Green’s Function Extraction from Atmospheric Acoustic Propagation

Understanding what affects acoustic waves propagating in the atmosphere is important for a variety of military applications including the development of new remote sensing techniques.

Acoustic waves propagating in the atmosphere may undergo many effects including refraction by temperature and wind velocity gradients, scattering by atmospheric turbulence, absorption by the atmosphere (fluid), diffraction by terrain features, and absorption and reflection by a porous ground. As a result, there may be insonification in acoustic shadow zones, amplitude and phase fluctuations of the propagating sound signals, loss of signal coherence, changes in the interference maxima and minima of the direct ground reflected waves, and multipath effects. Understanding these effects is important for a variety of military applications, such as acoustic source localization and classification, noise propagation in the atmosphere, and the development of new remote sensing techniques of the atmosphere.

Instrumentation Setups. Upper: two-axis array (left); three-axis array and sonic anemometer (right). Lower: propane cannon and speaker (left and center); met tower with Airmars (right)

By extracting the medium impulse response, or Green’s function, one may obtain information about the medium channel in order to overcome the medium effects or deduce information about the medium. For example, in acoustic communications, information is sent through a medium from a host station to client stations. The transmitted information is subjected to a variety of signal distortions and noise caused by the medium. Using time-reversal processing, it is possible to extract the channel medium impulse response from the transmission of a known pilot signal through the channel medium. This Green’s function was then used to modify the subsequent signals to overcome distortion in the channel.

Motivation for the current research is partially derived from atmospheric acoustic communications. In optics, phase conjugation, the frequency-domain equivalent of time reversal, is often used; time-reverse mirrors and cavities are other examples. Ultrasound, geophysics, underwater acoustics, and communications are yet more examples of fields where time reversal is employed.

Time reversal has been successful for source localization and medium imaging, yet much of the research requires spatial reciprocity and temporal invariance. These assumptions are often invalid for moving media and absorptive media. This is critical when considering atmospheric acoustic propagation. A key finding of many of the investigations is that time reversal is more successful when there is considerable multipath.

For diffuse media, it has been demonstrated that cross correlation (CC) of two recordings of the diffuse wave field at different receivers can be used to retrieve the Green’s function between these receivers. The theory was extended to include cases where time-reversal invariance and spatial reciprocity do not hold. The use of passive field fluctuations instead of an active point source has also been considered, where not only is the retrieval of the difference of the Green’s function and its time-reversed function considered, but the sum is as well. This formalism leads to applications for field fluctuations in static systems for potential field problems and direct current problems in conducting media, as well as for diffusive fields excited by injection sources or current sources. A unified theory was developed for Green’s function retrieval when time-reversal invariance does not hold.

Land mine detection exploits the highly elastically nonlinear property of land mines. Land mine detection has been successfully performed by using a nonlinear distortion of a highly focused time-reversed acoustic signal. The method was based on time-reversal techniques from the ultrasound community. The nonlinear acoustic method uses the excitation of two frequency waves that interact with the top surface of the mine. The mine and the ground near the mine have different vibration frequencies, thus this method allows detection near other dense material, such as isolated cobbles.

The objective of this project is to determine the feasibility of using time reversal in conjunction with flow reversal, or other similar methods, to extract a Green’s function for outdoor acoustic propagation using sources in audible frequency ranges. Several propagation factors unique to acoustic propagation in the atmosphere must be considered. First, inherent in the assumptions used in many time-reverse methods is that the medium is stationary. For moving media, a flow-reversal theorem may be used in conjunction with time reversal. Second, spatial reciprocity may not be valid due to terrain features or atmospheric conditions. Multidimensional deconvolution (MDD) has been successful for use in lossless media with homogeneous illumination of all receivers; for some atmospheric conditions, this may provide an alternative retrieval method.

Unlike previous research in other fields, the concept for this project is for military applications. Sources of opportunity (such as bell towers or fog horns) or limited active sources (such as a propane cannon) are considered, as well as limited acoustic sensor arrays. In theater, full illumination of all receivers is not a realistic scenario. However, such retrieval methods may provide sufficient information under certain environmental conditions.

This work was done by Sandra L. Collier, Max F. Denis, John M. Noble, W.C. Kirkpatrick Alberts II, David A. Ligon, Leng K. Sim, Deryck D. James, Christian G. Reiff, and Jericho E. Cain for the Army Research Laboratory. ARL-0222

This Brief includes a Technical Support Package (TSP).
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Green's Function Extraction from Atmospheric Acoustic Propagation

(reference ARL-0222) is currently available for download from the TSP library.

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