Sandra L. Collier –, Max F. Denis, David A. Ligon, Latasha I. Solomon, John M. Noble, W.C. Kirkpatrick Alberts, II, Leng K. Sim, Christian G. Reiff, Deryck D. James
U.S. Army Research Laboratory
2800 Powder Mill Rd
Adelphi, MD 20783-1138

Madeline M. Erikson
U.S. Military Academy
West Point, NY

Popular version of paper 1aSP2, “Propagation effects on acoustic particle velocity sensing”
Presented Monday morning, 7 May 2018, 9:20-9:40 AM, Greenway H/I
175th ASA Meeting Minneapolis, MN

Left: time series of the recorded particle velocity amplitude versus time for propane cannon shots. Right: corresponding spectrogram. Upper: 100 m; lower 400 m.

As a sound wave travels through the atmosphere, it may scatter from atmospheric turbulence. Energy is lost from the forward moving wave, and the once smooth wavefront may have tiny ripples in it if there is weak scattering, or large distortions if there is strong scattering. A significant amount of research has studied the effects of atmospheric turbulence on the sound wave’s pressure field. Past studies of the pressure field have found that strong scattering occurs when there are large turbulence fluctuations and/or the propagation range is long, both with respect to wavelength. This scattering regime is referred to as fully saturated. In the unsaturated regime, there is weak scattering and the atmospheric turbulence fluctuations and/or propagation distance are small with respect to the wavelength. The transition between the two regimes is referred to as partially saturated.

Usually, when people think of a sound wave, they think of the pressure field, after all, human ears are sophisticated pressure sensors. Microphones are pressure sensors. But a sound wave is a mechanical wave described not only by its pressure field, but also by its particle velocity. The objective of our research is to examine the effects of atmospheric turbulence on the particle velocity. Particle velocity sensors (sometimes referred to as vector sensors) in the air are relatively new, and as such, atmospheric turbulence studies have not been conducted before. We do this statistically, as the atmosphere is a random medium.  This means that every time a sound wave propagates, there may be a different outcome – a different path, a change in phase, a change in amplitude. The probability distribution function describes the set of possible outcomes.

The cover picture illustrates a typical transient broadband event (propane cannon) recorded 100 m (upper plots) away from the source. The time series on the left is the recorded particle velocity versus time. The spectrogram on the right is a visualization of the frequency and intensity of the wave through time. The sharp vertical lines across all frequencies are the propane cannon shots. We also see other noise sources: a passing airplane (between 0 and 0.5 minutes) and noise from power lines (horizontal lines). The same shots recorded at the 400 m are shown in the lower plots. We notice right away there are the numerous vertical lines – most probably due to wind noise. Since the sensor is further away, the amplitude of the sound is reduced, the higher frequencies have attenuated, and the signal-to-noise ratio is lower.

The atmospheric conditions (low wind speeds, warm temperatures) led to convectively driven turbulence described by a von Kármán spectrum. Statistically, we found that the particle velocity had similar probability distributions to previous observations of the pressure field with similar atmospheric conditions: unsaturated regime is observed for lower frequencies and shorter ranges; and the saturated regime is observed for higher frequencies and longer ranges. In the figure below (left), the unsaturated regime is seen as a tight collection of points, with little variation in phase (angle along the circle) or amplitude (distance from the center). The beginning of the transition into the partially saturated regime has very little amplitude fluctuations and small phase fluctuations, and the set of observations has the shape of a comma (middle). The saturated regime is when there are large variations in the amplitude and phase, and the set of observations appears to be fully randomized – points everywhere (right).

Scatter plots of the particle velocity for observations over two days (blue – day 1; green – day 2).  From left to right, the scatter plots depict the unsaturated regime, partially saturated regime, and saturated regime.

The propagation environment has numerous other states that we also need to study to have a more complete picture. It is standard practice to benchmark the performance of different microphones, so as to determine sensor limitations and optimal operating conditions.  Similar studies should be done for vector field sensors once new instrumentation is available.  Vector sensors are of importance to the U.S. Army for the detection, localization, and tracking of potential threats in order to provide situational understanding and potentially life-saving technology to our soldiers. The particle velocity sensor we used was just bigger than a pencil. Including the windscreen, it was about a foot in diameter. Compare that to a microphone array that could be meters in size to accomplish the same thing.


  1. Cheinet, M. Cosnefroy, D.K. Wilson, V.E. Ostashev, S.L. Collier and J.E. Cain, “Effets de la turbulence sur des impulsions acoustiques propageant près du sol (Effects of turbulence on acoustic impulses propagating near the ground),” Congrès Français d’Acoustique (French Congress of Acoustics), 11-15 April 2016, Le Mans, France.
  2. Ehrhardt, S. Cheinet, D. Juvé and P. Blanc-Benon, “Evaluating a linearized Euler equations model for strong turbulence effects on sound propagation,” J. Acoust. Soc. Am., 133, 1922-1933 (2013).
  3. L. Collier, “Fisher Information for a Complex Gaussian Random Variable: Beamforming Applications for Wave Propagation in a Random Medium,” IEEE Trans. Sig. Proc. 53, 4236-4248 (2005).
  4. E. Norris, D.K. Wilson and D.W. Thomson, “Correlations Between Acoustic Travel-Time Fluctuations and Turbulence in the Atmospheric Surface Layer,” Acta Acust. Acust., 87, 677-684 (2001).

This research was supported in part by an appointment to the U.S. Army Research Laboratory
Research Associateship Program administered by Oak Ridge Associated Universities.

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