ASSESSMENT OF THE IMPACT OF UNCERTAINTY IN
SEABED GEOACOUSTIC PARAMETERS ON PREDICTED
SONAR PERFORMANCE
M.K. PRIOR AND C.H. HARRISON
SACLANT Undersea Research Centre, Viale San Bartolomeo 400, 19138 La Spezia, Italy
E-mail: [email protected], [email protected]
S.G. HEALY
QinetiQ Unit, Southampton Oceanography Centre, Southampton, SO14 3ZH, UK
E-mail: [email protected]
'Uncertainty' can be distinguished from 'variability' as the lack of knowledge of the
input variables that a certain calculation must tolerate. In the case studied here, the
calculation concerns sonar performance, and uncertainty may stem from many sources
including the finite measurement precision of methods used to describe the physical
environment. Lack of knowledge of the environmental inputs causes uncertainty in the
predicted sonar performance. It is common for this uncertainty to be high but its impact
is rarely taken into account. In this paper we take, as an example of an environmental
descriptor, plane wave reflection loss already derived from measurements of ambient
noise directionality. An inverse method is developed that allows the reflection loss as a
function of angle and frequency to be converted to a geophysical description of the
seabed in terms of density, sound speed and attenuation. The uncertainty in these
geophysical 'inputs', i.e. the "error bar" associated with the inversion, is estimated and
the impact of this uncertainty on the prediction of sonar performance is calculated. This
is achieved by calculating reverberation and target echo in a series of environments
lying within the uncertainty bounds. These calculations are repeated using seabed data
derived from a geophysical description of a core. The relative impacts of the
uncertainties associated with the two methods of describing the seabed are compared.
The calculations performed also take into account uncertainty in sonar-related
parameters such as target reflectivity.
1
Introduction
When predicting sonar performance using sonar equation calculations, it is common
practise to consider environmental input data as being fixed with no uncertainty. This
approach is potentially misleading when one considers the sensitivity of acoustic
propagation loss, ambient noise and reverberation to environmental changes and the
poor quality of the environmental data that is often available. Sensitivity analyses can be
carried out to see how changes in the environmental description affect predicted
performance. This is usually not done because of lack of time or insufficient knowledge
concerning the spread of environmental parameters.
In this paper, we consider the impact, on one aspect of predicted sonar
performance, of uncertainty in the description of the seabed. Two types of seabed
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Sonar Performance, 531-538.
© 2002 Kluwer Academic Publishers. Printed in the Netherlands.
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description are used and the impacts of their uncertainties are assessed. These are
compared with the impact of uncertainty in a non-environmental parameter, namely the
target scattering strength. Calculations are carried out for monostatic and bistatic sonars
in a shallow water environment. Sonar performance is quantified via the calculation of
regions in which a target, if it were to be present, would result in a positive signal-tonoise ratio (SNR) at the receiver. In the context studied here, “noise” is actually the sum
of reverberation and the direct blast from the sonar transmission.
2
Seabed description
Two methods were used to describe the seabed in this study. The first used estimates of
plane-wave reflection loss derived from measurements of ambient noise. These
reflection losses were input to a genetic algorithm (GA) inversion to produce estimates
of the sound speed, density and attenuation of the seabed. The second method used a
core sample (core 255 from [1]) taken in the same geographic location as the ambient
noise data. This was used to produce a description of the seabed that allowed a range of
possible values for the seabed density, sound speed and attenuation to be determined
from a database of laboratory measurements on seabed sediment samples. Both
descriptions include only compressional wave properties. The methods are now
described in more detail.
2.1
Inversion of Reflection Loss Data
Measurements of the ambient noise in the ocean, made on a vertical line array (VLA),
can be processed to yield estimates of plane wave reflection loss [2]. While these
estimates could be input directly into ray tracing propagation and reverberation models,
there is a risk that “glitches” in the data might corrupt such model calculations.
Furthermore, it may be that the propagation/reverberation models do not use plane-wave
reflection loss directly in their calculations and require instead that the seabed should be
described in terms of sound speed, density and attenuation.
To translate from reflection coefficient as a function of angle and frequency to a
geoacoustic description, an inverse method was developed. The method used standard
techniques [3] based on genetic algorithms but employed a novel method for
determining the fitness of each solution. The fitness was determined to be the product of
two factors representing the closeness of fit and the geophysical “realness” respectively.
The closeness of fit was assessed by a simple root-mean-square (rms) difference
between the linear intensity reflection coefficients from the VLA data and Rayleigh
reflection coefficients [4] produced using the trial values of density, sound speed and
attenuation. The “realness” of each density and sound speed combination was assessed
by determining how close the pair lay to a regression curve fitted to a scatter plot of
density/sound-speed pairs taken from a database of laboratory measurements made on
seabed sediments [5]. The form of the realness function was
[
]
R = exp − ((c − c ρ ) / 150) 2 ; c ρ = 2104.2 − 1.029 ρ + 4.55 x10 − 4 ρ 2
(1)
where R is the realness, c is the sound speed in m/s, ρ is the density in g/cm3 and cρ is
the sound speed determined from the density, using the polynomial fit to the laboratory
measurements.
SEABED UNCERTAINTY AND SONAR PERFORMANCE
533
Figure 1 shows a contour plot of the
realness function, the data points used to
produce the polynomial fit and the fit
itself. The figure shows that the realness
function is high in regions with many
density/sound-speed points and low in
regions where the combination of these
two closely linked parameters was
unphysical. The attenuation of the seabed
was left out of the realness function,
effectively leaving the search for it
unconstrained. This was done because the
correlation between attenuation and the Figure 1. Realness function as contours with
other two seabed parameters is usually density/sound-speed data as points and
polynomial fit as line.
poor [6].
The GA inversion searched simultaneously for seven parameters describing a twolayer seabed; sound speed, density and attenuation for each layer and a thickness of the
upper layer. Figure 2 shows VLA-measured and inverted values of reflection loss as a
function of frequency and angle. The general agreement is shown to be good. The areas
of apparently zero loss around the edges of the figures arise due to array limitations (e.g.
grating lobes in the top right corner) and were removed from consideration in the
inversion. Uncertainty in the seabed description was obtained by running the inversion
method ten times to yield ten seabed descriptions.
Figure 2. Reflection loss for VLA and inverted data.
2.2
Geophysical Description
In the area of interest, a sediment core had been previously obtained (Core 255 from [1])
and laboratory analysis had indicated that the seabed at the location of the core was
silty-sand and sand. A range of sediment properties which may be attributed to sediment
of the same general type as Core 255 was obtained to determine the spread of likely
values of density, sound speed and attenuation. This information was extracted from the
GEOSEIS database [5], a repository of geotechnical, seismo-acoustic and geochemical
information on marine sediment and bedrock. 42 sediment records were selected from
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M.K. PRIOR ET AL.
GEOSEIS by choosing samples with properties that fitted the description of Core 255.
This approach relied on the premise that there were good inter-relationships between
sediment physical properties (e.g. porosity, grainsize) and the resulting geoacoustic
properties such as velocity and attenuation [6]. Geological materials are generally
complex, so samples with identical porosities or grainsizes may have significant
differences in structure and composition and so are likely to exhibit a range of possible
values of density, velocity and attenuation.
3
Sonar scenario
The impact of seabed uncertainty was translated into a spread of sonar performance
using the SUPREMO [7] multistatic model to predict target echo and reverberation in
one monostatic and one bistatic scenario. SUPREMO used the Gamaray [8] eigenray
model to calculate propagation paths for the prediction of target echo, reverberation and
direct blast (in the bistatic case). Gamaray allows the seabed to be described in terms of
its sound speed, density and attenuation. The seabed data from both sources was
therefore directly inserted into the model.
In both cases, an omnidirectional source was used, transmitting an 80 Hz bandwidth
LFM signal centred on 500 Hz. The signal was received by a 64-element horizontal line
array with 1.5 m spacing between elements. The target was represented as a cylinder
with hemispherical end-caps and had length 100 m and radius 5 m. Receiver and target
headings were arranged so that the source signal was specularly reflected and detected
by the receiver in its broadside beam. The environment had a 1500 m/s isovelocity
water column above a seabed described using data from the two methods. The area of
study was a 20 km (x,y) square grid centred on (0,0) with the monostatic sonar placed at
this central point. The bistatic scenario had the source at (-5km,0) and the receiver at
(5km,0).
Sonar performance was quantified by the SNR, calculated as the highest value of
the ratio of the intensities of the target echo and reverberation plus direct blast. It was
recognised that a positive SNR alone does not qualify as indicating a detection
possibility but the inclusion of sonar-specific terms such as detection threshold [9] was
rejected so as to avoid difficulties in widely disseminating the results of the study. In
addition to uncertainty arising from the environmental description, it is important to
remember that the non-environmental terms under consideration are also not known
perfectly. To reflect this, an uncertainty of +/-3 dB was arbitrarily placed on the target
strength calculated by SUPREMO.
Quantification of the impact of seabed uncertainty was achieved by calculation of
the area in which SNR was positive. Further description of the impact of uncertainty
was achieved by determining for each target location whether the SNR was always
negative, always positive or changed sign due to the changes in seabed description and
target strength. This approach resulted in five different descriptions of the SNR due to a
target at each possible location; 1) always positive, 2) always negative, 3) uncertain due
to environmental factors, 4) uncertain due to non-environmental factors 5) uncertain due
to both environmental and non-environmental factors.
SEABED UNCERTAINTY AND SONAR PERFORMANCE
4
4.1
535
Results
Seabed Data
Figure 3 shows the density and attenuation of the seabed plotted as a function of the
sound speed for the laboratory measurements and for the results of the inversion.
The results of the
inversion can be seen to
lie within the range of
the laboratory measurements but the attenuation
coefficient returned from
the inversion is large.
The reason for this is not
known but it is possible
that some process not
included in the stratified
fluid model of the seabed was interpreted as
extra attenuation when
the inversion was carried
out.
Figure 3. Seabed data from lab measurements and inversion.
4.2
Sonar Performance
Figure 4 shows the impact on sonar performance of uncertainty in the seabed
description and target strength with the seabed description derived from the laboratory
measurements. Figure 4a shows the SNR averaged over all target positions with mean
values plotted as crosses and the error bars indicating the standard deviation from the
mean. The x-axis of the plot is the value of the gradient of reflection loss versus angle
calculated using Weston’s equation [10]
αW =
ρα λ
10π log10 (e )
(cw / c ) 2 (1 − (cw / c ) 2 )−3 / 2
(2)
where αλ is the attenuation in dB per wavelength and αW is the gradient (Weston’s
Alpha). αW is a useful single value that expresses the impact of the seabed on reflection
and Harrison showed [11] that for targets beyond a critical range, Rc,
Rc = (8H ) / (α W θ c )
(3)
(where H is the water depth and θc is the critical angle) the SNR is a constant value for
shallow water conditions. Figure 4a shows that the mean SNR is linked to αW. SNR
remains constant for small values of αW then increases with it for values beyond –5dB.
This value corresponds to Rc being 10 km and the transition occurred when the area of
interest lay within the region where SNR was proportional to αW. The connection
between αW and SNR is further shown in Fig. 4b where the Area Of Positive SNR
(AOPS) is shown to increase with αW.
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M.K. PRIOR ET AL.
a
d
b
e
c
f
Figure 4. Sonar performance as quantified by SNR (top), area of positive SNR (middle) and SNR
description (bottom). Results for laboratory measurements. Monostatic sonar left, bistatic right.
The impact of the seabed uncertainty is high with changes in area of over 200 km2. The
error bars in Fig. 4b indicate the change in AOPS associated with the +/-3dB uncertainty
in target strength, plotted on the median value of AOPS from the environmental
uncertainty set. The impact of environmental uncertainty is greater than the nonenvironmental uncertainty. Figure 4c shows the area of interest with colour coding
indicating the nature of the uncertainty in SNR. Black, white, green, red and blue refer
to the numbers given in Sect. 3. The dominance of environmental uncertainty is
illustrated. Figure 4d-f shows the results for the bistatic configuration and the same
trends are shown to be present as for the monostatic case. The main differences are the
reduction in AOPS and the bistatic pattern in Fig. 4f.
SEABED UNCERTAINTY AND SONAR PERFORMANCE
a
537
d
b
e
c
f
Figure 5. Sonar performance as quantified by SNR (top), area of positive SNR (middle) and SNR
description (bottom). Results for inversion. Monostatic sonar left, bistatic right.
Figure 5 shows the sonar performance results for seabed uncertainty arising from
the ambient noise inversion method. The smaller uncertainty arising from this method of
determining the seabed type is reflected in the very small spread of values of αW present
on the x-axes of Fig. 5a. Non-environmental effects dominate the uncertainty in area.
Trends are the same for both monostatic and bistatic sonars with the main difference
between the two being the lower AOPS in the latter case.
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5
M.K. PRIOR ET AL.
Summary and discussion
The impact on sonar performance of uncertainty in seabed data was shown to differ for
the two types of seabed data. The inversion of acoustic measurements was shown to
yield a smaller spread in geoacoustic parameters and this spread was shown to predict a
negligible spread in sonar performance. This stemmed from the repeatability of the
inversion method and from the self-compensating nature of the process. That is, the
ambient noise measurements gave reflection loss estimates and the SNR was linked to
αW, a measure of reflection loss. The uncertainty arising from laboratory measurements
of sediments resulted in larger uncertainty in SNR. It is important that this uncertainty
should be compared with uncertainty arising from target strength and any assessment of
the impact of environmental uncertainty should also include estimates of uncertainty in
non-environmental factors. The work reported here illustrated the usefulness of
accompanying numerical calculations of sonar performance with mathematical analysis.
The importance of αW indicates a possible way in which the impact of uncertainty could
be estimated directly without the need for numerical models.
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