David I. Havelock

Spatial coherence of a sound field in a refractive shadow: Comparison of simulation and experiment

The coherence of a sound field in a refractive shadow near the ground has been examined for microphone separations which are transverse or longitudinal to the direction of propagation. Single tone test signals at 1 kHz, 500, and 100 Hz were measured at a range of 700 m by a microphone array, spanning 270 m longitudinally and 15 m transversely. Estimates of the spatial correlation, based on 10‐minute averages, indicate transverse coherence lengths less than 2 m and longitudinal correlation lengths less than 7 m for moderately strong upward refraction conditions. Numerical simulations were done which emulate the experimental conditions. The Green’s‐function method for the parabolic equation was used to generate two‐dimensional sound fields within a refractive shadow. An upward refracting atmospheric model with homogeneous isotropic Gaussian turbulence was used. The coherence in the simulated sound fields compares well, qualitatively, with the experimentally measured coherence. Both simulation and experiment...

The effect of turbulent intermittency on scattering into an acoustic shadow zone

Classical scattering theory predicts that the intensity of a saturated, scattered signal will have an exponential probability density function (pdf). However, the classical theory does not account for intermittency of the turbulence, which causes quantities such as the scattering cross section to vary in space and time. The classical theory can be modified to include intermittency by making the strength of the turbulence (i.e., the dissipation rate of turbulent kinetic energy) a local property of the scattering volume. The dissipation rate averaged over the scattering volume has a log‐normal pdf. The intermittent theory is compared to measured pdf’s obtained for scattering into an outdoor, ground‐based, acoustic shadow zone. Deviations from the exponential pdf are observed readily in the data, and are predicted well by the intermittent theory. Intermittency is shown to dramatically increase the probability of measuring large values of the scattered intensity.

A large microphone array for outdoor sound propagation studies

A sound field propagating outdoors is perturbed by the turbulence in the atmosphere. To study the fluctuations due to turbulence, the sound field is measured simultaneously at a large number of points using a microphone array. The array consists of 64 microphones which can be configured in a variety of geometries ranging from small patches of only a few square meters to an elongated array spanning 700 m. Remote ‘‘satellite’’ arrays are also possible. The data are collected and processed in a mobile equipment trailer. The microphones, electronics, data collection, and processing are described and practical aspects of deploying the array are discussed. The design criteria and example applications of the array are also discussed.

Phase and amplitude fluctuations in a refractive shadow

For a point source in an upwardly refracting atmosphere, an acoustic shadow region exists beyond the limiting sound ray that grazes the ground. A receiver located within the shadow will have no direct ray path for sound propagation and sound energy arrives at the receiver through other mechanisms. Experiments using an array of microphones at a range of about 1 km and source tones of about 1 kHz indicate that the character of the phase and amplitude fluctuations of the received signal within an acoustic shadow region can vary dramatically. Relationships between the characteristics of the fluctuations and physical propagation mechanisms are explored. In particular, the possibility is investigated that the mechanisms of scattering, diffraction, and ‘‘line‐of‐sight’’ propagation, each intermittently, dominate the received sound field. Application to adaptive beamforming in the atmosphere is discussed.

Estimation of the time‐varying phase (instantaneous frequency) in atmospheric sound propagation

Atmospheric turbulence affects both the amplitude and phase (instantaneous frequency) of transmitted sound. The effect is similar to that of random variations in sound propagation velocity. Two methods to estimate the time‐varying phase are discussed, one based on an FFT with optimum data windows and the other based on the discrete Hilbert transform. Accuracy of the two methods is compared using synthesized single‐frequency test signals. Comparisons are made between the methods applied to acoustic data obtained from sound propagating through a turbulent atmosphere. a)On leave from the University of Hawaii.

Experimental observation of the effects of turbulence intermittency on scattered sound

Fully developed turbulence follows the well‐known Kolmogorov spectrum and, within the inertial subrange, is governed by a single parameter e called the viscous dissipation rate. Under stationary conditions the intensity of sound scattered from turbulence follows an exponential distribution with mean intensity I0 determined by e. In a more realistic turbulence model, the viscous dissipation rate for a given scattering volume fluctuates with a log‐normal distribution. The corresponding fluctuations in I0 cause the intensity distribution to deviate from the exponential distribution. In particular, the tail of the distribution is raised, providing more frequent occurrences of higher intensity levels. This effect impacts on target detection probability in acoustic remote sensing applications. It is shown that the deviations from an exponential distribution are clearly observable in direct measurements of sound intensities within a refractive shadow near the ground. The variance σ of the fluctuations in the dis...

Wideband sound propagation in a refractive shadow zone: Tests of turbulence models

A wideband sound propagation experiment using discrete tones from 40 to 940 Hz has been conducted and analyzed to determine sound‐pressure levels in a refractive shadow zone. It was found that at 40 and 90 Hz, the effect of turbulence was negligible. At 210 Hz and above, turbulence effects were significant. From 380 to 940 Hz, the shadow zone levels showed a relatively weak dependence on frequency. To test two turbulence models (Gaussian and Kolmogorov), the experimentally observed levels in the shadow zone were compared with parabolic equation calculations. The parameters of the turbulence models were determined from meteorological measurements. The Gaussian model, which agreed with acoustic data only over a fairly narrow range of frequencies, gave a strong frequency dependence for the levels in the shadow zone. The Kolmogorov model, on the other hand, gave good agreement with experiment over the entire band of frequencies, showing a relatively weak dependence on frequency from 380 to 940 Hz. It was conc...

Comparison of the spatial coherence in a refractive shadow as calculated using measurement and simulation data

In an upward refracting atmosphere an acoustic shadow is generated near the ground. Sound arrives deep within a shadow region by scattering from atmospheric turbulence. The Green’s function method for the parabolic equation (GF‐PE) can be used to simulate the (complex) sound field in such a shadow region. Signals from an array of microphones can be beamformed to detect coherent signals. To better understand the performance of a beamforming array within an acoustic shadow, knowledge of the coherence of the sound field is important. The transverse and longitudinal coherence of a sound field within a shadow region near the ground are examined using the GF‐PE and experimental measurements obtained with a 24‐element array. Propagation distances of 400–700 m and signal frequencies of 100–1000 Hz are considered. The simulation and measurements are in good agreement and show greater longitudinal coherence than transverse coherence. Variations with frequency and range are also observed. a)Present address: 503 Walk...

Estimation of time‐varying phase for multiple tones in atmospheric sound propagation

Atmospheric turbulence affects both the amplitude and phase of transmitted sound. Tones at different frequencies will be affected differently. In an earlier presentation [J. C. Burgess and D. I. Havelock, ‘‘Estimation of time‐varying phase (instantaneous frequency) in atmospheric sound propagation,’’ J. Acoust. Soc. Am. 95, 2838(A) (1994)], the time‐varying phase of a single tone was estimated by two methods, one based on an FFT with optimum data windows, the other based on the discrete Hilbert transform. In this presentation, the optimum data window method is extended to multiple tones. Accuracy of the method is examined using a synthesized signal with and without additive noise.

Short term fluctuations in the sound field within a shadow region near the ground

An acoustic shadow region can be created near the ground by an upwardly refracting atmosphere or masking by prominent terrain features. Acoustic energy arrives deep within the shadow region principally by scattering from turbulence in the insonified region above the shadow. It is expected that the structure and dynamics of the turbulence ultimately determine the characteristics of the sound field observed in the shadow region. By identifying observable characteristics of this sound field, it is hoped that useful relationships between meteorological dynamics and sound field fluctuations within the shadow region can be established. A large array of microphones has been deployed on an asphalt runway to investigate the sound field fluctuations in a refractive shadow. The frequency range being investigated is 40–1000 Hz, at ranges up to 700 m. The evolution of the sound field over the period of a few seconds is discussed. Examples of the observed sound field are presented.