Ostashev Vladimir E, Wilson D Keith, Muhlestein Michael B, Attenborough Keith
United States Army Engineer Research and Development Center, 72 Lyme Road, Hanover, New Hampshire 03755, USA.
Open University, Milton Keynes, MK7 6AA, United Kingdom.
J Acoust Soc Am. 2018 Feb;143(2):1194. doi: 10.1121/1.5024904.
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.
尽管声音在森林中的传播在多个应用领域中都很重要，但目前尚无严格且计算上易于处理的预测方法。由于森林中声音散射的复杂性，自然而然地要从随机角度来阐述这个问题。本文表明，如果两种介质的散射特性用微分散射和总截面来表示，那么在森林中传播的声场统计矩方程与在湍流大气中声音传播的方程具有相同的形式。利用现有的湍流大气中声音传播理论，这种类比能够推导出一些用于预测森林声学的结果。特别是，针对在具有微气象的森林中阻抗地面上方传播的声场空间相关函数，推导了二阶矩抛物方程。在大气声学中已经开发出了求解该方程的有效数值技术。再举一个例子，得到了描述森林对直达波与地面反射波之间干涉影响的公式。离散和连续随机介质中波传播之间形成的这种对应关系也可用于物理学的其他领域。
