IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 33, NO. 4, OCTOBER 2008
367
Compressional Wave Speed Dispersion and
Attenuation in Carbonate Sediments,
Kaneohe Bay, Oahu, HI
Eva-Marie Nosal, Chunhui Tao, Stefano Baffi, Shunsheng S. Fu, Michael D. Richardson, and Roy H. Wilkens
Abstract—In situ compressional wave speed and attenuation
measurements between 20 and 100 kHz were made at two carbonate sediment sites in Kaneohe Bay, on the windward side of the
Hawaiian island of Oahu. Velocities increased with frequency from
1691 to 1708 m/s at a coarse sediment site (HC, porosity 0.45)
and from 1579 to 1585 m/s at a fine-grained sediment site (HF,
porosity
0.56). Effective attenuation increased with frequency
from 15 to 75 dB/m at HC and from 22 to 62 dB/m at HF. Values of
sound speed at these sites are within the range of those reported in
the literature for silicate sands of the same porosity. Attenuation
values of these reef-derived carbonate sands are higher than
many of those reported in the literature for silicate sands and
.
they appear to be linearly related to frequency
Sound-speed and attenuation data were compared to predictions
of two sediment geoacoustic models, Biot–Stoll and grain shearing
(GS). In both models, two unknown parameters were varied to
find best fits at each site to: 1) both attenuation and sound-speed
data and 2) sound-speed data only. Both models yielded similar
fits, which differ significantly from the measured data.
=
=
( = 0 65 )
Index Terms—Attenuation measurement, carbonate sediment,
geoacoustic, seafloor, sound-speed measurement.
I. INTRODUCTION
T
HE seabed and its acoustic properties are of interest to geologists, geophysicists, and ocean engineers in relation to
marine construction, interpretation of sidescan sonar data, locating buried toxic waste materials, and in naval military applications. The interest in such waves has been focused on different
Manuscript received April 21, 2007; revised January 23, 2008; accepted
January 31, 2008. First published August 28, 2008; current version published
February 06, 2009. This work was supported by the U.S. Office of Naval
Research Ocean Acoustics and Coastal Geosciences Programs, the Naval
Research Laboratory, the National Science Foundation of China under Grant
NSFC49906004, the State Oceanic Administration of China under Grant
2000502, and the Hi-Tech Research and Development Program of China under
Grant 2002AA615130.
Associate Editor: J. F. Lynch.
E.-M. Nosal is with the Department of Geology and Geophysics, School of
Ocean and Earth Science and Technology, University of Hawaii at Manoa, Honolulu, HI 96822 USA (e-mail: [email protected]).
C. Tao is with the Second Institute of Oceanography (SOA) China, Hang Zhou
310012, China (e-mail: [email protected]).
S. Baffi is with the Horizon Energy Partners B.V., The Hague 2595 BR, The
Netherlands (e-mail: [email protected]).
S. S. Fu is with the Solid and Hazardous Waste Branch, Hawai’i State Department of Health, Honolulu, HI 96814 USA (e-mail: [email protected]).
M. D. Richardson is with the Marine Geosciences Division, Naval Research Laboratory, Stennis Space Center, MS 39529-5004 USA (e-mail:
[email protected]).
R. H. Wilkens is with the Hawaii Institute of Geophysics and Planetology, University of Hawaii at Manoa, Honolulu, HI 96822 USA (e-mail:
[email protected]).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JOE.2008.920212
frequency and amplitude ranges, generally, a function of the researcher’s main interest. In situ experiments over a range of frequencies at the same site are rare, with most studies reporting
data from many sites at a single frequency, or one frequency
in situ and a second, higher frequency measurement made on
cored material in the laboratory (see [16, Ch. 5] for a review).
Published studies deal almost exclusively with silicate sediments, while in situ properties of reef-derived carbonate sediments, common in shallow waters surrounding tropical islands,
are rarely reported. Richardson et al. [21] published perhaps the
most complete study to date, reporting a number of in situ measurements from the Dry Tortugas, Key West, FL, recorded at a
frequency of 38 kHz. A later summary of both carbonate and
silica sediment in situ data is presented in [16]. In this paper, we
present the analysis and discussion of in situ acoustic data in a
frequency range between 20 and 100 kHz, collected in carbonate
sediments at two different locations in Kaneohe Bay, Oahu, HI.
We observed sound-speed dispersion at both sites, with greater
dispersion seen in coarser sediments. Attenuation at both sites
was high relative to reported silicate sand measurements and appears to fit a linear dependence on frequency over the frequency
range investigated.
Compressional wave speed dispersion has long been a topic
of discussion in studies of the acoustic properties of marine sediments (e.g., [2], [13], and [24]). Both laboratory and field studies
have demonstrated sound-speed dispersion in sandy quartz sediments (e.g., [5], [7], [14], [25], and [29]–[32]) and have had
varying success in modeling their observations. In this work,
data were compared to predictions of two common sediment
geoacoustic models: Biot–Stoll [24] and grain shearing (GS)
[2]–[4]. In both models, two unknown parameters were varied to
find best fits at each site to: 1) both attenuation and sound-speed
data, and 2) sound-speed data only. Both models yielded similar fits. In the fits to both attenuation and sound-speed data, both
models predicted greater sound-speed dispersion than was measured. In the fits to sound speed only, both models predicted attenuation well below measured values.
II. SETTING AND SEDIMENTS
Kaneohe Bay is located on the northeast coast of the island of
Oahu, HI (Fig. 1). The sediments in Kaneohe Bay consist primarily of calcium carbonate, with some input, particularly near
stream mouths, of kaolinite clay derived from the weathering
of the volcanic basalt that makes up most of the island. Large
proportions of the lagoon sediments are reef derived, as indicated by the sediment mineralogy [9]. Short diver push cores
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IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 33, NO. 4, OCTOBER 2008
TABLE I
IN SITU SOUND SPEED AND ATTENUATION DATA
Fig. 1. Map of the island of Oahu, HI, showing experiment site (box).
Fig. 2. Example of waveforms used in this study: 50-kHz signals for the near
and far receivers recorded at site HC. A cross correlation of the first five cycles
was used to pick the delay time between arrivals. The first five cycles were also
used to compute the power spectra.
were taken at each of the two experimental sites. Plastic cylinders were pushed into the sediment and sealed from below. Laboratory measurements of porosity, bulk density, and grain size
were carried out at 2-cm intervals shortly after core retrieval.
The coarse sand found at the coarse site (HC) is moderately
sorted with no remarkable variation in classification over the
whole core length. The sand size fraction (grain diameter
62.5 m–2 mm) represents about 82% of the total volume, silts
(3.90625–62.5 m), and clays ( 3.90625 m) represent about
4% each. Very fine gravel (2–4 mm) represents about 9% of the
sample, while fine gravel (4–8 mm) is primarily represented by
mollusk and gastropod shells or reef fragments and accounts for
less than 1% of grain sizes. Mean grain size is approximately
750 m. Porosity ranges between 0.41 and 0.49, with a spike
of 0.63 at 5-cm depth, most likely due to a layer of silt and clay
sized particles. Excluding this value (which is reasonable since
the measurements were made deeper in the sediments), average
porosity is about 0.45.
The lagoonal site (HF) is represented by a poorly sorted and
generally finer grained sediment whose classification varies,
Fig. 3. Sound-speed ratio plotted against porosity from various in situ experiments. See the first paragraph of Section IV for references to other data. Closed
symbols are carbonate sands and open symbols are silicate.
changing from silty to muddy sand, to slightly gravelly sand at
some depth intervals. Very fine gravel size is present in traces
( 0.1%), while sand, silt, and clay are around 71%, 20%, and
9% of the volumetric fraction, respectively. Mean grain size
is 69 m and porosity ranges between 0.52 and 0.61 with an
average value of 0.56.
Porosity was calculated from wet and dry weights and
measured and calculated values of grain and pore water density. Grain density was measured using a gas displacement
pycnometer. The samples were relatively uniform, with an
average grain density of 2750 kg/m (one standard deviation
20 kg/m ). Water temperature at the time of the measurements
was 23 C.
III. METHODS
We used a scaled-down in situ sediment acoustic measurement system (ISSAMS) [32] to record acoustic waveforms in
seawater and sediments at both Kaneohe Bay sites (HC and HF)
over a frequency range from 20 to 100 kHz. The system included a source and two inline receivers separated by 0.289 m.
The active parts of the probes were buried about 10–20 cm in
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NOSAL et al.: COMPRESSIONAL WAVE SPEED DISPERSION AND ATTENUATION IN CARBONATE SEDIMENTS, KANEOHE BAY, OAHU, HI
369
Fig. 4. Attenuation data from this study plotted against frequency. Closed symbols are carbonate sands and open symbols are silicate. The line of best fit is to
Hawaii data (HC, HF, and Waikiki) only. See the first paragraph of Section IV for references to additional data.
Fig. 5. Attenuation factor k plotted against bulk porosity of sediments.
the seafloor in 6-m-deep water at each location. An example of
waveforms recorded at near and far receivers is shown in Fig. 2.
The waveforms recorded at each receiver over the first five cycles were generally clean, with little evidence of any multipath
secondary energy that might affect attenuation calculations.
We recorded the signals in a frequency range between 20 and
100 kHz, with steps of 5 kHz below 50 kHz and 10 kHz above
50 kHz. A 1- s sampling rate was used. In situ compressional
group speeds were calculated using the arrival time difference
between the receivers and the fixed horizontal transducer spacing.
Delay timeswere evaluated after Buckinghamand Richardson [5]
by cross correlating the first five cycles at each receiver. Errors
based on the sampling rate and probe position uncertainty are
on the order of 10 m/s. Buckingham and Richardson [5] found
that with pulses of the type we have used there is little difference
between the group speed and the phase speed.
Measuring attenuation is generally a difficult task, especially when there is scattering in the sediment and unknown
material phenomena are affecting low- and high-frequency
responses. Therefore, we used both power spectrum and amplitude methods for attenuation calculation. The power spectrum
method [5] is described as
(1)
where is the interreceiver distance,
is the near receiver
is the far receiver spectral power,
sediment spectral power,
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Fig. 6. Sound-speed and attenuation data plotted versus frequency. Also included are model results of best fit models for sound speed and attenuation together.
is the near receiver seawater spectral power, and
is the
far receiver seawater power. We used the first five cycles of each
signal to compute the power spectrum. Geometrical spreading
effects and the mismatch between the two receivers are included
.
in
The amplitude method [20] is described as
(2)
where is the peak amplitude of the waveforms and the subscripts are as in (1). In practice, we used an average of the amplitudes of the first five high-amplitude cycles in each signal as
a value for . As with the spectral method, division of the sediment signals by the water signals cancels the effects of geometrical spreading and receiver mismatch. Results of the aforementioned two methods are almost identical and we have presented
in Table I attenuations calculated using (1). Errors based on the
sampling rate and probe position uncertainties are estimated to
be within 5%.
IV. RESULTS
In situ compressional speed ratios (sediment sound speed normalized by seawater sound speed) at sites HC and HF are plotted
in Fig. 3 versus the average porosity measured in the diver cores.
Also plotted in the figure are carbonate sediment data from the
Dry Tortugas, Key West, FL, from [21] and near-surface measurements from Waikiki, HI, in [10]. Silicate sand is represented
by data from offshore San Diego, CA [11], and from the Sediment Acoustic Experiment (SAX99) off Panama City, FL [22],
[27]. Also shown is the regression from [16, Table 5.4], which
was fit to ISSAMS data for 88 siliciclastic and carbonate sites
at 38 and 58 kHz. Although reef-derived carbonate sands have
intragrain porosity estimated at 5% of total sediment volume
[10], the sound-speed data reported here fall well within the
range of observations for silicate sand composed of solid grains.
Richardson and Briggs [23] have recognized the same coincidence of carbonate and silicate sediment data on plots of soundspeed measurements made on cores at 400 kHz. Apparently, the
presence of pores within the grains, as well as the rougher nature of the surface of reef sands, is not sufficient to separate
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NOSAL et al.: COMPRESSIONAL WAVE SPEED DISPERSION AND ATTENUATION IN CARBONATE SEDIMENTS, KANEOHE BAY, OAHU, HI
Fig. 7. Sound-speed and attenuation data plotted versus frequency. Also included are model results of best fit models for sound speed only. The line is the same line as plotted in Fig. 4.
these sandy data into distinct silicate and carbonate sound speed
versus porosity relationships.
We have plotted attenuation versus frequency for our data
in Fig. 4, along with data from some of the same studies that
were added to Fig. 3. Also included are the laboratory results
of a study by Wingham [31] involving medium quartz sands.
Hamilton [11] suggested that attenuation measured in decibels
per unit length is approximately dependent on frequency to the
. The Kaneohe Bay data combined with that
power
from Waikiki [10] support this observation, with a value for
of 0.65 dB m
kHz providing a reasonable fit
to Hawaii data.
It has long been recognized that there is a relationship between porosity and grain size in near-surface unconsolidated
sediments. Fine-grained sediments generally have greater
porosity than course grained sediments. Hamilton [11] examined the relationship between grain size, porosity, and the
. His regression lines and
factor from the relationship
estimated limits for porosity versus are plotted in Fig. 5 along
with our data and data from the literature incorporated in Fig. 4.
371
= 0:65f
The fine-grained reef sands at HF fit well within Hamilton’s
limits, as do the data from [21] and [10]. Coarse-grained
site HC, however, behaves more like a sample with greater
porosity, with values greater than what would be predicted by
Hamilton’s relationships. A plot of the fit given in [16, Fig. 5.9]
falls below our Kaneohe Bay results.
In situ sound-speed and attenuation data are plotted versus
frequency in Figs. 6 and 7. The in situ compressional wave
speeds at sites HC and HF exhibit a slight dispersion. At sites
HC and HF, speeds vary between 1691.6 and 1707.6 m/s for
the former and from 1578.8 to 1585.8 m/s for the latter. Sound
speed is lower at site HF than at site HC corresponding to
the higher porosity at HF compared to HC sites. Attenuation
ranges from 15 to 75 dB/m at HC and from 22 to 62 dB/m
at HF.
V. MODELING
The measured values for compressional wave speed and attenuation are compared to predictions made using the Biot–Stoll
[24] and the GS [2], [3] sediment acoustic models in Figs. 6
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TABLE II
MEASURED AND ESTIMATED MODEL PARAMETERS
TABLE III
BIOT–STOLL PARAMETERS
and 7. Ideally, both models would make predictions using parameters that were measured, calculated, or known from literature. Unfortunately, this could not be done because of unknown
values for dynamic permeability and the structure factor in
Biot–Stoll and unknown values for the strain-hardening index
and the modulus constant
in GS (the comand the shear modulus conpressional modulus constant
always appear together as
in GS comstant
pressional sound-speed and attenuation formulas, so they need
not be separated here). Model predictions did not fit the data
when estimates for these values were found from the literature
(e.g. by using the Kozeny–Carman equation [6], [15] for permeability; Berryman’s formula [1] for the structure factor; and
inverting measured shear and compressional properties made on
carbonate sediments from the Florida Keys by [21] for GS parameter values).
To deal with these unknown parameter values, we found the
values that yielded best fits (in a least squares sense) to: 1)
both sound-speed and attenuation data (Fig. 6) and 2) soundspeed data only (Fig. 7). Measured and estimated parameter
values common to both models are listed in Table II. Table III
lists the estimated, calculated, and best-fit parameter values for
Biot–Stoll and Table IV lists best-fit parameter values for GS.
The fits for both models are remarkably similar. When both
attenuation and sound-speed data are fit, both models predict
greater sound-speed dispersion than was observed. In the fits to
sound speed only, both models predicted attenuation well below
measured values. This result can be partially attributed to scattering since the models predict intrinsic attenuation only and the
abundant shell material at both sites suggests that scattering loss
should be significant.
It is interesting to note in the case of the sound-speed-only
fits that the difference between predicted and measured values
TABLE IV
GS PARAMETERS
of attenuation increase with frequency. This might be expected
because scattering should increase with increasing frequency.
On the other hand, it is hard to imagine that scattering should
contribute as large a portion of total attenuation as is suggested
by the differences between models and measurements displayed
in Fig. 7. It would be expected that such a large amount of
scattering would be accompanied by considerable signal distortion—and this was not the case in our experiments.
VI. CONCLUSION
Reef-derived carbonate sands appear to be indistinguishable
from silicate sands in terms of sound speed versus porosity, but
exhibit stronger attenuation than silicate sands. At any given
frequency, the carbonate attenuation may be twice as much as
for silicates. The overall relationship between reef sand attenuation and frequency, however, agrees with previous studies that
show a linear relationship. The reef sands that were measured in
this study exhibited a small but observable sound-speed dispersion. Two differing models were inverted to fit dispersion and
sound-speed data with equal success. In the case where sound
speed only was fit, modeled attenuation values were considerably lower than those measured. Part of the difference may lie
in the contrast between overall attenuation, which includes scattering, and model outputs of intrinsic attenuation only.
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NOSAL et al.: COMPRESSIONAL WAVE SPEED DISPERSION AND ATTENUATION IN CARBONATE SEDIMENTS, KANEOHE BAY, OAHU, HI
ACKNOWLEDGMENT
The authors would like to thank S. Griffin of OMNI Technologies for help with making measurements in Kaneohe Bay,
and K. Briggs of NRL for the sediment property measurements.
The comments of two anonymous reviewers helped to significantly streamline and improve this paper.
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Eva-Marie Nosal received the B.Sc. degree in
pure mathematics, the B.Sc. degree in applied
mathematics, the B.Mus. degree in piano from the
University of Calgary, Calgary, AB, Canada, in
2000, the M.Sc. degree in mathematics from the
University of British Columbia, Vancouver, BC,
Canada, in 2003, and the Ph.D. degree in geology
and geophysics from the University of Hawaii at
Manoa, Honolulu, in 2007.
Currently, she is an Assistant Researcher at the
School of Ocean and Earth Science and Technology,
University of Hawaii at Manoa. Her primary research interests involve developing and applying passive acoustic detection, classification, and tracking
methods. She also studies underwater ambient noise and geoacoustic properties
of the seafloor.
Chunhui Tao received the Ph.D. degree in geology
from Zhejiang University, Zhe Jiang, China, in 2005.
Currently, he is a Researcher at the Second Institute of Oceanography, Hang Zhou, China, and an
Adjunct Professor of Geosciences at China University. He is the Duty Scientist of polymetallic sulfide
deposits of COMRA and was the Duty Scientist of
deep sea technology of China Ocean Mining and
Research Association (COMRA). He was the Chief
Scientist of the DY19 Cruise, which found the first
active hydrothermal vent field on the south–west
Indian Ocean in 2007. His research focuses on hydrothermal sulfide survey and
research, in situ studies of sediments, marine geophysics, and survey equipment
integration.
Stefano Baffi received a degree in geology from the
Università degli Studi di Genova, Italy, in 1994 and
the M.Sc. degree in geology and geophysics from the
University of Hawaii at Manoa, Honolulu, in 1999.
Currently, he is a Senior Geoscientist at Horizon
Energy Partners B.V., The Hague, The Netherlands.
He has been working internationally in the oil and gas
exploration for operators and consulting companies.
The main focus of his work is on seismic interpretation, reservoir geophysics, and seismic attributes.
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IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 33, NO. 4, OCTOBER 2008
Shunsheng S. Fu received the Ph.D. degree in
geophysics from the University of Hawaii at Manoa,
Honolulu, in 1998.
He was a Postdoctoral Researcher at the Hawaii Institute of Geophysics and Planetology for two years.
Currently, he is an Environmental Specialist working
at Solid and Hazardous Waste Branch, Department
of Health, Honolulu, HI. His research interests are in
the physical properties of the seafloor and underwater
acoustic instrumentation.
Michael D. Richardson received the B.S. degree
in oceanography from the University of Washington, Seattle, in 1967, the M.S. degree in marine
science from the College of Williams and Mary,
Williamsburg, VA, in 1971, and the Ph.D. degree
in oceanography from Oregon State University,
Corvallis, in 1976.
He began working at the Naval Ocean Research
and Development Activity, now part of the Naval Research Laboratory (NRL), Stennis Space Center, MS,
in 1977. Except for a five-year assignment as Principle Scientist at NATO’s SACLANTCEN, La Spezia, Italy (1995–1989), he has
worked at NRL as a Research Scientist and is currently Head of the Seafloor Sciences Branch in the Marine Geosciences Division. His research interests include
the effects of biological and physical processes on sediment structure, behavior,
and physical properties near the sediment-water interface in both shallow-water
coastal regions and in the deep sea. His current research is linked to high-frequency acoustic scattering from and propagation within the seafloor and prediction of mine burial.
Dr. Richardson is a member of the Acoustical Society of America, the American Geophysical Union, the European Geophysical Society, and Sigma Xi.
Roy H. Wilkens received the Ph.D. degree in geology from the University of Washington, Seattle, in
1981.
Currently, he is a Senior Research Scientist at the
Hawaii Institute of Geophysics & Planetology, University of Hawaii, Honolulu. For six years, he was
with the Massachusetts Institute of Technology, first
as a Schlumberger Research Fellow and later as an
Associate Scientist. He has been with the University
of Hawaii since 1987. He has been a Distinguished
Visiting Scientist with the Naval Research Laboratory and also spent two years as a Visiting Program Officer in Marine Geology
& Geophysics, Office of Naval Research. His research interests are in the physical properties of the seafloor and marine instrumentation.
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