, Keith (2018). Correspondence between sound propagation in discrete and continuous random media with application to forest acoustics. The Journal of the Acoustical Society of America, 143(2) pp. 1194–1205.

DOI: https://doi.org/10.1121/1.5024904

Abstract

Although sound propagation in a forest is important in several applications, there are currently no rigorous yet computationally tractable prediction methods. Due to the complexity of sound scattering in a forest, it is natural to formulate the problem stochastically. In this paper, it is demonstrated that the equations for the statistical moments of the sound field propagating in a forest have the same form as those for sound propagation in a turbulent atmosphere if the scattering properties of the two media are expressed in terms of the differential scattering and total cross sections. Using the existing theories for sound propagation in a turbulent atmosphere, this analogy enables the derivation of several results for predicting forest acoustics. In particular, the second-moment parabolic equation is formulated for the spatial correlation function of the sound field propagating above an impedance ground in a forest with micrometeorology. Effective numerical techniques for solving this equation have been developed in atmospheric acoustics. In another example, formulas are obtained that describe the effect of a forest on the interference between the direct and ground-reflected waves. The formulated correspondence between wave propagation in discrete and continuous random media can also be used in other fields of physics.

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