Statistical Characterization of Sound Propagation Over Vertical and Slanted Paths in a Turbulent Atmosphere

Most previous research on sound propagation in the turbulent atmosphere has focused on nearly horizontal propagation. Sound propagation over vertical and slanted paths is fundamentally different from horizontal propagation in that the variances and length scales of the turbulence depend on the height above the ground. In this paper, propagation over vertical and slanted paths is studied using approaches and methods developed for wave propagation through inhomogeneous, random media. Statistical characteristics of sound signals such as the extinction coefficient of the mean sound field, the strength parameter, the transverse mutual coherence function, the coherence radius, and the correlation functions and variances of the phase and log-amplitude fluctuations are calculated for arbitrary spectra of temperature and wind velocity fluctuations, and then specialized to the von Kármán model for the turbulence spectra. The extinction coefficient and coherence radius are analyzed numerically for various meteorological conditions of the atmospheric boundary layer. The results obtained are compared with those for near-horizontal sound propagation. The theory has applications to localization of elevated sound sources with ground-based microphone arrays, and the detection of ground-based sources with elevated arrays.