Ostashev Vladimir E, Muhlestein Michael B, Wilson D Keith
U.S. Army Engineer Research and Development Center, 72 Lyme Road, Hanover, New Hampshire 03755, USA.
J Acoust Soc Am. 2017 Dec;142(6):3767. doi: 10.1121/1.5018430.
The radiative transfer equation (RTE) is outlined and then applied to forest acoustics. The RTE is an integro-differential equation for the radiance, which is the angular Fourier transform of the spatial correlation function of the sound field. It correctly accounts for propagation phenomena such as multiple scattering, absorption, and the transformation of the coherent sound field into the incoherent field. In this formulation, acoustical properties of a forest are described by the total cross sections and differential scattering cross sections of different scatterers. In this paper, the four-layer forest model is used with the following distinct layers: ground, trunk layer, canopy layer, and open air. The trunk layer is modeled with finite vertical cylinders, while the canopy layer is modeled with diffuse scatterers. The total and differential scattering cross sections in these layers are calculated. The boundary condition for the radiance at the interface between the ground and trunk layers is formulated. Using a modified Born approximation, the RTE is solved for a plane sound wave normally incident on the edge of a forest. The mean intensities transmitted and backscattered from a stand of trees are calculated and analyzed.
