Pulse scattering in a turbulent atmosphere with applications to acoustic remote sensing of the atmosphere with sodars

Abstract

A new, rigorous theory of acoustic pulse scattering in a turbulent atmosphere with spatial-temporal fluctuations in temperature and wind velocity is developed. The theory generalizes the classical theory of sound scattering to broadband signals and coupled spatial-temporal fluctuations of random fields. The scattered sound field is obtained as a Born approximation of a set of equations for the sound pressure and acoustic particle velocity. The spatial-temporal correlation function of the scattered field is calculated. These results are obtained without using the quasi-static approximation, which is employed in the classical theory, and enable analysis of this approximation. The spatial, temporal, and frequency coherences of the scattered signal are studied. The results obtained are applied to acoustic remote sensing of the atmosphere with sodars. It is proposed that the frequency spectrum of the temporal correlation function could be used to measure the wind velocity and the variance of the convective velocity fluctuations. An ad hoc approach for increasing the spatial resolution in acoustic sounding of the atmosphere is suggested. The theory developed is rather general and applicable to acoustic pulse scattering in other media such as the ocean with temperature, salinity, and current velocity fluctuations.