Cross-frequency coherence and pulse propagation in a turbulent atmosphere

Cross-frequency coherence of acoustic signals in a turbulent atmosphere is an important consideration for source localization with acoustic sensor arrays and for remote sensing of the atmosphere with sodars and tomography techniques. This paper takes as a starting point recently derived, closed-form equations for the spatial-temporal correlation function of a broadband acoustic signal propagating in a turbulent atmosphere with coupled spatial-temporal fluctuations in temperature and wind velocity. This theory is employed to calculate, based on the Rytov approximation, the two-point, two-time, two-frequency mutual coherence function of plane and spherical waves in the weak scattering regime. The cross-frequency coherence for these waveforms is then obtained and compared with that in the geometrical acoustics approximation. The coherence bandwidth is calculated and analyzed for typical meteorological regimes of the atmospheric surface layer and parameters of sound propagation. The results obtained are compared with available experimental data. The cross-frequency coherence is also used to study the effect of atmospheric turbulence on the mean intensity of an acoustic pulse propagating in a turbulent atmosphere.