Acoustic reflection coefficients are reported for water-saturated granular media at frequencies from 1.2 to 2.0 MHz using a narrow-beam broadband transducer in a monostatic geometry at near-normal incidence. Natural sand and glass beads with median grain diameters ranging from 0.22 to 0.40 mm were used. For each granular medium, bed elevation and root-mean-square roughness were measured using side-on photographs of the sediment-water interface. The probability density distributions of the bed elevations are Gaussian. The roughness parameter is close to 1, indicating that the reflected pressure field is mainly due to coherent scattering. The probability distribution of the observed reflection coefficients is nearly Gaussian, consistent with the predictions from a coherent single-scattering model. The horizontal decorrelation length of the observed reflection coefficients is 4 mm, with no consistent dependence on either frequency or grain size, and approximately equal to 20% of the transducer diameter. This behaviour, which is reproduced by the single-scattering model, is due to speckle. The size/frequency-dependence of the reflection coefficients are well described by Eckart's [(1953). J. Acoust. Soc. Am. 25(3), 566–570] prediction for a rough surface with Gaussian-distributed surface elevations. Comparisons are made to previously reported reflection coefficient measurements.

1.
Abbott
,
J. G.
, and
Thurstone
,
F. L.
(
1979
). “
Acoustic speckle: Theory and experimental analysis
,”
Ultrasonic imaging
1
(
4
),
303
324
.
2.
Beckmann
,
P.
, and
Spizzichino
,
A.
(
1963
).
The Scattering of Electromagnetic Waves from Rough Surfaces
(
MacMillan
,
New York)
, p.
503
.
3.
Burckhardt
,
C. B.
(
1978
). “
Speckle in ultrasound B-mode scans
,”
IEEE Trans. Sonic. Ultrason.
25
(
1
),
1
6
.
4.
Chotiros
,
N. P.
(
1994
). “
Reflection and reverberation in normal incidence echo-sounding
,”
J. Acoust. Soc. Am.
96
(
5
),
2921
2929
.
5.
Chotiros
,
N. P.
(
2002
). “
Acoustic modeling of sandy ocean sediments
,” in
Proceedings of the IEEE Underwater Technology Conference
, April 19, Tokyo, Japan, pp.
231
236
.
6.
Chotiros
,
N. P.
,
Lyons
,
A. P.
,
Osler
,
J.
, and
Pace
,
N. G.
(
2002
). “
Normal incidence reflection loss from a sandy sediment
,”
J. Acoust. Soc. Am.
112
(
5
),
1831
1841
.
7.
Clay
,
C. S.
, and
Medwin
,
H.
(
1977
).
Acoustical Oceanography: Principles and Applications
(
Wiley-Interscience
,
New York
).
8.
Eckart
,
C.
(
1953
). “
The scattering of sound from the sea surface
,”
J. Acoust. Soc. Am.
25
(
3
),
566
570
.
9.
Gonzalez
,
R. C.
,
Woods
,
R. E.
, and
Eddins
,
S. L.
(
2004
).
Digital Image Processing Using MATLAB
(
Pearson Education
,
New Delhi, India
).
10.
Goodman
,
J. W.
(
1976
). “
Some fundamental properties of speckle
,”
J. Opt. Soc. Am.
66
(
11
),
1145
1150
.
11.
Hare
,
J.
, and
Hay
,
A. E.
(
2018
). “
Attenuation and group speed in water-saturated granular materials at MHz frequencies
,”
J. Acoust. Soc. Am.
143
(
5
),
2744
2755
.
12.
Hare
,
J.
, and
Hay
,
A. E.
(
2020
). “
Phase speed in water-saturated sand and glass beads at MHz frequencies
,”
J. Acoust. Soc. Am.
148
(
4
),
2301
2310
.
13.
Hay
,
A. E.
,
Zedel
,
L.
,
Cheel
,
R.
, and
Dillon
,
J.
(
2012
). “
Observations of the vertical structure of turbulent oscillatory boundary layers above fixed roughness beds using a prototype wide-band coherent Doppler profiler: 1. The oscillatory component of the flow
,”
J. Geophys. Res.
117
,
C03005
, .
14.
Hipp
,
A. K.
,
Storti
,
G.
, and
Morbidelli
,
M.
(
1999
). “
On multiple-particle effects in the acoustic characterization of colloidal dispersions
,”
J. Phys. D: Appl. Phys.
32
(
5
),
568
576
.
15.
IOC, SCOR, and IAPSO
(
2010
).
The International Thermodynamic Equation of Seawater - 2010: Calculation and Use of Thermodynamic Properties,
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56 (
UNESCO
,
Paris, France
).
16.
Isakson
,
M. J.
,
Chotiros
,
N. P.
,
Abraham Yarbrough
,
R.
, and
Piper
,
J. N.
(
2012
). “
Quantifying the effects of roughness scattering on reflection loss measurements
,”
J. Acoust. Soc. Am.
132
(
6
),
3687
3697
.
17.
Jackson
,
D.
, and
Richardson
,
M.
(
2007
).
High-Frequency Seafloor Acoustics
(
Springer Science & Business Media
,
New York
).
18.
Kimura
,
M.
(
2011
). “
Velocity dispersion and attenuation in granular marine sediments: Comparison of measurements with predictions using acoustic models
,”
J. Acoust. Soc. Am.
129
(
6
),
3544
3561
.
19.
Kimura
,
M.
(
2014
). “
Erratum: Velocity dispersion and attenuation in granular marine sediments: Comparison of measurements with predictions using acoustic models [J. Acoust. Soc. Am. 129, 3544-3561 (2011)]
,”
J. Acoust. Soc. Am.
135
(
4
),
2126
2127
.
20.
Kreith
,
F.
, and
Goswami
,
D. Y.
(
2004
).
The CRC Handbook of Mechanical Engineering
(
CRC Press
,
Boca Raton, FL
).
21.
Le Gonidec
,
Y.
, and
Gibert
,
D.
(
2007
). “
Multiscale analysis of waves reflected by granular media: Acoustic experiments on glass beads and effective medium theories
,”
J. Geophys. Res.
112
,
B05103
, .
22.
Lee
,
K.
,
Humphrey
,
V.
,
Kim
,
B.-N.
, and
Yoon
,
S.
(
2007
). “
Frequency dependencies of phase velocity and attenuation coefficient in a water-saturated sandy sediment from 0.3 to 1.0 MHz
,”
J. Acoust. Soc. Am.
121
(
5
),
2553
2558
.
23.
Lloyd
,
P.
, and
Berry
,
M. V.
(
1967
). “
Wave propagation through an assembly of spheres: IV. Relations between different multiple scattering theories
,”
Proc. Phys. Soc.
91
(
3
),
678
688
.
24.
Montgomery
,
D. C.
, and
Runger
,
G. C.
(
2010
).
Applied Statistics and Probability for Engineers
(
John Wiley & Sons
,
New York
).
25.
Nolle
,
A. W.
,
Hoyer
,
W. A.
,
Mifsud
,
J. F.
,
Runyan
,
W. R.
, and
Ward
,
M. B.
(
1963
). “
Acoustical properties of water-filled sands
,”
J. Acoust. Soc. Am.
35
(
9
),
1394
1408
.
26.
Ogilvy
,
J. A.
(
1991
).
Theory of Wave Scattering from Random Rough Surfaces
(
CRC Press
,
Boca Raton, FL
).
27.
Pace
,
N. G.
,
Al-Hamdani
,
Z. K. S.
, and
Thorne
,
P. D.
(
1985
). “
The range dependence of normal incidence acoustic backscatter from a rough surface
,”
J. Acoust. Soc. Am.
77
(
1
),
101
112
.
28.
Peters
,
F.
, and
Petit
,
L.
(
2000
). “
Propagation of ultrasound waves in concentrated suspensions
,”
Acta Acust united Acust.
86
(
5
),
838
846
.
29.
Richardson
,
M. D.
,
Williams
,
K. L.
,
Briggs
,
K. B.
, and
Thorsos
,
E. I.
(
2002
). “
Dynamic measurement of sediment grain compressibility at atmospheric pressure: Acoustic applications
,”
IEEE J. Ocean. Eng.
27
(
3
),
593
601
.
30.
Rohatgi
,
A.
(
2015
). “
Webplotdigitizer 4.3
,” https://automeris.io/WebPlotDigitizer/ (Last viewed October 26, 2020).
31.
Rossing
,
T.
(
2007
).
Springer Handbook of Acoustics
(
Springer
,
New York
).
32.
Schwartz
,
L.
, and
Plona
,
T. J.
(
1984
). “
Ultrasonic propagation in close-packed disordered suspensions
,”
J. Appl. Phys.
55
(
11
),
3971
3977
.
33.
Sen
,
P. N.
, and
Johnson
,
D. L.
(
1983
). “
Topological limitations of effective-medium approximations in fluid-solid systems having two longitudinal-acoustic modes
,”
Phys. Rev. B
27
(
6
),
3133
3137
.
34.
Sessarego
,
J.-P.
, and
Guillermin
,
R.
(
2012
). “
High-frequency sound-speed, attenuation, and reflection measurements using water-saturated glass beads of different sizes
,”
IEEE J. Ocean. Eng.
37
(
3
),
507
515
.
35.
Sessarego
,
J.-P.
,
Guillermin
,
R.
, and
Ivakin
,
A. N.
(
2008
). “
High-frequency sound reflection by water-saturated sediment interfaces
,”
IEEE J. Ocean. Eng.
33
(
4
),
375
385
.
36.
Thorne
,
P. D.
, and
Pace
,
N. G.
(
1984
). “
Acoustic studies of broadband scattering from a model rough surface
,”
J. Acoust. Soc. Am.
75
(
1
),
133
144
.
37.
Thorne
,
P. D.
,
Pace
,
N. G.
, and
Al-Hamdani
,
Z. K. S.
(
1988
). “
Laboratory measurements of backscattering from marine sediments
,”
J. Acoust. Soc. Am.
84
(
1
),
303
309
.
38.
Thorsos
,
E. I.
(
1988
). “
The validity of the Kirchhoff approximation for rough surface scattering using a gaussian roughness spectrum
,”
J. Acoust. Soc. Am.
83
(
1
),
78
92
.
39.
Trahey
,
G. E.
,
Smith
,
S. W.
, and
Von Ramm
,
O. T.
(
1986
). “
Speckle pattern correlation with lateral aperture translation: Experimental results and implications for spatial compounding
,”
IEEE Trans. Ultrason. Ferroelectr. Freq. Control
33
(
3
),
257
264
.
40.
Waterman
,
P. C.
, and
Truell
,
R.
(
1961
). “
Multiple scattering of waves
,”
J. Math. Phys.
2
(
4
),
512
537
.
41.
Williams
,
K. L.
(
2001
). “
An effective density fluid model for acoustic propagation in sediments derived from Biot theory
,”
J. Acoust. Soc. Am.
110
(
5
),
2276
2281
.
42.
Wilson
,
G. W.
, and
Hay
,
A. E.
(
2017
). “
Short-pulse method for acoustic backscatter amplitude calibration at MHz frequencies
,”
J. Acoust. Soc. Am.
142
(
3
),
1655
1662
.
43.
Yang
,
H.
,
Seong
,
W.
, and
Lee
,
K.
(
2018
). “
Model-data comparison of high frequency compressional wave attenuation in water-saturated granular medium with bimodal grain size distribution
,”
Ultrasonics
82
,
161
170
.
44.
Zemanek
,
J.
(
1971
). “
Beam behavior within the nearfield of a vibrating piston
,”
J. Acoust. Soc. Am.
49
(
1B
),
181
191
.
You do not currently have access to this content.