INTRA- AND INTER-REGIONAL GEOACOUSTIC
VARIABILITY IN THE LITTORAL
CHARLES W. HOLLAND
Pennsylvania State University, Applied Research Lab, PO Box 30, State College, PA 16804
E-mail: [email protected]
Spatial variability of seabed geoacoustic properties generates uncertainty in the
prediction of sonar system performance in littoral regions. In order to investigate
geoacoustic variability within a region and variability between two regions, extensive
geoacoustic and acoustic measurements were conducted in two areas in the Italian
littoral. While it is not surprising that significant geoacoustic and acoustic variability is
observed in each region, the surprising result is the marked similarity between the two
regions. Geoacoustic properties were quite consistent when compared at commensurate
water depths even with inter-region separation in excess of 800 km. Not only was the
variability comparable between the two regions, but the geoacoustic regimes
themselves were similar. The similarities have important implications for extrapolation
of sparse geoacoustic data.
1
Introduction
Active and passive sonar systems that operate in littoral regions must contend with
significant spatial variability of the ocean acoustic environment. An important and
often dominating component of the variability is the seabed, or the geoacoustic
properties. For geoacoustic point (e.g., cores) or line (e.g., propagation loss)
measurements the concomitant question is: “how do the geoacoustic properties vary a
few meters, kilometers, or tens of kilometers away from the measurement point?” In the
extreme, the question becomes, “how can geoacoustic properties be estimated or
extrapolated from very distant (hundreds of km) measurements, i.e., beyond the
boundaries of the physiographic region?”
These two questions, the former termed intra-regional variability and the latter
inter-regional variability, are addressed here from a measurements-based approach.
Two study regions were selected: one on the Tuscany shelf and one in the Straits of
Sicily (see Fig. 1). Each region has dimensions of order 50x50 km and the regions are
separated by ~800 km. Limitations of a measurement-based approach are that state-ofthe-art measurement techniques under-resolve some of the scales of geoacoustic
variability and provide estimates of variability only for specific regions. However, the
strength of a measurements-based approach is that very little is understood about interregional and intra-regional geoacoustic variability. Thus, measurements are badly
needed to begin to bound the scales of variability and to identify potential techniques for
describing and predicting the variability.
73
N.G. Pace and F.B. Jensen (eds.), Impact of Littoral Environmental Variability on Acoustic Predictions and
Sonar Performance, 73-82.
© 2002 Kluwer Academic Publishers. Printed in the Netherlands.
74
C.W. HOLLAND
The observation and description of seabed variability is cast with the underlying
motive of understanding the impact of geoacoustic variability on acoustic variability.
Thus, while it may be true that within 1 meter of a core, the sediment microscopic and
macroscopic structure is variable, that variance may or may not have impact on sonar
performance. For this study, the focus is on geoacoustic variability that has significant
impact on acoustic variability in the 500–5000 Hz range.
Ita
ly
Figure 1. North Elba and Malta Plateau regions with site locations; depths are in meters. Seismic
survey tracks are in gray.
2
Methodology
Extensive geologic/geophysical measurements (e.g., cores, grab samples, seismic
reflection, swath bathymetry, and seafloor photography) as well as acoustic
measurements (e.g., local seabed reflection/scattering and transmission loss/
reverberation) were conducted in both regions. Although each measurement type is
useful for probing seafloor variability, the key measurements for this study are the local
reflection [1] and scattering [2] measurements which provide much higher vertical and
lateral resolution of the geoacoustic properties (of order O(0.1) and O(100) m
respectively) than traditional propagation/reverberation measurements. Site locations
were based on seismic data; at each site a suite of the above-listed measurements were
conducted.
Generally, geoacoustic variability is expected to be greatest in a direction
perpendicular to the isobaths. Thus, sites selected for this study lie roughly along a line
perpendicular from the coast: North Elba (NE) sites are 5,1,2,3. Sites were chosen for
the Malta Plateau (MP) at commensurate water depths, Sites 4,1,2,7, since geoacoustic
properties may be correlated with water depth.
Geoacoustic variability is manifest over a continuum of scales. In order to describe
variability it is useful to define distinct scales that capture the critical aspects of the
environment; for purposes of this study they are: geoacoustic regimes, sedimentary
REGIONAL GEOACOUSTIC VARIABILITY
75
classes, and seabed features. Within a region, geoacoustic regimes are defined as areas
in which the physical mechanisms that govern reflection and scattering are similar. The
angular and frequency dependence of the reflection/scattering may be spatially variable
within a regime, but the variability is expected to be continuous rather than abrupt.
Variability within a regime generally arises from geometric factors, e.g., variability in
layer thicknesses. The boundaries between geoacoustic regimes may or may not be
abrupt. Within a geoacoustic regime, sediment classes are defined as distinct
sedimentary units. Seabed features are defined as 1–100 m scale discrete sedimentary
objects that may produce sonar clutter.
3
North Elba geoacoustic variability
The Tuscan shelf was created (along with the Northern Apennines and the Adriatic Sea)
from the collision of the Adria microplate and the Corsica-Sardinia Massif [3]. In the
northern part of the shelf (north of Elba Island), the Elba valley running northwest from
Elba Island separates two distinct regions, the basin to the east dominated by finegrained sediments, and the Elba Ridge to the west, which exhibits coarser grained sand.
At water depths between 115–130 m swath bathymetry reveals erosional features
perpendicular to the isobaths (~0.5 m rms height, O(500) m spacing) apparently formed
during the last sea level transgression. Near the southern edge of the region, are parallel
ribbon fields (~0.5 m rms height) oriented east-northeast. Generally, seafloor and subbottom layer slopes are very small (less than 1o), with the exception being the Elba
Ridge flank, which has slopes of ~15–20o.
The frequency and angular dependence of the reflection loss (defined as -20 log |R|,
where R is the complex reflection coefficient) for various sites in NE is shown in Fig. 2
along with the associated water depth. The salient feature in the data is the critical angle,
θc , defined as the “knee” where the reflection loss rapidly increases from near zero. At
grazing angles below θc, the reflection coefficient is small and normal modes/rays
propagate efficiently. The critical angle is a crucial indicator for long-range propagation;
generally the higher θc, the better the propagation. For a homogenous half-space, the
reflection coefficient is independent of frequency. However, θc can be frequency
dependent due to several factors including: velocity dispersion (e.g., [4]), layering, and
sound speed gradients. For velocity dispersion, theory predicts that θc should increase
with increasing frequency. Sediment layering produces resonant effects in angle and
frequency; a single layer produces nulls such as that observed at MP Site 1. Sediment
sound speed gradients are generally positive and generate an apparent θc inversely
proportional to frequency because the loss along refracted paths is proportional to
frequency. An example of this is NE Site 3, where θc changes from ~30o at 500 Hz to
~18 o at 5000 Hz.
The reflection data of Fig. 2 along with the associated raw time series were
analyzed following the technique described in [1] to produce in-situ sediment
geoacoustic properties, i.e., velocity, density, and attenuation. Of these, the controlling
factor in shallow water propagation is generally the velocity, which is shown in Fig. 3 as
an indicator of geoacoustic variability. The sound speed of the water near the seabed
interface was nearly constant between sites and is shown to clarify the relative sound
speed between the water and the seabed.
76
C.W. HOLLAND
The predominant (i.e., covering the vast majority of the region) geoacoustic regime,
Regime I, in NE is fine-scale layering (see Fig. 3 Sites 1 and 2 and Fig. 4b) consisting of
a background mud matrix with interstitial high-velocity layers composed of sand with
shell and coral fragments (see Fig. 4c,e). This layering structure was created by high
frequency glacio-eustatic sea-level changes during the Pleistocene era [5]. Even though
the interstitial layers are thin (of order tens of centimeters), the layers have a measurable
Figure 2. Reflection loss (dB) at various sites in North Elba (NE) and the Malta Plateau (MP).
Depth (m)
NE Site 5; 102 m
NE Site 1; 128 m
NE Site 3; 103 m
0
0
0
10
10
10
10
20
20
20
20
30
30
30
MP Site 4; 102 m
Depth (m)
NE Site 2; 151 m
0
MP Site 1; 128 m
30
MP Site 2; 153 m
MP Site 7; 107 m
0
0
0
0
10
10
10
10
20
20
20
20
30
1600
1800
Velocity (m/s)
30
1600
1800
Velocity (m/s)
30
1600
1800
Velocity (m/s)
30
1600
1800
Velocity (m/s)
Figure 3. Sediment sound speed variability at the two study regions (see Fig. 1 for locations).
effect on seabed reflection above ~500 Hz [1]. At lower frequencies, reflection/propagation is dominated by paths that refract through the sediment. The intercalating layers
are the dominant scattering mechanism across the entire frequency range of interest. At
1800 Hz and below, scattering is apparent from the intercalating layer at 25 m subbottom [2]. The variability of this geoacoustic regime is continuous in the sense that the
dominant reflection/scattering mechanism (the intercalating shelly layers) have non-
77
REGIONAL GEOACOUSTIC VARIABILITY
parallel dips (see Fig. 4b), however, the geoacoustic properties of each layer unit are
constant with at least to lateral offsets of 5 km [6] and perhaps even to much longer
scales. The geoacoustic variability within in this regime produces a minimal impact on
the acoustic variability; i.e., there is relatively little variability in the reflection
coefficient (i.e., compare NE Sites 1, 2 of Fig. 2; Site 8, not shown is also similar) and
scattering strength [7]. The eastern boundary to this regime is abrupt and well-defined
by the Elba Ridge; the boundary to the east is not abrupt, but continuous. Analysis of the
reflection coefficient at Site 8 indicates that this regime persists to the southern part of
the region to at least the 110 m contour.
Geoacoustic regime II is defined as the band between about 110–75 m in the
northeastern part of the region where the uppermost silty clay layer rapidly increases to
thicknesses of 10–15 m. In this zone, the dominant regime switches from fine-scale
layering to a few thicker/higher impedance layers, which eventually wedge out to a
silty-clay/basement contact at ~80 m depth contour. The basement is the flanks of the
Secche di Vada Ridge which according to [3] is a Late Cretaceous flysch (largely
sandstone). In this regime, the reflection/ scattering is dominated by the high impedance
layer at the base of the thick silty-clay layer (see NE Site 5, Fig. 3) and at the shallowest
depths, the basement. The sediment thins over the basement contact to a 1 meter or less
in the northeast and southeast corners. The composition of the basement in the southeast
is unknown. The relatively few sites in the regime makes it hard to estimate geoacoustic
and acoustic variability in regime II, nevertheless the variability in regime II appears to
be largely governed by the presence/absence of the basement contact and geometric
effects (especially the thickness of the uppermost silty-clay layer). The reflection at Site
4 is quite similar to that at Site 5, with indication of refraction at the lowest frequencies.
c)
b)
a)
d)
e)
f)
Figure 4. Images from top left to bottom right: a) seafloor at NE Site 5, black tape marks spaced
10 cm apart; b) NE Sites 1 and 2 seismic reflection data; c) NE Site 2 recovered shell material
from a 10 cm section of core; d) seafloor on Ragusa Ridge showing rock outcrop in upper left,
scale is about 30x40 cm; e) split cores south of MP Site 1 showing intercalating shelly layers, core
lengths are about 80 cm; f) MP Site 1 shell and cobble in core nose, coin is 2.5 cm diameter.
78
C.W. HOLLAND
Geoacoustic regime III is (an ostensibly homogeneous) sand, with a thin (0.5 m)
sandy silt cover. Due to the paucity of data in this regime, very little is known about its
lateral variability.
While there is considerable complexity in the sediment fabrics found in NE, there
are distinct sediment classes that can be identified. These classes with their associated
geoacoustic properties are given in Table 1. Silty-clay sediment completely blankets the
seafloor east of the Elba Ridge. Acoustic measurements, core data, and seafloor
photography indicate that the surficial properties of this layer are spatially uniform.
Observations show a characteristic distribution of small (cm scale) holes from biologics
(Fig. 4a). The sound speed gradients in this upper layer increase as a function of
distance from the source (the Cecina River at ~43.3o N); e.g., at Site 5 the gradient is 1.5
s-1 at Site 4, 7 s-1 and at Site 2 at least 30 s-1. The density gradient does not appear to
vary with distance from the source and is ~0.1 g/m3/m over the first meter, with the
upper 10 cm gradient being substantially higher. Sand covers the remaining ~10% of
the region, surficial sand being found only on the Elba Ridge. Consolidated sediment
(rock) within the upper ten meters of sediment is found in the northeast and southeast
corner of the region. There are probably magmatic rock outcrops on the Elba Ridge but
these have not been sampled.
Numerous shells, shell and coral fragments (Fig. 4c) were found in core and grab
samples with sizes ranging up to the order of the core barrel (10 cm). Shell/coral
fragments tend to exist in greatest number in layers that have a sand matrix, and are
found much less frequently in the mud layers. The variability in the geoacoustic
properties of these layers is quite high, depending on the volume fraction and size
distribution of the shell and coral fragments. Between the shelly sand layers over much
of the region there are mud layers. The sound speed gradient in the mud can be
approximated by: c( z ) = co [(1 + β ) (1 + 2 g o z / (co (1 + β ))) 1/ 2 − β ] where co is the interface
sound velocity, β the curvature and go the initial gradient [1]. Table 1 provides values
for go and β; which differ from [1] because the mud and silty-clay classes have been
separated in this study.
The primary features observed in the region are gas, and buried sand ridges. Gas
charged sediments appear to be sprinkled throughout the region although they are
generally deeper than 10m sub-bottom; pockmarks (presumably from escaped gas) were
observed in the southeastern corner [5]. Lowstand coastal ridges observed in the seismic
data are buried 3-5m below water-sediment interface, about 3–4 m high, 100–200 m in
width, 0.5–2 km in length and ~3 km spacing in 100–130 m water depth (see also [5]).
The composition of the ridges is probably coarse sand and gravel, although no core
samples were obtained.
Table 1. Geoacoustic properties in North Elba region, see text for details. No entry means that the
property could not be reliably estimated; cs is shear velocity.
Silty-clay
Mud
Sand
Shelly sand
sandstone
Velocity
(m/s)
1475
1500
1640
1650±100
cs: 1600
Vel grad
(s-1)
1.5 +
5, β=-0.9
10
---
Density
(g/cm3)
1.3
1.5
1.8
1.9±0.2
--
Den grad
(g/cm3/m)
0.1
via vel.[8]
----
Attenuation
(dB/m/kHz)
0.01
0.015
0.3
0.1
--
REGIONAL GEOACOUSTIC VARIABILITY
4
79
Malta Plateau intra- and inter-regional geoacoustic variability
The Malta Plateau occupies the northern edge of the North African passive continental
margin and is a submerged section of the Hyblean Plateau of mainland Sicily [9]. The
region (see Fig. 1) is divided by the Ragusa Ridge, roughly defined by depths shallower
than 110 m, which forms a spine ~20 km wide between Sicily and Malta. The area west
of the ridge is blanketed with a silty-clay sediment discharged from the Irminio River
and other small streams from the flanks of Monte Lauro.
The seabed reflection coefficient on the Malta Plateau (Fig. 2) bears a striking
resemblance with that at North Elba at corresponding water depths. Note the similarities
between MP Site 4 and NE Site 5, also the strong similarity between MP Site 2 and NE
Site 2, as well as the similarity between MP Site 7 and NE Site 3. Other than MP/NE
Site 1, the comparison of sites within a region shows substantially more variability than
from region to region at the same water depth.
Since the reflection coefficient (unlike propagation or reverberation) is independent
of water depth and sound speed profile in the water column, similarity in reflection
means similarity in sediment structure. This is borne out by examining the sediment
sound speed of Fig. 3, which show numerous similarities. The sediment regimes of MP,
in fact, closely parallel those in NE. Geoacoustic regime I occupies a large area in MP,
dominated by fine-scale layering (see MP Site 2 Fig. 3 and Fig. 4e) of similar character
to that in NE, i.e., shelly sand layers interspersed in mud layers.
Geoacoustic regime II is also analogous to NE. It exists from the 110 m contour
shoreward composed of a silty-clay layer, thickening shoreward, over highly reflective
layers that thin to a silty-clay/basement contact in several places. As an example of this
regime, at MP Site 4, there is an 8-m layer of low velocity sediment (1480 m/s;
1.32 g/cm3) that corresponds remarkably well to the 7.4 m thick layer at NE Site 5
(1477 m/s; 1.32 g/cm3). The uncertainties in the velocity and density estimates are
±4 m/s and ±0.04 g/cm3 respectively. Both sites have at least one intercalating highspeed layer, however, in both regions the strata at a depth of ~10m sub-bottom controls
the reflection/scattering. Differences between the regions include the complexity of the
basement topography and perhaps the basement geoacoustic properties (believed to be
limestone, although geoacoustic properties have not been measured). Lineated basement
outcrops occur both shallower than 110 m water depth and along the westward and
eastward boundaries of the ridge. The outcrops are up to 2 km wide along the western
edge of the ridge.
Geoacoustic regime III, on the Ragusa Ridge, is composed of ponded sand between
small-scale rocky outcrops, 1–100 m in width and 1–8 m in height (see Fig. 4d). The
thickness of the ponded sand thins towards the parallel escarpments which are ~12 km
apart. At Site 7, the consolidated basement is not shallower than 44 m sub-bottom. The
sand has a comparable interface velocity to that on the Elba Ridge, but MP Site 7 does
not show the same strong frequency dependence of θc as NE Site 3 (see Fig. 3),
indicating a smaller velocity gradient. In fact, the velocity gradient is small enough that
it appears to play a negligible role and thus is not included in the geoacoustic model. A
thin low velocity layer causes the high loss peak in the data from 40–65o.
The ostensible exception to inter-regional similarities is between MP and NE Site 1.
At MP Site 1, a high velocity sub-bottom layer existed, composed of gravel and cobble
sized stones and cemented sediments (Fig. 4f) that dominate the reflection/scattering
processes [10]. This layer appears to be associated with a buried river channel. During
80
C.W. HOLLAND
the last glacial period, when the coastline was at the 80–90 m depth, the Irminio River
was capable of transporting cobbles up to 25 cm in diameter [11]. The extent of the
buried river channel network is believed to be relatively small and is probably better
characterized as a feature rather than a geoacoustic regime.
The sediment classes closely parallel those found in NE. Sediment geoacoustic
properties for each class are provided in Table 2.
Features observed in the Malta Plateau region include: gas plumes, small-scale rock
outcrops (e.g., Fig. 4d), buried carbonate banks, and buried river channels. Two types
of gas plumes were observed: large plumes, 100–300m in lateral extent rising within
~5 m of the seafloor, and small-scale plumes, 5–20 m in lateral extent and rising to
seafloor interface. Both kinds of gas plumes tend to occur in clusters of multiple plumes.
These plumes have been positively correlated with clutter events on low frequency
active sonar in this area. Carbonate structures are found in the northwest part of the
region [9]. They appear to be highly reflective and are found about 10 m below the
seafloor, but may not be an important factor for producing clutter below 1 kHz. Buried
river channels in the northern sector of the region have been associated with clutter
events in 600 Hz sonar systems [12]. However, an alternative explanation in that area
may be small-scale gas plumes, which because of their size may easily be missed in
seismic surveys with coarse line spacing.
Table 2. Geoacoustic properties in the Malta Plateau region.
Silty-clay
Mud
Sand
Shelly sand
Cobble
5
Velocity
(m/s)
1480
1500
1650
1650±100
1780
Vel grad
(s-1)
1.5 +
15, -0.99
----
Density
(g/cm3)
1.3
1.5
1.8
1.9±.2
1.85
Den grad
(g/cm3/m)
0.1
Via vel.[8]
----
Attenuation
(dB/m/kHz)
0.01
0.015
-0.1
0.2
Summary and Conclusions
Geoacoustic variability was examined in and between two regions in the Italian littoral.
Within a region the variability was described by geoacoustic regimes, sediment classes,
and sedimentary features. The predominant regime in both regions is characterized by a
mud host material with a sound speed gradient larger than Hamilton [13] would predict
and thin intercalating layers of sand mixed with shell and coral fragments. In this
regime, the variability in layer geometry appears to have a minor effect on the acoustic
response (i.e., reflection and scattering) of the seabed, simplifying the level of detail
required for sonar performance prediction requirements.
In geoacoustic regime II, the sound speed gradients in the uppermost layer appear
to be a function of distance from the sediment (riverine) source. This relationship may
be general to littoral environments, and to the author’s knowledge has not been
heretofore published. Critical factors required to predict these gradients need to be
identified and suitable models developed. There is tantalizing evidence that the sound
speed gradients in the deeper layers may also be a function of identifiable and
predictable factors. Note that at MP Site 2, the sound speed gradient is significantly
REGIONAL GEOACOUSTIC VARIABILITY
81
higher than that at NE Site 2; it is conjectured that there is an underlying and perhaps
predictable relationship between the gradients and the location on the shelf.
Between the two regions, remarkable similarities were observed. The surficial siltyclay sediment is uniform across large areas of each region and has almost identical
properties between the two regions though the regions are separated by ~800 km. The
similarities between the two regions go deeper. Each region has a similar layering
structure (mud host with intercalating sandy-shelly layers) and concomitant reflection
characteristics over a broad part of the region. Each region also has a broad area around
the 100 m depth contour where the surficial silty-clay layer deepens to O(10) m in
thickness. Significant differences in reflectivity were observed between the two regions
at about the 130 m depth contour. Nearby core and seismic data suggest that the two
regions are similar at these water depths, but that in the Malta Plateau, the reflection
measurement sampled a feature (i.e., buried river channel) rather than the predominant
regime.
The inter-regional similarities raise numerous questions: are these inter-regional
similarities expected around the entire littoral Italian zone?, in other parts of the
Mediterranean? Are these inter-regional similarities predictable and if so, at which
level: the geoacoustic regimes? their boundaries? sediment classes? Is intra-regional
variability predictable at some level? These questions are important because acoustic
models will always be faced with insufficient geoacoustic data. The ability to
extrapolate geoacoustic measurements from region-to-region could provide an important
advance for sonar performance prediction. Geologic/geophysical models (e.g.[14]) may
provide the framework for addressing many of these issues.
While the existing measurement techniques were capable of generally defining the
geoacoustic regimes and general bounds, description of the variability within a regime is
quite poor, i.e., only a few measurements (in some cases only 1) exist within a regime.
By hosting the reflection and scattering measurement techniques on an AUV, rapid
detailed surveys within a regime could be conducted, thus resolving much finer scales of
variability that impact sonar system employment.
Acknowledgements
This research was sponsored by both the NATO SACLANT Undersea Research Centre
and the Office of Naval Research. The author gratefully acknowledges the captain,
officers, crew and the outstanding scientific staff aboard the R/V Alliance for their skill
and dedication that contributed significantly to the success of the measurement program.
Core photos were taken by Adolf Legner.
References
1. Holland, C.W. and Osler J., High-resolution geoacoustic inversion in shallow water: A
joint time and frequency domain technique, J. Acoust. Soc. Am. 107, 1263–1279 (2000).
2. Holland, C.W., Hollett, R. and Troiano L., A measurement technique for bottom scattering
in shallow water, J. Acoust. Soc. Am. 108, 997–1011 (2000).
3. Pascucci, S., Merlini, S. and Martini P., Seismic stratigraphy of the Miocene-Pleistocene
sedimentary basins of the Northen Tyrrhenian Sea and western Tuscany, Basin Res. 11,
337–356 (1999).
82
C.W. HOLLAND
4. Biot, M.A., Generalized theory of acoustic propagation in porous dissipative media, J.
Acoust. Soc. Am. 34, 1254–1264 (1962).
5. Brizzolari, E., Chiocci, F.L., Orlando, L. and Sacchi, L., Pleistocene evolution of the
Tuscan shelf from Piombino headland to San Vincenzo (Tyrrhenian Sea, Italy), Giornale
di Geologia 5312, 11–30 (1991).
6. Holland, C.W., Regional extension of geoacoustic data. In Proc. 5th European Conference
on Underwater Acoustics, edited by P. Chevret and M.E. Zakharia, Lyon, France (2000)
pp. 793–798.
7. Holland, C.W., Spatial variability of shallow water bottom scattering: a case study. In
Proc. 5th European Conference on Underwater Acoustics, edited by P. Chevret and M.E.
Zakharia, Lyon, France (2000) pp. 1141–1146.
8. Bachman, R.T., Acoustic and physical property relationships in marine sediments, J.
Acoust. Soc. Am. 78, 616–621 (1985).
9. Osler, J. and Algan, O., A high resolution seismic sequence analysis of the Malta Plateau,
SACLANTCEN SR-311, 1999.
10. Holland, C.W., Shallow water coupled scattering and reflection measurements, IEEE J. of
Oceanic Eng. (in press 2002).
11. Amore, C., and Randazzo, G., First data on the coastal dynamics and the sedimentary
characteristics of the area influenced by the River Irminio basin, Catena 30, 357–368
(1997).
12. Max, M.D., Portunato, N., and Murdoch, G., Sub-seafloor buried reflectors imaged by low
frequency active sonar, SACLANTCEN SM-306 (1996).
13. Hamilton, E.L., Geoacoustic modeling of the seafloor, J. Acoust. Soc. Am. 68, 1313–1339
(1980).
14. Syvitski, J.P.M., Pratson, L. and O’Grady, D., Stratigraphic predictions of continental
margins for the Navy. In: Numerical Experiments in Stratigraphy: Recent Advances in
Stratigraphic and Computer Simulations, edited by J.W. Harbaugh, L.W. Whatney, E.
Rankay, R. Slingerland, R. Goldstein and E. Franseen, SEPM special publication, No. 62
(1999) pp. 219–236.