A STUDY OF PING-TO-PING COHERENCE
OF THE SEABED RESPONSE
L. PAUTET, E. POULIQUEN AND G. CANEPA
SACLANT Undersea Research Centre, Viale San Bartolomeo 400, 19038 La Spezia, Italy
E-mail: pautet@saclantc.nato.int
Coherence in acoustic backscatter is used to perform reverberation based micronavigation in SAS imaging. To evaluate limits of ping-to-ping coherence, this paper examines
how interface characteristics and acoustic source parameters influence ping-to-ping signal stability. To study these effects independently from other medium variations, a
time series model was developed. This model, BORIS-SSA, is an improved version of
BORIS which applies the fourth order Small Slope Approximation for treating interface
scattering.
1 Introduction
When performing high frequency Synthetic Aperture Sonar (SAS) imaging, platform and
medium instabilities of fractions of wavelengths should be avoided or compensated for. If
not, signals from successive pings do not sum coherently and produce poor quality images.
Platform motion can be compensated for by the use of phase compensation micronavigation using the Displaced Phase Center Antenna (DPCA) technique >dH. This technique
requires minimum coherence between successive pings in order to estimate phase error.
When successive pings are incoherent, it becomes impossible to compare them and to
deduce the movements of the physical antenna. Estimating the effects of platform movements and medium variations on signal fluctuations is essential. An experimental study,
MAPLE 2001, was performed in July 2001 off the coast of Halifax to evaluate limits of
ping-to-ping coherence >1H. An acoustic transducer mounted on a 5 m high tower was
pinging repeatedly at the seafloor while a pan and tilt mechanism changed the heading of
the source. This experimental configuration was designed to reproduce the conditions of
a platform enduring yaw which is the most difficult motion to measure using DPCA. One
of the results of this experiment is that successive signals rapidly loose coherence (after
a heading variation larger than dH ). The angular spread of the scatterers is much smaller
than the dEH beam aperture used in the experiment. The conclusion is that the persistence
of coherence depends on the size and number of scatterers. Strong scatterers provide omnidirectional response but smaller ones combine to form an interference structure which
is directional. In most cases, there is no dominant scatterer and the seabed response is
highly directional. It was found, that this property depends on source properties (pulse,
beam aperture, position), and on interface properties (roughness, heterogeneity, level of
clutter). In order to study how these factors influence the angular response of the seafloor
and to multiply scattering scenarios, a time-series snapshot model, valid at low grazing
angles and high frequency, was developed. BORIS-SSA is based on the Small Slope
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N.G. Pace and F.B. Jensen (eds.), Impact of Littoral Environmental Variability on Acoustic Predictions and
Sonar Performance, 489-496.
© 2002 Kluwer Academic Publishers. Printed in the Netherlands.
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Approximation. After briefly describing the concept of BORIS-SSA, this paper presents
some preliminary results on signal fluctuations from a moving source.
2
BORIS-SSA
The model BORIS was developed primarily to compute time-domain seafloor backscatter
at normal incidence [3, 4]. The input parameters of the model are the source parameters
and a realization of the seabed having some predefined statistics. Contributions from each
element of the interface are calculated using the Kirchhoff approximation (KA), whereas
contributions from the volume are treated under the small perturbation theory. The KA
is valid at normal incidence but is often inaccurate at low grazing angles [5]. The small
slope approximation (SSA) however is a promising method which shows, in the 1-D
case, good agreement with exact solutions at all angles [6, 7]. The SSA takes the form
of a series expansion in generalized surface slope. The two orders commonly used are
the second (SSA-2) and the fourth (SSA-4) orders. The order refers to the development
order of the surface slope in the surface scattering strength expression. Figure 1 shows a
comparison between the exact solution, the KA, the SSA-2 and the SSA-4 for a power law
interface (i.e., an interface having a power spectral density proportional to (k2 +kβ2 )−γ/2
c
for k < kmax , where k is the wave number and kc is an arbitrary cutt-off frequency).
The coefficient of proportionality is adjusted to obtain the correct RMS-height for the
interface. In Fig. 1, the agreement between the exact solution and the SSA-4 is very
good at all angles. This justifies the use of the SSA-4 in place of the KA in BORIS as
in BORIS-SSA. The mathematical development of this approach will be described in a
further paper.
3
Simulations
A comparison between simulations obtained using BORIS-SSA and signals acquired from
an acoustic source mounted on a tower [2] is made. A description of the experimental
configuration is shown in Fig. 2. In the simulation, a transducer transmits 1 ms bursts
with a carrier frequency of 100 kHz and a TX/RX Gaussian beam aperture of 16◦ . The
source is located 5 m above the seafloor and transmits with a nominal grazing angle of
50◦ . The interface is generated with a power spectral density being a modified power
law (γ = 3.2, kmax = 1000 rad/m, kc = 10 rad/m) with a RMS-height of 1 cm. Figure 3
shows a realization of a simulated signal. A tile of the interface is shown in Fig. 4.
Simulated signals are displayed in a polar plot as the source changes its heading
(Fig. 5). Figure 6 presents a similar plot of real signals recorded at sea. The angular
spread of scatterers in the simulated data appears larger than in the real data but shows a
significantly smaller spread than intuitively expected with a source beam aperture of 16◦ .
The discrepancy between the real and simulated seafloor responses could be caused by the
different statistical properties of the water-sediment interface generated by BORIS-SSA
compared to the actual interface around the tower. Interface generation will be improved
in the near future. However, BORIS-SSA appears to be an accurate model applicable to
scenarios encountered by SAS systems using DPCA.
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A STUDY OF PING-TO-PING COHERENCE
Figure 1. Comparison between scattering strength computed using the integral equation and three
approached solutions obtained using the Kirchhoff approximation (KA) and the second and fourth
order small slope approximations (SSA-2 and SSA-4 respectively). Scattering strength is the result
of an averaging over 50 interface realizations. Each interface is obtained using a modified “powerlaw” power spectral density - γ = 3.2, kmax = 1000 rad/m, kc = 10 rad/m with 2 cm RMS-height.
The incident angle is 45◦ . The fourth order SSA is accurate even at lower grazing angles.
pan / tilt
motor
000
111
000
111
111
000
000
111
Source Tx / Rx
heading
Tower
roll
Figure 2. Experimental configuration with an acoustic source located on a 5 m high tower. A
pan/tilt motor allows the source to change heading and roll.
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Figure 3. Example of simulated data obtained by a source/receiver located 5 m above the seabed.
The nominal grazing angle is 50◦ . The pulse is 1ms long with a carrier frequency of 100 kHz.
The source beam aperture is 16◦ . Scales are arbitrary.
Figure 4. Tile of the generated interface used in the simulation. The power spectral density is a
power-law (γ = 3.2, kmax = 1000 rad/m, kc = 10 rad/m). The RMS-height is 1 cm.
A STUDY OF PING-TO-PING COHERENCE
493
Figure 5. Polar plot of the simulated signals obtained using the interface in Fig. 4. Intensity is
coded in color. The absolute level is arbitrary.
Figure 6. Polar plot of real data received from the acoustic transducer mounted on a tower under
similar conditions of roll and height as in Fig. 5. The absolute level is arbitrary.
4
Ping-to-ping coherence
Considering the heading 90◦ as a reference, the amplitudes obtained at 90±4◦ and 90±8◦
are plotted in Fig. 7. The high amplitude observed at t = 0.0103 s at the 90◦ heading,
is not present at other headings. At a heading of 86◦ , this high amplitude is masked
by a stronger amplitude (caused by a dominant scatterer) centered around t = 0.0011 s.
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Figure 7. Simulated data for 5 pings panning a total of 16◦ . The reference ping is at a heading of
90◦ (represented as a dashed line in the other plots). The pulse length is 1 ms and the interface
RMS-height is 1 cm.
This is in agreement with conclusions of the experimental study [2] which state that the
coherent summation of seabed contribution is strongly dependent on heading. When a
shorter pulse is used, less scatterers are integrated in the seafloor response. Coherence is
expected to hold over a greater range of yaw. Figure 8 is similar to Fig. 7 but with a 0.4
ms pulse instead of a 1 ms pulse. The interface is the same. Three independent scatterers
can be identified in the signal at a heading of 90◦ . These three scatterers can also be
identified at the heading of 86◦ . So it appears that a shorter pulse leads to a greater
ping-to-ping coherence. In Fig. 9, the interface RMS-height is doubled with respect to
Fig. 7. The scatterer at t = 0.013 s has now become a very dominant scatterer. It can
be identified in all the other pings and in particular in the 94◦ and 98◦ pings. As the
interface becomes rougher, the number of scatterers increases, but some scatterers stand
above the average amplitude. It was noted in the experiment that strong scatterers would
remain coherent over a large angular range. In this case, the presence of a dominant
scatterer improves ping-to-ping coherence.
5
Conclusion
Conclusions from observation of the signals acquired from a tower, especially on the
impact of the number and size of scatterers on the ping-to-ping coherence [2] seem to be
confirmed by BORIS-SSA simulations. Dominant interface features (e.g., strong facets)
scatter omnidirectionnaly which preserve strong ping-to-ping coherence. When the number of scatterers that are integrated in the response increases (e.g., long pulse, many
scatterers per unit surface), the seabed response becomes more directional because an
interference structure caused by a unique combination of scatterers is formed.
A STUDY OF PING-TO-PING COHERENCE
495
Figure 8. Simulated data for 5 pings panning a total of 16◦ . The reference ping is at a heading
of 90◦ (represented as a dashed line in the other plots). The pulse length is reduced to 0.4 ms
compared to 1 ms in Fig. 7.
Figure 9. Simulated data for 5 pings panning a total of 16◦ . The reference ping is at a heading of
90◦ (represented as a dashed line in the other plots). The interface RMS-height is multiplied by 2
with respect to the simulations in Fig. 7.
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In terms of model improvements, generated interfaces will be improved to account for
the presence of discrete scatterers, patchiness, adequate interface spectral density, volume
scattering, etc. In parallel, comparisons with other acquired signals will be made in the
near future.
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