ACOUSTIC INTENSITY VARIABILITY
IN A SHALLOW WATER ENVIRONMENT
BRUCE H. PASEWARK, STEPHEN N. WOLF AND MARSHALL H. ORR
Naval Research Laboratory, Acoustics Division, Code 7120, Washington D.C. 20375, USA
E-mail: pasewark@wave.nrl.navy.mil
JAMES F. LYNCH
Woods Hole Oceanographic Institution, Department of Applied Ocean Physics and Engineering,
Woods Hole, MA 02543, USA
Acoustic signals with center frequencies 224 and 400 Hz were recorded for 63-hours
during an experiment on the New Jersey Shelf, USA (SWARM95). Acoustic energy
statistics have been extracted for both narrowband and broadband signals at a fixed
range of 42 km. The statistics have been found to be non-stationary and depth
dependent. There is frequency and bandwidth dependence to the signal properties and
no unique probability distribution representation.
1
Introduction
Narrowband and broadband acoustic signal scintillation index and intensity probability
distributions extracted from a 63-hour section of the Shallow Water Acoustic Random
Medium 1995 (SWARM95) experimental dataset are presented.
The (SWARM95) experiment was performed from the later part of July through
early August of 1995. The experiment was located on the New Jersey Shelf off the east
coast of the United States [1]. The experiment investigated the impact of water column
sound speed variability induced by a variety of fluid processes on the spatial and temporal
variability of acoustic signals. During the measurement period the sound speed field was
perturbed by linear and nonlinear internal waves and internal tides.
The SWARM95 experiment used several acoustic sources and receivers. The
acoustic signals presented in this paper were generated by two broadband acoustic
sources and received by a 32-element acoustic vertical line array (AVLA). The acoustic
sources projected pseudo random number (PRN) signals centered at 224 Hz (16 Hz
bandwidth) and 400 Hz (100 Hz bandwidth) and were moored in ~54.5 m of water. The
source depths were 48 m and 29 m, respectively. Source levels for both projectors were
approximately 181 dB re 1µPa @ 1m. The AVLA receiver was moored 42 km seaward
of the acoustic sources in 89 m of water. The AVLA receiver spanned the water column
from 23 to 85 m with elements equally spaced every 2 m.
The narrowband acoustic energies were extracted from a single frequency bin of a
Fast Fourier Transform (FFT) of the calibrated hydrophone time-series. The FFT length
was equal to the duration of the PRN sequence (3.9375 s for the 224 Hz data and 5.110 s
for the 400 Hz data). The single frequency signal was squared and calibrated to provide
11
N.G. Pace and F.B. Jensen (eds.), Impact of Littoral Environmental Variability on Acoustic Predictions and
Sonar Performance, 11-18.
© 2002 Kluwer Academic Publishers. Printed in the Netherlands.
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B.H. PASEWARK ET AL.
the narrowband energy. The broadband acoustic energy was calculated by cross
correlating the received acoustic signal with the transmitted PRN sequence (i.e. replica
correlation). The resulting cross correlation time series was integrated over the PRN
sequence duration and calibrated to provide total broadband energy.
2
Acoustic energy probability distribution function histograms
The narrowband (Figs. 2 and 3) and broadband (Figs. 4 and 5) acoustic energy
probability distribution functions are presented as histograms of the acoustic energy
versus the number of received PRN sequences with that energy. The narrowband energy
histograms exhibit the exponential energy (or Rayleigh pressure) distribution expected for
an ensemble of vectors obtained by coherently adding randomly phased sinusoids of the
same frequency [2]. For this narrowband case, each sample has two degrees of freedom.
The exponential-like distribution is found at both signal frequencies and for all receiver
depths.
Figure 1. Histograms of the 224 Hz narrowband energies measured over 63 hours (21,593 data
points) at nine water depths. Histogram bin size is 1010 µPa2s.
Figure 2. Histograms of the 400 Hz narrowband energies measured over 63 hours (13,245 data
points) at nine water depths. Histogram bin size is 1010 µPa2s.
ACOUSTIC INTENSITY VARIABILITY IN SHALLOW WATER
13
In the case of the broadband replica correlation processing, each energy sample is
formed by adding the narrowband components over the entire signal bandwidth. Not all
of these signal components are statistically independent. The number of statistically
independent components realized over the bandwidth will be equal to the number of
temporally resolved arrivals observed in the time correlated matched filter output. Each
statistically independent component in the energy sum increases its number of degrees of
freedom by two and the energy distribution is described by the Chi-squared distribution
with N degrees of freedom [2]. As the number of degrees of freedom becomes very large,
the distribution approaches the lognormal distribution. In the matched filter time domain
data (not shown here), the 224 Hz signals typically showed two or three temporally
resolved pulse arrivals, with the number usually smaller near the boundaries and larger
near the center of the water column. At 400 Hz, a larger number (4–10) of pulse
components was typically seen. The increase in number is attributed to the larger number
of acoustic modes of propagation, the larger signal bandwidth, and the variable presence
of signal components scattered by internal waves.
The significant difference in the number of degrees of freedom for the 224 Hz and
400 Hz signals produces a significant difference in their energy distribution functions.
Near the boundaries at 224 Hz, we find an exponential-like distribution associated with a
single degree of freedom. At mid depth, the peak in the distribution moves to a small, but
nonzero value. The mode (most probable value) continues to increase as we consider the
400 Hz data. The complexity of the pulse structure in the 400 Hz data was observed to be
greatest near mid-depth and to vary considerably over periods of time approaching tidal
cycles, consequently the number of degrees of freedom in the signal should be expected
to be variable.
Figure 3. Histograms of the 224 Hz broadband energies measured over 63 hours (21,593 data
points) at nine water depths. Histogram bin size is 1010 µPa2s.
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B.H. PASEWARK ET AL.
Figure 4. Histograms of the 400 Hz broadband energies measured over 63 hours (13,245 data
points) at nine water depths. Histogram bin size is 1010 µPa2s.
3
Functional form of the histograms
The study of wave propagation in random media and the response of acoustic receiver
arrays to signal variability requires quantification of the acoustic signal statistics in simple
functional forms. In addition, it is necessary to characterize the stationarity of the signal
statistics.
The scintillation index of narrowband signal intensity for a shallow water channel has
recently been predicted to increase exponentially as a function of range, with the signal
exhibiting a lognormal PDF for the saturated scattering case [3–6]. This situation
contrasts with deep-water random media propagation, which is characterized as having
three narrowband acoustic scattering régimes [7–9]. The first is the case where weak
scattering or very short ranges are involved. In this case acoustic fluctuations are
dominated by phase variability and described by the lognormal PDF. The scintillation
index is much less than 1. The second régime is the partially saturated case where the
scintillation index is greater than 1 due to focusing of the acoustic field and the signal
amplitude varies considerably as phase variability creates strong interferences of the
multipath components. Current theory does not provide a closed-form prediction for the
intensity PDF in this régime. The third régime is the saturated scattering case where
strong scattering or long ranges are involved and, over the statistical ensemble, the
multipath components add completely incoherently. In this saturated regime the
narrowband intensity statistics (with each sample having two degrees of freedom) are
described by the exponential PDF, for which the scintillation index has value of 1.
Although we only present shallow water data for one range (and thus can not address
the range dependence properties of the probability distribution functions) we have
attempted to quantify the functional form of the measured probability distributions at the
42 km range using the Kolmogorov-Smirnov Test to compare predicted PDFs to
measured PDFs and provide an estimate of the probability that the measured acoustic
ACOUSTIC INTENSITY VARIABILITY IN SHALLOW WATER
15
energy PDFs are either exponential or lognormal. The Kolmogorov-Smirnov Test has
been applied to both the narrow and broadband 224 and 400 Hz data. It was calculated
using acoustic data from receivers from 23 to 85 meters depth at 2 m intervals, over 63
contiguous 1-hour periods.
The narrowband Kolmogorov-Smirnov Probability (Fig. 6) for both the 224 and 400
Hz data sets indicates that the functional form of the probability distribution is depth
dependent and variable in time. The test for the narrowband 400 Hz data shows frequent
occurrences of the exponential distribution of energy, consistent with classical saturated
scattering theory. The reason for the infrequency of a good fit of the 224 Hz narrowband
data to the exponential distribution (in spite of its histogram's appearance) is likely due to
the small number of multipath components at this frequency.
Figure 5. Probability as a function of time and depth that the 224 Hz and 400 Hz narrowband
energies have an Exponential or Lognormal probability distribution function. Probabilities were
calculated every 2 meters from 23 to 85 meters water depth, over 63 contiguous 1-hour periods.
The broadband Kolmogorov-Smirnov Probability (Fig. 7) is also both depth and time
dependent and shows that the acoustic energy PDF is unlikely to be exponential in nature,
a result that can be anticipated by noting that the broadband acoustic signals have much
more than two degrees of freedom. There are several times and depths at which the
number of degrees of freedom appears to be large enough that the PDF fits the lognormal
distribution (particularly at 400 Hz), however there are also many times and depths where
neither exponential nor lognormal distributions accurately describes the acoustic energy
PDF.
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B.H. PASEWARK ET AL.
Figure 6. Probability as a function of time and depth that the 224 Hz and 400 Hz broadband
energies have an exponential or lognormal probability distribution function. Probabilities were
calculated every 2 meters from 23 to 85 meters water depth, over 63 contiguous 1-hour periods.
The Kolmogorov-Smirnov tests indicate that the probability distribution function for
both the narrow and broadband 224 and 400 Hz acoustic intensity distributions are nonstationary and depth dependent. At this point in time we do not have a strong individual
correlation between the probability distribution variability and the each of the different
types of fluid processes that are randomizing the sound speed profile.
4
Scintillation index
The scintillation index (SI) is often used to characterize acoustic fluctuations. The
narrowband scintillation indices measured over 1-hour periods (Fig. 8, c and d) show a
strong time and depth dependence with values varying from 0.5 to 3.0. The larger values
are apparently associated with signals whose fluctuations are controlled by phase
modulations of partially coherent components as mentioned above. The narrowband 400
Hz data shows a slightly larger SI than the 224 Hz data.
For a Chi-squared energy distribution having N degrees of freedom, the scintillation
index assumes a value of 2/N. The measured broadband scintillation indices (Fig. 8, a
and b) have values varying from 0.2 to 1.0 with the 400 Hz SI slightly smaller than the
224 Hz SI, a result consistent with the observation of a richer resolved multipath
structure in the 400 Hz matched filter results. Careful observation of the narrowband
scintillation index variability shows an apparent 12 hr. cycle between small and large SI
ACOUSTIC INTENSITY VARIABILITY IN SHALLOW WATER
17
values, particularly on the 400 Hz deep receivers. Finette [10] has also seen a periodicity
in SI in his numerical simulations of narrowband acoustic signal propagation through
sound speed fields that are perturbed by linear and nonlinear internal waves.
Figure 7. Scintillation Index as a function of time and water depth. Scintillation indices were
calculated every 2 meters from 23 to 85 meters water depth, over 63 contiguous 1-hour periods.
Large scintillation index value (arrow) is due to noise interference from a small boat and
illustrates some of the dangers of measuring acoustic signal statistics in the real ocean.
5
Conclusion
At a source receiver range of 42 km, the SWARM 95 224 and 400 Hz narrowband and
broadband acoustic signal intensity probability distribution functions are strongly nonstationary and depth dependent. Kolmogorov-Smirnov Tests show that the 1-hr averaged
narrowband energy probability distributions can be better approximated by an exponential
than a lognormal distribution, a sign that the range in the experiment was too short to
observe the statistical signal properties predicted by Creamer [3]. This conclusion is
reinforced by the direct evaluation of the narrowband scintillation index. Broadband
signal statistics are not exponentially distributed and, in general, poorly described by the
lognormal distribution. Scintillation indices measured for the broadband signals are
indicative that the energy estimates have ~4 (at 224 Hz) to ~10 (at 400 Hz) statistical
degrees of freedom. The larger number of degrees of freedom at the higher frequency is
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B.H. PASEWARK ET AL.
consistent with the observed multipath structure and the more frequent occurrences of the
400 Hz broadband energy approximating a lognormal distribution.
Acknowledgements
This work was supported by the Office of Naval Research. The SWARM 95 experiment
was a major multi-disciplinary endeavor and would not have been successful without the
contributions of many individuals. We thank the other members of the SWARM
GROUP: J. Apel, M. Badiey, J. Berkson, K.P. Bongiovanni, J. Bouthillette, E. Carey, C.
Chiu, T. Duda, C. Eck, S. Finette, R. Headrick, J. Irish, J. Kemp, A. Newhall, J. Presig, B.
Racine, S. Rosenblad, S.A. Shaw, D. Taube, D. Tielbuerger, A. Turgut, K. von der Heydt
and W. Witzell.
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