Quiet heights and pulse tails: The modal structure of near ground to near ground sound propagation in the nocturnal duct

Abstract

On clear nights over land a temperature inversion forms, creating an acoustic duct in the first few hundred meters of the atmosphere. Assuming a flat, locally reacting ground surface and a stratified atmosphere, the sound field can be expressed as a superposition of independently propagating vertical modes [J. Acoust. Soc. Am. 112 (6), 2540–2552 (2002) and 115 (4), 1437–1448 (2004)]. The modes account for refraction due to sound-speed gradients as well as for the compliance and resistance of the ground. For typical nocturnal ducts and ground surfaces one finds two types of modes: a surface mode and a set of higher modes. The surface mode is more slowly propagating and more rapidly attenuated than the higher modes. The higher modes’ amplitudes all have a sharp minimum several meters above the ground. Two consequences of this modal structure have been observed: At long ranges, narrow-band signals have a range-independent quiet height at which sound levels are reduced by 10 to 15 dB from the levels on the ground [J. Acoust. Soc. Am. 119 (1) 86–95 (2006)] while impulsive signals develop a bandlimited low-frequency tail [J. Acoust. Soc. Am. 88 (1), 455–461 (1990)].