VARIABILITY OF BOTTOM BACKSCATTERING STRENGTH
IN THE 10–500 KHZ BAND AT SHALLOW GRAZING ANGLES
NICHOLAS P. CHOTIROS
Applied Research Laboratories, The University of Texas at Austin,
P.O. Box 8029, Austin TX 78713-8029, USA.
E-mail: [email protected]
Bottom backscatter is often the dominant component of reverberation for sonars
operating in the band from 10 to 500 kHz in littoral waters. A grazing angle of 10° is at
the intersection of the range of angles encountered by operational minehunting sonars
and the angles reported in most experimental studies. Analysis of the measured values
provides an indication of the processes involved. The effectiveness of models may be
gauged by comparison with measured values.
1
Introduction
The variations in the first order statistic, that is the backscattering strength, are
fundamental. The variability in question is the difference in backscattering strength
between different areas of the seafloor that seem to be similar. The similarity may be
quantified in several ways. The simplest and most popular metric is mean grain size. The
expectation has been that areas with the same mean grain size should have the same
backscattering strength at the same acoustic frequency, but the reality is more
complicated. In this study, measured backscattering strength will be examined as a
function of frequency and grain size, and from which simple deductions will be made.
The data are compared with models to gauge their fidelity.
2
Bottom backscattering strength
Backscattering strength is defined as the mean backscattered intensity referenced to a unit
distance, produced by a unit area of the bottom, in any direction, in response to an
incident wave of unit intensity. It is often plotted as a function of grazing angle.
Most sonar applications, particularly in minehunting, involve grazing angles 10° and
below, because of the need to maximize detection range within a limited water depth.
Most measurements of backscattering strength reported in the literature are made at
grazing angles 10° and above because of the difficulty in obtaining reliable measurements
at smaller angles. Therefore, this angle lies at the intersection of the needs of the
applications and the availability of measurements. The reported values [1–22] are shown
in Fig. 1(a) and the key to the data source is shown in Fig 1(b).
The data points cover published backscattering strength values up to 1997. Although
the collection is not completely up to date, the histogram adequately shows a mean and
standard deviation. The global mean of –34 dB is significant, because it appears to be
applicable across the band.
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N.G. Pace and F.B. Jensen (eds.), Impact of Littoral Environmental Variability on Acoustic Predictions and
Sonar Performance, 203-210.
© 2002 Kluwer Academic Publishers. Printed in the Netherlands.
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Figure 1. (a) Measured bottom backscattering strength at 10° grazing angle as a function of
frequency, histogram and the best-fit normal distribution curve. (b) Key to data sources.
VARIABILITY OF BOTTOM BACKSCATTERING STRENGTH
205
Figure 2. Values of bottom backscattering strength at 10° grazing angle as a function of
normalized mean grain size.
There are measurement sites and frequency ranges in which backscattering strength
increases with frequency, but they are counter-balanced by others that have the opposite
trend. To show the trends, data points from the same site are connected. With very few
exceptions, the values lie between –20 and –50 dB. A normal distribution curve with a
standard deviation of 7 dB appears to fit the histogram.
To examine the connection with sediment properties, the backscattering strength was
plotted against the mean grain size of the sediment, normalized by the acoustic
wavelength in water, as shown in Fig. 2. Laboratory measurements [16], made with
graded sands of various mean grain diameters and a flat interface, follow a power law
with a slope of 30 dB per decade of normalized grain size. It appears to be a lower bound
for all data points with normalized grain sizes less than 1, and it represents the intrinsic
backscattering strength of the granular structure. Since all the other measurements, most
of which were taken in situ, give values that are significantly higher, it must be concluded
that other factors dominate the backscattering process in ocean sediments. These factors
include perturbations caused by hydrodynamic forces and biological activity, which result
in roughness of the interface and volume inhomogeneities. In many cases, biological
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activity causes sediment grains to be cemented together into larger pellets, giving the
sediment a larger effective acoustic grain size [23].
At normalized grain sizes greater than 0.1, the scattering strength trend levels off at a
saturation value. It is possible to estimate the saturation value for certain simple cases.
With reference to Fig. 3(a), if Lambert's rule may be assumed, i.e. the average scattered
signal intensity is isotropic in azimuth and varies as the sine of the elevation angle θ2,
then conservation of energy requires that the saturation value should not exceed –21 dB.
Most of the data points at normalized grain sizes less than 10 appear to fall below this
upper bound, with a few exceptions. Of those that exceeded this upper bound, one was a
gravel sediment in the English Channel measured at frequencies between 20 and 40 kHz
[8] and the other a sand sample in the laboratory at 1 MHz [16]. With reference to Fig.
3(b), if the average scattered intensity were isotropic in elevation and azimuth, then
conservation of energy would limit the saturation value to –16 dB. This appears to cover
the values of all data sets at normalized grain sizes up to 10.
Figure 3. Illustration of (a) Lambert's rule, (b) isotropic and (c) directional scattering.
At normalized grain sizes greater than 10, the situation is complicated by outliers in
both directions. A directional scattering surface may account for such a wide range of
variations. With reference to Fig. 3(c), if the backscattered intensity followed a
directional beam pattern that was directed back toward the sonar, then it is possible to
obtain values in the region of 0 dB, which is consistent with the highest outlier. The
process is one of specular reflection from a large perpendicular facet rather than
scattering from a randomly rough surface. Conversely, if the sound beam made oblique
angles to all of the facets, then the backscattered intensity would be extremely small and
consistent with the lowest outliers. Both the high and low outliers were from areas
containing solid rock [12] and coral reefs [4].
The data are separable into three regimes. In the first regime, at normalized grain
sizes less than 0.1, the values lie between the isotropic scattering upper bound, and the 30
dB per decade lower bound. In the second regime, at normalized grain sizes between 0.1
and 10, the values lie between the isotropic scattering upper bound and an empirical
lower bound of –30 dB. In the third regime, at normalized grain sizes above 10, the
scatterers may be either large grains or facets. In the former, the upper and lower bounds
are similar to that of the second regime. In the latter, the range of possible values will be
very large depending on the alignment of the facets.
VARIABILITY OF BOTTOM BACKSCATTERING STRENGTH
207
Figure 4. Comparison of generic bottom backscattering strength curves from APL-UW9407 with
measured values as a function of frequency.
3
Comparison with APL/UW 9407
Since the collection of models in APL-UW9407 [24] has been accepted into the
Oceanographic and Atmospheric Master Library (OAML), it is worth examining its
bottom backscattering strength model predictions in the light of the data available. The
model addresses the 10 to 100 kHz band and grazing angles greater than 8°. It is
completely defined by six input parameters. In practice, one is often unable to obtain all
six parameter values. For this eventuality, the authors have provided a set of 23 generic
bottom types, and may be invoked by name (e.g. rock, gravel, or sand) or by a numerical
mean grain size (φ). Each one contains a preprogrammed set of parameter values that
were judged to be typical. For comparison, the backscattering strength curves from a
broad sampling of generic bottom types are superimposed on the measured values as a
function of frequency in Fig. 4. The generic curves fall on top of a large proportion of
measured values, but they do not cover the lower range of measured values. The generic
curves show backscattering strengths that are constant or increasing with frequency, but
never decreasing with frequency.
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Figure 5. Comparison of generic bottom backscattering strength curves from APL-UW9407 with
measured values as a function of normalized grain size.
In Fig. 5, the generic curves are superimposed on the measured values as a function
of normalized grain size. For normalized grain sizes less than 0.1, the generic curves are
clustered in a narrow region in the middle of the range of measured values. In this sense,
the generic curves may be considered typical. However, they are clustered in a very
narrow region, representing only a small subset of the trends manifested in the measured
data. For example, none of the generic curves can represent the instances where the
backscattering strength drops below –40 dB, rises above –25 dB, or where the
backscattering strength decreases with normalized grain size, of which there are quite a
few. It is evident that the generic curves represent only a small subset of the
backscattering strength trends that are found in the database. For normalized grain sizes
between 0.1 and 10, the generic curves lie between –30 and –16 dB in agreement with the
data. For normalized grain sizes greater than 10, the generic curves continue their upward
trend. As deduced earlier, the backscattering in this regime may be due to large grains or
facets. The generic curves overestimate the range of values of the former, and are unable
to track the wide variations of the latter.
VARIABILITY OF BOTTOM BACKSCATTERING STRENGTH
4
209
Conclusions
The database of bottom backscattering strength values, at a grazing angle of 10°, was
examined. The global average is –34 dB with a standard deviation of 7 dB. The values
appeared to follow a normal distribution. Overall, no significant frequency dependent
trends were discernible, but different frequency dependent trends exist at individual sites.
When plotted against normalized grain size, the data are separable into three distinct
regimes. (1) At normalized grain sizes below 0.1, scattering is dominated by extrinsic
features, such as interface roughness and inclusions. The values lie between the isotropic
scattering upper bound, and the intrinsic scattering lower bound. (2) Between 0.1 and 10,
scattering is dominated by the intrinsic scattering strength, and the values lie between the
isotropic scattering upper bound, and an empirical lower bound. (3) Beyond 10,
scattering may be due to large grains or facets. In the former, the values fall within the
same bounds as (2), and in the latter the values have a very wide range of variation.
The generic bottom backscattering strength curves provided by APL-UW9407 were
compared with the measured data. The generic curves are most successful in regime (2).
In (3), the generic curves are unable to track the facet scattering process, and
overestimate the backscattering strength of the large grain scattering process. In (1), the
generic curves occupy a small region in the middle of the range of measured values. In
this sense, the generic curves are typical, but they represent only a small subset of the
measured data. For this reason, they are not suitable for inversion applications, in which a
best-fit generic bottom type is inverted from measured reverberation data. For inversion
purposes, the six input parameter values should be independently adjusted.
Acknowledgements
This work is sponsored by the Office of Naval Research (ONR), Code 321 OA, under the
management of J. Simmen.
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