Doppler Velocity Extraction from Atmospheric Acoustic Echoes Using a Zero-Crossing Technique

Abstract

The scattering of a narrow-band acoustic signal from atmospheric turbulence generates an echo of randomly varying amplitude and frequency. The mean frequency of the power spectrum of this echo is of interest, as it is related by a Doppler shift to the mean motion of the turbulent air. A data processing technique based on the theory which was developed by Srivastava and Carbone (1969) for application to microwave radars is discussed, wherein this mean frequency may be deduced from measurements of the instantaneous frequency of the echo. The theory demonstrates that the probability density of instantaneous echo frequency is dependent on only the first two moments of the power spectrum and that these moments may be determined simply by averaging data in the time domain. Although a typical echo-sounder receiver generates as output only one Cartesian component of the complex-valued echo, an equation due to Rice (1945) is cited which demonstrates that for the narrow band random signals typical of atmospheric echoes, the mean rate of zero crossing of this component is a good estimate of the mean frequency of the signal spectrum. Thus, the addition of an interval timer to an echo sounder gives it radial wind sensing capability. Because only averaging of measurements is necessary to estimate this mean, this approach to Doppler velocity extraction is computationally more efficient than fast Fourier transform methods usually applied. In addition, the electronic hardware required is much less expensive. The validity in echo sounding of the further step of equating the instantaneous rate of zero crossing to the instantaneous frequency of the signal is demonstrated by application of the technique to an electronically simulated echo. Use of an actual atmospheric echo in this demonstration was precluded by the marked statistical nonstationarity of such echoes. Statistical data for instantaneous zero crossing were found to be in good agreement with theoretical predictions for instantaneous frequency. Similar statistical analyses are presented of the echoes from snow, of those from atmospheric thermal turbulence and of the acoustic noise background. On the basis of the demonstrated statistical behavior of echo sounder signals, a procedure is described for the estimation from digitized data of this kind of mean-scattering cross sections and mean velocities of turbulent air parcels, and for the suppression of the effects of background noise.