THE INFLUENCE OF NOISE AND COHERENCE
FLUCTUATIONS ON A NEW GEO-ACOUSTIC
INVERSION TECHNIQUE
C.H. HARRISON
SACLANT Undersea Research Centre, Viale S. Bartolomeo 400, 19138 La Spezia, Italy.
E-mail: [email protected]
Distributed noise sources at the sea surface (wind, rain, waves) and distant shipping
provide an ideal plane wave spectrum for investigating geo-acoustic properties. Using
the fact that the vertical noise directionality is closely related to the bottom properties, a
technique has recently been established theoretically and experimentally [C.H. Harrison,
D.G. Simons, “Geoacoustic Inversion of Ambient Noise: A Simple Method.” Submitted
to JASA] for deducing geo-acoustic properties from the noise directionality. Theory
suggests that the simple ratio of up-to-down beam-steered power is, in fact, the power
reflection coefficient of the seabed – potentially a function of angle and frequency.
Experiments at six sites in the Mediterranean and on the New Jersey Shelf with a 64element vertical array have shown that stable solutions can be obtained in a few
minutes. In preparation to extend the technique to the use of a vertical synthetic aperture
the sptial and temporal variability of the coherence has been investigated by selecting
pairs of hydrophones still from the VLA. Surprisingly the coherence for a pair is quite
unstable on a period of 10 seconds while the reflection loss derived from the entire array
remains reasonably stable. The paper discusses reasons for the fluctuations and
implications for the inversion technique when synthesising an aperture.
1
Introduction
A new method of deriving bottom reflection loss from ambient noise [1–3] has been
tried at five Mediterranean sites (during ADVENT99 and MAPEX2000bis) and most
recently at one site on the New Jersey Shelf (during Boundary2001). It can be shown by
ray or flux arguments [1,2,4] that if the wind provides a sheet source (with or without
distant shipping) the ratio of down-going to up-going noise at a given angle to the
horizontal is simply the bottom power reflection coefficient. This results from the
peculiarity of sheet sources that the propagation does not undergo the usual geometric
spreading with range. Instead there is a geometric series of noise contributions resulting
from the surface interaction once per ray cycle. The downward beam has exactly the
same geometric series as the upward beam but with one extra bottom reflection near the
receiver. Therefore a VLA can measure reflection loss almost directly as a function of
angle and frequency. From this measurement one can then deduce the geoacoustic
parameters (if necessary!) by employing a model of plane wave reflection loss, such as
OASR [5] or more simply, the formulae in [6] for multiple fluid layers with an
underlying solid bottom. The only significant effect of refraction is to modify angles
according to Snell’s law and the sound speeds at the bottom and receiver. A numerical
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Sonar Performance, 139-146.
© 2002 Kluwer Academic Publishers. Printed in the Netherlands.
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demonstration of the fidelity of the theory was given in [1,7], and it was shown in [7,8]
that the measured properties are within about a water depth of the receiver.
In this paper we take the experimental results from two Mediterranean sites and the
New Jersey Shelf site to demonstrate geographic variability. Then at the first site we
look at the influence of spatial and temporal variability on the deduced reflection loss.
One aim is to investigate the feasibility of using a synthetic aperture rather than a full
VLA, and we will find that variability has a dramatically different impact in the two
cases.
2
Geographic variation of reflection loss
If the method really works we naturally expect to see changes from site to site since
bottom properties are known to vary. Here we demonstrate geographic changes with
examples from three out of the six sites visited to date. The full array method is
deliberately insensitive to non-uniformity of noise source distribution.
Figure 1. Sicily sand VLA beam response.
One of the sites visited in November 2000 during MAPEX2000bis was south of
Sicily at the northern end of the Ragusa Ridge, where the bottom was thought to be
sandy. The vertical beam response of the central 32 elements (0.5m spacing) of the 62m
VLA is shown in Fig. 1. The “noise-notch” is evidence of the strong downward
refraction. The “up-to-down” ratio is shown in Fig. 2. Interpreting this as reflection loss
we immediately see the classical interference fringes [6] (indeed these can be seen in the
lower part of Fig. 1 when we know what to look for).
By inspection we can deduce several things, the most obvious of which is the
critical angle (about 30°). In this example the fringes are regular in frequency
(notwithstanding the experimental artefacts caused by grating lobes at high frequencies
and broad beams at low frequencies [1]) which means there must be only two dominant
reflectors or boundaries. Also the layer separation is directly related to the fringe
separation (see later). The strength of the reflection and the depth of modulation of the
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141
fringes provide information about the combined speed and density in the two layers.
Volume absorption in the sediment will certainly affect the low loss region to the left of
the critical angle, but experimentally this region is rather unreliable since the up-todown ratio is so close to unity. Inversions and goodness of fit are discussed in [1,7].
Figure 2. Sicily sand: Experimentally deduced reflection loss.
Figure 3. Elba mud: Experimentally deduced reflection loss.
A contrasting site in the same experiment was ‘lossy mud’ east of Elba. This
resulted in the reflection loss plot of Fig. 3. Here we see evidence of higher losses at low
angles, i.e. an absence of a clear critical angle. Also we see two superimposed fringe
patterns, one fine – with seven or eight loss maxima visible at, say 90°, and one coarse –
with only one maximum and one minimum visible. It is immediately obvious that one
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cannot use a simple three layer (i.e. two boundary) model to explain this data. Indeed
the pattern suggests three boundaries, two of which are wide apart and two of which are
close together. In fact this can be matched very well with a three boundary calculation
[1,7]; furthermore the deduced layer spacing agrees with independent experiments in the
vicinity.
At the New Jersey Shelf site (39°19’N 72°33’W), where we expect a ‘stiff clay’, we
see in Fig. 4 a clear critical angle again (about 30°) but subjectively either many
complicated fringes or none at all. This suggests many equally weakly reflecting layers,
effectively a half-space.
Figure 4. New Jersey Shelf clay: Experimentally deduced reflection loss.
3
Spatial variability of coherence
Spatial variability is a crucial issue for vertical synthetic aperture processing. By
definition we build a cross-spectral density (CSD) matrix for the synthetic aperture by
taking real pairs of hydrophones at real depths. For the sake of economy we keep one
hydrophone fixed, so we rely on the coherence estimates being only dependent on
separation and independent of depth (i.e. the CSD matrix must be Toeplitz). However
normal mode theory tells us to expect non-Toeplitz behaviour especially within a few
wavelengths of boundaries. In the current applications where water depths are about 100
m and frequencies are between 100 Hz and 2000 Hz we expect only residual effects.
There are various experimental ways of demonstrating this. One is to plot the CSD
matrix as a colour contour surface; we expect to see bands parallel to the diagonals and
no variation along the diagonals. Another way is to use each row of the CSD matrix to
plot a graph of coherence vs separation; a spread indicates deviation from Toeplitz. A
more enlightening way, in the current context, is to compare full array reflection loss
with a forced Toeplitz array reflection loss. “Forced Toeplitz” means that we use instead
a Toeplitz array whose diagonals are the average values along the diagonals of the true
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CSD matrix. In practice it is difficult to see any difference at all in these reflection loss
plots, which means the Toeplitz assumption is good enough for this application.
4
Temporal variability of coherence, beam response, and deduced
reflection loss
Using the full array this geoacoustic inversion technique is remarkably insensitive to
variations in noise directionality. However, temporal variability becomes important
when we build the CSD matrix from the coherence between hydrophone pairs taken at
different times. In this section we try out several processing options solely to investigate
behaviour. It is hoped that the requirement for averaging can be moderated by future
processing schemes.
4.1
Full Array Processing (Unmodified CSD Matrix)
Figure 2 shows the average of 20 batches of 10-second files (3 minutes’ worth of data).
The noise is sampled at 6kHz, enabling several hundred 128-point FFTs to be averaged
during each 10 seconds. In fact the solution is fairly well converged after only one 10second file, as Fig. 5 shows.
Figure 5. Experimental reflection loss deduced from a single 10 second file, cf the 20 file average
shown in Fig. 2.
4.2
“Forced Toeplitz” Processing (Toeplitz Array built from Complete Array)
Our first option is to build a Toeplitz array from the full array for one time. However, as
noted in Section 3 there is hardly any difference between this and the original. The next
possibility is to take each diagonal (whilst retaining Hermitian symmetry) from a
different 10-second file. Naturally we need 32 files to construct each new array. Figure
6 shows that even allowing for this, after 7×32 files (exhausting the file supply!), we
still have relatively poor convergence compared with Figs. 2 and 5. So even with the
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spatial averaging (along the diagonals) combining coherence measurements from
different times introduces instability.
Figure 6. Reflection loss deduced via the average beam response (over 224 (=7×32) 10-second
files) from a Toeplitz CSD matrix constructed from averages along diagonals taken from separate
10-second files.
Figure 7. Reflection loss deduced via the average beam response (over 30 10-second files) from a
Toeplitz CSD matrix constructed from simultaneous hydrophone pairs 32 and n.
4.3
Hydrophone Pair Processing (Toeplitz Array built from Hydrophones 1 and n)
If we now select hydrophone pairs (1 and n, up to 32) from the full array for one time
we find that the response is poor to start with but converges reasonably well after 30 or
so 10-second files (Fig. 7). Thus taking hydrophones pairs is worse than taking the full
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145
array, but remembering that here we have only N independent coherences whereas the
full array has (N2−N)/2, it is not surprising that we need a further N averages (~ 30) to
achieve similar stability.
Finally if we take each hydrophone pair from a different 10-second file we find
very slow convergence. The supply of files is exhausted long before we achieve
convergence (Fig. 8).
Figure 8. Reflection loss deduced via the average beam response (over 192 (=6×32) 10-second
files) from a Toeplitz CSD matrix constructed with hydrophone pairs from separate 10-second
files.
4.4
Explanation of these Anomalies
So why is there such a big discrepancy between the required averaging time for the full
array and for the various synthetic apertures? Obviously to build a n-element array takes
at least n times longer, but the above results demonstrate an extra factor. Imagine a
small array near the seabed with “point splashes” at the surface. Each splash (with
beam-forming and up-down comparison) gives straight away an estimate of R at that ray
angle and the frequencies of the broad-band splash. No averaging is required at all, we
just need to fill in each angle and frequency. Therefore we have to wait for sounds to
have arrived from all the required directions, but we don’t need to wait for any evening
out or convergence process. It’s rather like scribbling on a piece of paper pressed on a
coin; the image of the head appears wherever you scribble – scribbling harder doesn’t
help.
In contrast when we take hydrophone pairs we cannot do any steering at all until we
have a complete set of Cnm . Since each Cnm originates at different times they each have
been generated by a different splash (potentially a different angle and frequency). The
resulting correlation matrix consists of a set of numbers that are all incorrect in as far as
they are not the average for a sheet. To a certain extent there will be some averaging
when we perform the ΣΣCnm process to get the beam response, however it is not at all
obvious that the average of ‘wrong’ numbers converges to the right answer! What is
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true, though, is that we certainly have to wait for the ‘filling-in’ time in order to more or
less cover all angles. In addition now, however, we need to ensure that we have the
same angle distribution (i.e. source spatial distribution) for each n,m and this requires
some time for the average to settle down. In short, the reason for the discrepancy is that
the original full array method is self-compensating and builds its reflection loss picture
from estimates of reflection loss (that need no averaging) rather than from coherence
(which certainly does need averaging).
5
Conclusions
A technique has been established for determining bottom reflection loss and hence
geoacoustic parameters from noise directionality. It has already been shown that the
theory is sound and that the measurement is local to the receiver array. In order to test
the feasibility of using a synthetic aperture array instead of a full vertical array we have
investigated the dependence on variability. Geographic, spatial (water column), and
temporal variability were addressed. It is found that the averaging time for synthetic
aperture is much more than n times the time for a n-element full array. This surprising
finding is explained by the self-compensating nature (and therefore rapid convergence)
of the full array technique rather than any anomalies with synthetic aperture.
Acknowledgements
The authors would like to thank the Captain and crew of RV Alliance and the chief
scientists on the three cruises Jürgen Sellschopp (ADVENT99), Martin Siderius
(MAPEX2000bis), Charles Holland (BOUNDARY2000) for making time available for
these experiments.
References
1. Harrison, C.H. and Simons, D.G., Geoacoustic inversion of ambient noise: a simple
method, J. Acoust. Soc. Am. (submitted Nov. 2001).
2. Harrison, C.H. and Simons, D.G., Geoacoustic inversion of ambient noise: a simple
method. In Proc. Inst. of Acoust. Conf. on Acoustical Oceanography, Southampton, UK
(April 2000).
3. Aredov, A.A. and Furduev, A.V., Angular and frequency dependencies of the bottom
reflection coefficient from the anisotropic characteristics of a noise field, Acoustical
Physics 40, 176–180 (1994).
4. Harrison, C.H., Noise directionality for surface sources in range-dependent environments,
J. Acoust. Soc. Am. 102, 2655–2662 (1997).
5. Schmidt, H., OASES user’s guide and reference manual. Dept of Ocean Engineering, MIT
(1999).
6. Jensen, F.B., Kuperman, W.A., Porter, M.B. and Schmidt, H., Computational Ocean
Acoustics (AIP Press, New York, 1994) pp. 46, 50, 54.
7. Harrison, C.H. and Baldacci, A., Bottom reflection properties by inversion of ambient
noise. In Proc. 6th European Conf. on Underwater Acoustics, Gdansk, Poland (2002).
8. Harrison, C.H. and Baldacci, A., Simulated geoacoustic inversion of ambient noise, J.
Acoust. Soc. Am. (in preparation).