Statistical moments of broadband acoustic signals propagating in a refractive, turbulent atmosphere with spatial-temporal fluctuations in temperature and wind velocity

Abstract

Propagation of broadband acoustic signals in a refractive, turbulent atmosphere with spatial-temporal fluctuations in temperature and wind velocity is considered. Starting from a parabolic wave equation, and using the Markov approximation and the hypothesis of locally frozen turbulence, closed-form equations for the statistical moments of arbitrary order of the sound-pressure field are derived for both sound propagation above an impedance ground and line-of-sight propagation. These equations generalize those obtained previously [Wilson and Ostashev, J. Acoust. Soc. Am. 109, 1909–1922 (2001)], where the case of monochromatic sound waves and spatial fluctuations in temperature and wind velocity was considered. The general theory can be used for analysis of many statistical characteristics of broadband acoustic signals propagating in the atmosphere, e.g., temporal coherence, frequency decorrelation, and the pulse spread and wonder. Using this theory, the spatial-temporal coherence function of a broadband acoustic signal is calculated and analyzed. Knowledge of the theoretical coherence function is important for performing source localization with physics-based estimators, particularly maximum-likelihood estimators.