MEASUREMENTS OF BOTTOM VARIABILITY DURING
SWAT NEW JERSEY SHELF EXPERIMENTS
A. TURGUT
Naval Research Laboratory, Washington DC 20375, USA
E-mail: [email protected]
D. LAVOIE
Office of Naval Research, VA 22217, USA
D. J. WALTER AND W.B. SAWYER
Naval Research Laboratory, Stennis Space Center, MS 39529, USA
Chirp sonar and vibracore measurements of bottom variability from scales of
centimeters to tens of meters have been conducted during the recent Shallow Water
Acoustic Technology (SWAT) experiments at the New Jersey Shelf. Chirp sonar (2–12
kHz) data were used to invert bottom geoacoustic properties with sub-meter resolution.
Sediment properties such as density, porosity and sound-speed profiles are inverted
from coherent acoustic returns at several sites with well-characterized subbottom
reflectors. Also, centimeter-resolution geaoacoustic properties were measured from
several vibracores collected along the survey tracks. Chirp sonar inversion results
compare favorably with those of co-located sediment core measurements. Both
deterministic and stochastic features are deduced from the sonar surveys and co-located
sediment core data. Effects of measured bottom spatial variability on the broadband
acoustic propagation are also studied by using a Parabolic Equation (PE) model. It was
concluded that, in addition to the oceanographic variability, the seafloor and subbottom
spatial variability might further spatially decorrelate the acoustic signals propagating in
shallow waters.
1
Introduction
In shallow waters, the performance of both active and passive sonar systems is strongly
influenced by interaction of acoustic energy with the seabed. Proper knowledge of
certain bottom geoacoustic properties such as compressional wave speed, attenuation,
and density structure is needed for the accurate performance prediction of most sonar
systems. The structure of geoacoustic parameters in the sediment is rather complex so
that a deterministic description of such a field is almost impossible for a given site
considering the length scales of interest (a few centimeters to tens of meters). Stochastic
description and parameterization of the field in terms of its statistical properties might be
more useful for an acoustic propagation/scattering prediction model. The structure of a
sediment geoacoustic parameter is described by partitioning the field into a deterministic
part and a stochastic part. The deterministic part represents site-specific large-scale
features of a given geological province. The stochastic part represents small-scale sound91
N.G. Pace and F.B. Jensen (eds.), Impact of Littoral Environmental Variability on Acoustic Predictions and
Sonar Performance, 91-98.
© 2002 Kluwer Academic Publishers. Printed in the Netherlands.
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speed structure that is modeled as a zero-mean quasi-stationary random process. Secondorder statistics of the field are described by a 3-D power spectrum. Several forms of
spectral representations of volume inhomogeneities were proposed by previous
researchers with certain spectral parameters to be estimated from available sediment core
samples (see [1] for references).
2
Deterministic and stochastic description of New Jersey Shelf
Core data and chirp sonar inversion results are used to obtain both deterministic and
stochastic structure of the New Jersey shelf. Similar to previous studies (see e.g., [2,3]),
several deterministic subbottom features such as the marine/non-marine erosional
subsurface “R”, a network of buried river channels as well as several seafloor features
such as erosional channels, sand ridges, and iceberg scours are well characterized by the
chirp sonar surveys.
Figure 1. Spatial scales of a) internal solitary waves, b) erosional channels, and c) buried river
channels observed at the New Jersey Shelf.
Figure 1 compares the typical spatial scales of buried river channels and erosional
channels (geologic features) with an Internal Solitary Wave (ISW) packet (oceanographic
feature) observed in the same area. Notice the similarities in the spatial scales between
these geologic and oceanographic features that might influence acoustic wave
propagation in the area. Chirp sonar inversions and vibracore measurements provided the
high-resolution geoacoustic description of upper sediment layers as deep as 30 m. Figure
2 shows a comparison of sound-speed profiles obtained from vibracores and chirp sonar
inversion at core sites H5 and H5A (Figs. 2a and 2b - see Fig. 2e for locations). The
comparison was limited to the top few meters (maximum vibracore lengths), and the
agreement is satisfactory. Notice also that both results show a sharp stiff-clay/sand layer
interfaces verified by down-core photographic images (see Figs. 2c an 2d). A statistical
modeling approach was used to characterize sediment volume inhomogeneities and
bathymetry variation using an anisotropic von Kármán spectrum.
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BOTTOM VARIABILITY MEASUREMENTS
(a)
(c)
Sand/Stiff-Clay
interface
Long.
(deg W)
72.5
73.25
39.5
Lat.
(deg N)
(b)
(d)
Sand/Stiff-Clay
interface
39.0
H10
H5
H5A
(e)
Figure 2. Comparison of sound-speed profiles obtained from vibracores and chirp sonar inversion
at core sites a,c) H5, and b,d) H5A. Core locations are shown in (e).
The typical spectral parameters such as the spatial scale factors, variance, and the
spectral exponent are obtained from the chirp sonar inversion results and vibracore
measurements. The 3-D sediment sound-speed or density inhomogeneities can be
described by an ellipsoidal von Kármán spectrum as
S (ξ ) = µ ax a y a zπ −3/ 2
where µ
Γ (m)
Γ ( m − 3/ 2)
(1 + ax2ξ x2 + a 2yξ y2 + az2ξ z2 ) − m ,
m > 3 / 2,
(1)
is the variance, a x , a y , and, a z are spatial scale factors, Γ is the Gamma
function, m is the spectral exponent, and ξ x , ξ y , ξ z are the components of the
wavenumber vector ξ. The 2-D and 1-D wavenumber spectra can be obtained by
integrating the above spectrum over one and two components of wavenumber,
respectively [1]. In Fig. 3a, 1-D form of the above spectrum was fitted to the spectra
obtained from chirp sonar inversions and vibracore measurements of sound-speed
profiles at core sites H5, H5A, and H10. Statistical parameters for the spectrum were
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A. TURGUT ET AL.
estimated as µ = 0.002, a z = 1.5 m, and m = 1.9. Figure 3b shows the wavenumber
spectrum of cross-shelf and along-shelf bathymetry calculated from the hull-mounted
chirp sonar survey tracks. Statistical parameters obtained for the surface roughness were
µ = 1.5, a x = 5000 m, a y = 1500 m, and m = 2.1.
Figure 3. One-dimensional wavenumber spectra of a) sound-speed profiles obtained from chirp
sonar and vibracore measurements, and b) seafloor roughness spectra obtained form chirp sonar
surveys. 1-D von Kármán model predictions are also superimposed.
3
Numerical simulations for broadband acoustic propagation over
deterministic and stochastic bottoms
In this section, both 2-D and 3-D numerical simulations are performed to study the
coupling and refraction of the acoustic modes when they propagate through deterministic
features such as erosion channels, buried river channels, and ISWs (see Fig. 4a). The
vertical displacement of the deterministic features is described by η(r) = Asech2[(r-rs)/L],,
where A is the amplitude, r and rs are the range variables, and L is the horizontal scale
factor. Broadband acoustic propagation over stochastic bottoms is also studied using the
statistical parameters of the seafloor roughness and sediment volume inhomogeneities
presented in the previous section. As an example, a realization of both seafloor and
sediment volume are depicted in Figs. 4b and 4c, respectively. First, we calculate the
frequency and horizontal-scale dependency of mode coupling by propagating individual
modes through a hyperbolic-secant range-dependency using a PE routine [4]. Figures 5a,
5b and 5c show the coupling of the first three modes as a function of the frequency and
horizontal-scale factor, L, of the hyperbolic-secant function representing an ISW, an
erosional channel, and a buried river channel, respectively. In general, coupling is
stronger for the modes 2 and 3 in all three cases and slight differences can be
detected in the frequency and horizontal-scale dependency. A relatively stronger
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BOTTOM VARIABILITY MEASUREMENTS
coupling is observed in the ISW case. Also, mode coupling is stronger for the erosional
channel case than that of buried river channel case.
(a)
(b)
(c)
Figure 4. a) Deterministic description of an erosion channel, a buried river channel, and an ISW
by a hyperbolic secant function. Stochastic description of b) seafloor morphology (rms height =
1.5 m), and c) sediment volume inhomogeneities by a von Kármán statistical model (gray scale
covers from –6% to +6% variability).
mode
1
2
3
mode
1
2
3
Figure 5. Frequency and horizontal-scale dependency of mode coupling for acoustic propagation,
a) through an ISW, b) over an erosion channel, and c) over a buried river channel. Coupling of
first three modes is displayed. The columns indicate starting-field mode number and the rows
indicate the coupled-mode components. For display purposes, the panels on the main diagonals in
(b) and (c) are subtracted by 0.65 and 0.85, respectively.
An adiabatic-mode PE modeling approach [5] was used to study the horizontal
refraction of broadband acoustic signals propagating over deterministic and stochastic
bottoms. The main difference between our modeling approach and that of Ref. [5] is that
we used the PE formulation in a Cartesian coordinate system instead of a cylindrical or
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spherical coordinate system. Figures 6a, 6b, and 6c show the refraction of 70–190 Hz
broadband signals obliquely propagating through a hyperbolic-secant range dependency
of an ISW, an erosional channel, and a buried river channel, respectively. The azimuthal
angle between acoustic propagation vector and the straight hyperbolic-secant disturbance
is 8 deg., A = 10 m, and L = 130 m. The waterfall plots show the amplitude of pressure
field received at 15 km range and 40 m water depth. The total cross-range extension is 5
km and the source is placed at 2.5 km cross-range distance. The 8-deg. angle corresponds
to the cross-range distances of the maximum of the straight hyperbolic-secant disturbance
being at rs = 3 km at the source range (0 km), and rs = 1.1 km at the receiver range (15
km). For the ISW case, the amplitude of the pressure field is larger at the leading edge of
the disturbance, indicating a relatively stronger refraction. Also, similar to the mode
coupling results, mode refraction is stronger for the erosional channel case than for the
buried river channel case (note the smaller pressure amplitude in the disturbed field).
In Figs. 6d, 6e, and 6f, pressure amplitudes at 15 km range and 40 m water depth are
compared for the environments with no range dependency, with bathymetric variability,
and with sediment sound-speed and density variability, respectively. The pressure
amplitudes in Figs. 6e and 6f are calculated for single realizations of bathymetry and
sediment volume using the von Kármán spectra with the statistical parameters given in
the previous section ( ax = a y = 1000 m is assumed for the sediment variability). To
quantify the effects of the environmental variability on pulse propagation, we define a
spatial correlation coefficient for the transient pressure amplitude as [6]
ρ (ς ) =
∫ p(t; 0) p(t; ς )dt
1
2
( ∫ p(t; 0) dt ) ( ∫ p(t; ζ ) dt )
2
2
1
2
(2)
where t is the time and ζ is the cross-range distance. The integrals in the above equation
are evaluated over the width of the calculated pulses. In Fig. 6g, the spatial correlation
functions are calculated for the deterministic cases along a 600 m aperture horizontal line
array located at 15 km range, 40 m depth, and between 2.2 and 2.8 km cross-range
distances (reference position is at 2.5 km).
For reference, the correlation function for the range independent case is also plotted
since the source-receiver distance is different for the each element of the array. We note
that the spatial decorrelation is stronger for the ISW case since the bottom interacting
higher order modes are attenuated at the 15 km range. In Fig 6h, the spatial correlation
functions for the stochastic bottoms are compared with range independent case. Note
that bathymetric variability introduces stronger spatial decorrelation than does the
sediment volume variability. In a recent numerical study, weak spatial decorrelation of
CW signals are also observed in the case of acoustic propagation through diffuse
background internal wave field [7].
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BOTTOM VARIABILITY MEASUREMENTS
(a)
(b)
(c)
(d)
(e)
(f)
(g)
-300
0
Cross-range (m)
(h)
300
-300
0
Cross-range (m)
300
Figure 6. Transient pressure amplitudes calculated at 15km range and 40 m depth (source depth =
20 m) depicting horizontal refraction effects for deterministic and stochastic environments. A
hyperbolic-secant disturbance is used to represent (a) ISW, b) erosional channel, and c) buried
river channel. The transient pressure amplitudes for d) range independent, e) bathmetric
variability, and f) sediment volume variability case. Corresponding spatial decorrelations
reference to the mid-point (at 2.5 km cross-range) are shown in (g) and (h).
98
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Discussion
In this study, we established a procedure for obtaining deterministic and stochastic
bottom properties from vibracore and chirp sonar reflection measurements. Seafloor
morphology and 1-D (vertical) sediment inhomogeneities are statistically characterized
by using several data sets from the SWAT New Jersey Shelf experiments. Further
analysis of chirp sonar inversions is underway to estimate horizontal scale factor of the
sediment variability. Vibracore measurements and chirp sonar inversions of sound-speed
profiles are compared at core sites H5 and H5A and a good agreement is observed.
Numerical simulations of horizontal refraction of broadband signal indicated that several
deterministic features, observed during the recent SWAT experiments, might introduce
significant mode coupling and horizontal refraction. Also, in addition to oceanographic
effects, measured levels of bottom variability might further decrease the spatial
correlation of the low-frequency acoustic signals in shallow waters.
Acknowledgments
This work was supported by the Office of Naval Research. We thank Keith Ludwig of the
USGS and Bruce Pasewark, Chad Vaughan, and Allen Reed of the NRL for participating
in the SWAT vibracoring/chirp sonar experiment.
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