A model for nonlinear gas bubble pulsation in marine sediments is presented. This model is then linearized to determine the resonance frequency and the damping terms for linear radial oscillations. The linear model is then used to predict the effects that such bubble pulsations will have on the sound speed and attenuation of acoustic waves propagating in gassy marine sediment. The results are compared for monodisperse populations against the predictions of a model of Anderson and Hampton and, furthermore, the additional abilities of the model introduced in this paper are discussed. These features include the removal of the sign ambiguities in the expressions, the straightforward implementation for acoustic propagation through polydisperse bubble populations, the capability to estimate bubble size distributions through a full acoustic inversion, and the capability to predict nonlinear effects.
References
1.
G. C.
Sills
and S. J.
Wheeler
, “The significance of gas for offshore operations
,” Cont. Shelf Res.
12
(10
) 1239
–1250
(1992
).2.
G. C.
Sills
, S. J.
Wheeler
, S. D.
Thomas
, and T. N.
Gardiner
, “Behaviour of offshore soils containing gas bubbles
,” Geotechnique
41
, 227
–241
(1991
).3.
K. B.
Briggs
and M. D.
Richardson
, “Variability in in situ shear strength of gassy muds
,” Geo-Mar. Lett.
16
, 189
–195
(1996
).4.
T. G.
Leighton
and P. R.
White
, “Quantification of undersea gas leaks from carbon capture and storage facilities, from pipelines and from methane seeps, by their acoustic emissions
,” Proc. R. Soc. A
468
, 485
–510
(2012
).5.
E. J.
Sauter
, S. I.
Muyakshin
, J. L.
Charlou
, M.
Schlüter
, A.
Boetius
, K.
Jerosch
, E.
Damm
, J. P.
Foucher
, and M.
Klages
, “Methane discharge from a deep-sea submarine mud volcano into the upper water column by gas hydrate-coated methane bubbles
,” Earth Planet. Sci. Lett.
243
, 354
–365
(2006
).6.
I.
Leifer
, D.
Roberts
, J.
Margolis
, and F.
Kinnaman
, “In situ sensing of methane emissions from natural marine hydrocarbon seeps: A potential remote sensing technology
,” Earth Planet. Sci. Lett.
245
, 509
–522
(2006
).7.
A. I.
Best
, M. D.
Richardson
, B. P.
Boudreau
, A. G.
Judd
, I.
Leifer
, A. P.
Lyons
, C. S.
Martens
, D. L.
Orange
, and S. J.
Wheeler
, “Shallow bed methane gas could pose coastal hazard
,” EOS Trans.
87
(22
), 213
–217
(2006
).8.
J.
Blackford
, H.
Stahl
, J. M.
Bull
, B. J. P.
Bergès
, M.
Cevatoglu
, A.
Lichtschlag
, D.
Connelly
, R. H.
James
, J.
Kita
, D.
Long
, M.
Naylor
, K.
Shitashima
, D.
Smith
, P.
Taylor
, I.
Wright
, M.
Akhurst
, B.
Chen
, T. M.
Gernon
, C.
Hauton
, M.
Hayashi
, H.
Kaieda
, T. G.
Leighton
, T.
Sato
, M. D. J.
Sayer
, M.
Suzumura
, K.
Tait
, M. E.
Vardy
, P. R.
White
, and S.
Widdicombe
, “Detection and impacts of leakage from sub-seafloor deep geological carbon dioxide storage
,” Nat. Clim. Change
4
, 1011
–1016
(2014
).9.
J.
Blackford
, J. M.
Bull
, M.
Cevatoglu
, D.
Connelly
, C.
Hauton
, R. H.
James
, A.
Lichtschlag
, H.
Stahl
, S.
Widdicombe
, and I. C.
Wright
, “Marine baseline and monitoring strategies for carbon dioxide capture and storage (CCS)
,” Int. J. Greenhouse Gas Control
38
, 221
–229
(2015
).10.
B. J. P.
Berges
, T. G.
Leighton
, and P. R.
White
, “Passive acoustic quantification of gas fluxes during controlled gas release experiments
,” Int. J. Greenhouse Gas Control
38
, 64
–79
(2015
).11.
T. G.
Leighton
and G.
Robb
, “Preliminary mapping of void fractions and sound speeds in gassy marine sediments from subbottom profiles
,” J. Acoust. Soc. Am.
124
(5
), EL313
–EL320
(2008
).12.
G. B. N.
Robb
, S. P.
Robinson
, P. D.
Theobald
, G.
Hayman
, V. F.
Humphrey
, T. G.
Leighton
, L. S.
Wang
, J. K.
Dix
, and A. I.
Best
, “Absolute calibration of hydrophones immersed in sandy sediment
,” J. Acoust. Soc. Am.
125
(5
), 2918
–2927
(2009
).13.
T. G.
Leighton
, A. D.
Phelps
, D. G.
Ramble
, and D. A.
Sharpe
, “Comparison of the abilities of eight acoustic techniques to detect and size a single bubble
,” Ultrasonics
34
, 661
–667
(1996
).14.
E. A.
Zabolotskaya
and S. I.
Soluyan
, “Emission of harmonic and combination frequency waves by air bubbles
,” Sov. Phys. Acoust.
18
, 396
–398
(1973
).15.
T. G.
Leighton
, D. G.
Ramble
, and A. D.
Phelps
, “The detection of tethered and rising bubbles using multiple acoustic techniques
,” J. Acoust. Soc. Am.
101
, 2626
–2635
(1997
).16.
S. V.
Karpov
, Z.
Klusek
, A. L.
Matveev
, A. I.
Potapov
, and A. M.
Sutin
, “Nonlinear interaction of acoustic wave in gas-saturated marine sediments
,” Acoust. Phys.
42
, 527
–533
(1996
).17.
F. A.
Boyle
and N. P.
Chotiros
, “Nonlinear acoustic scattering from a gassy poroelastic seabed
,” J. Acoust. Soc. Am.
103
, 1328
–1336
(1998
).18.
Z.
Klusek
, A.
Sutin
, A.
Matveev
, and A.
Potapov
, “Observation of nonlinear scattering of acoustical waves at sea sediments
,” Acoust. Lett.
18
, 198
–203
(1995
).19.
T. G.
Leighton
, “The Rayleigh—Plesset equation in terms of volume with explicit shear losses
,” Ultrasonics
48
, 85
–90
(2008
).20.
T. G.
Leighton
, “Theory for acoustic propagation in marine sediment containing gas bubbles which may pulsate in a non-stationary nonlinear model
,” Geophys. Res. Lett.
34
, L17607
, doi: (2007
).21.
E. L.
Hamilton
, “Compressional wave attenuation in marine sediments
,” Geophysics
37
, 620
–646
(1972
).22.
S. S.
Fu
, R. H.
Wilkens
, and L. N.
Frazer
, “In situ velosity profiles in gassy sediments: Kiel Bay
,” Geo-Mar. Lett.
16
, 249
–253
(1996
).23.
M. D.
Richardson
and K. B.
Briggs
, “In situ and laboratory geoacoustic measurements in soft mud and hard-packed sand sediments: Implications for high-frequency acoustic propagation and scattering
,” Geo-Mar. Lett.
16
, 196
–203
(1996
).24.
G. B. N.
Robb
, A. I.
Best
, J. K.
Dix
, J. M.
Bull
, T. G.
Leighton
, and P. R.
White
, “The frequency dependence of compressional wave velocity and attenuation coefficient of intertidal marine sediments
,” J. Acoust. Soc. Am.
120
, 2526
–2537
(2006
).25.
E. L.
Hamilton
, G.
Shumway
, H. W.
Menard
, and C. J.
Shipek
, “Acoustics and other physical properties of shallow-water sediments off San Diego
,” J. Acoust. Soc. Am.
28
, 1
–15
(1956
).26.
E. L.
Hamilton
, “Attenuation of shear waves in marine sediments
,” J. Acoust. Soc. Am.
60
, 334
–338
(1976
).27.
E. L.
Hamilton
and R. T.
Bachman
, “Sound velocity and related properties of marine sediments
,” J. Acoust. Soc. Am.
72
, 1891
–1904
(1982
).28.
G.
Shumway
, “Sound speed and absorption studies of marine sediment by a resonance method
,” Geophysics
25
, 451
–467
(1960
).29.
G.
Shumway
, “Sound speed and absorption studies of marine sediment by a resonance method—Part II
,” Geophysics
25
, 659
–681
(1960
).30.
A. I.
Best
, Q. J.
Huggett
, and A. J. K.
Harris
, “Comparison of in situ and laboratory acoustic measurements on Lough Hyne marine sediments
,” J. Acoust. Soc. Am.
110
, 695
–709
(2001
).31.
M. D.
Richardson
, K. B.
Briggs
, L. D.
Bibee
, P. A.
Jumars
, W. B.
Sawyer
, D. B.
Albert
, R. H.
Bennett
, T. K.
Berger
, M. J.
Buckingham
, N. P.
Chotiros
, P. H.
Dahl
, N. T.
Dewitt
, P.
Fleischer
, R.
Flood
, C. F.
Greenlaw
, D. V.
Holliday
, and Hulbert
, “Overview of SAX99: Environmental considerations
,” IEEE J. Oceanic Eng.
26
, 26
–53
(2001
).32.
J.
Yang
, D.
Tang
, and K. L.
Williams
, “Direct measurement of sediment sound speed in Shallow Water '06
,” J. Acoust. Soc. Am.
124
, EL116
–EL121
(2008
).33.
A.
Turgut
and T.
Yamamoto
, “Measurements of acoustic wave velocities and attenuations in marine sediment
,” J. Acoust. Soc. Am.
87
, 2376
–2383
(1990
).34.
G.
Robb
, A.
Best
, J.
Dix
, P.
White
, T.
Leighton
, J.
Bull
, and A.
Harris
, “The measurement of the in situ compressional wave properties of marine sediments
,” IEEE J. Oceanic Eng.
32
, 484
–496
(2007
).35.
A. B.
Wood
and D. E.
Weston
, “The propagation of sound in mud
,” Acustica
14
, 156
–162
(1964
).36.
F. A.
Bowles
, “Observations on attenuation and shear-wave velocity in fine-grained marine sediments
,” J. Acoust. Soc. Am.
101
, 3385
–3397
(1997
).37.
R. D.
Stoll
, “Experimental studies of attenuation in sediments
,” J. Acoust. Soc. Am.
66
(4
), 1152
–1160
(1979
).38.
B. A.
Brunson
and R. K.
Johnson
, “Laboratory measurements of shear wave attenuation in saturated sand
,” J. Acoust. Soc. Am.
68
, 1371
–1375
(1980
).39.
M. A.
Biot
, “Theory of propagation of elastic waves in fluid-saturated porous solids: I. Low-frequency range
,” J. Acoust. Soc. Am.
28
(2
), 168
–178
(1956
).40.
M. A.
Biot
, “Theory of propagation of elastic waves in fluid-saturated porous solids: II. Higher frequency range
,” J. Acoust. Soc. Am.
28
(2
), 179
–191
(1956
).41.
R. D.
Stoll
, “Marine sediment acoustics
,” J. Acoust. Soc. Am.
77
(5
), 1789
–1799
(1985
).42.
J. G.
Berryman
, “Confirmation of Biot's theory
,” Appl. Phys. Lett.
37
(4
), 382
–384
(1980
).43.
K. L.
Williams
, D. R.
Jackson
, E. I.
Thorsos
, and D.
Tang
, “Comparison of sound speed and attenuation measured in a sandy sediment to predictions based on the Biot theory of porous media
,” IEEE J. Ocean. Eng.
27
, 413
–428
(2002
).44.
D. R.
Jackson
and M. D.
Richardson
, High-Frequency Seafloor Acoustics
(Springer
, New York
, 2007
), pp. 1
–616
.45.
J. A.
Hawkins
and A.
Bedford
, “Variational theory of bubbly media with a distribution of bubble sizes. 2: Porous solids
,” Int. J. Eng. Sci.
30
(9
), 1177
–1186
(1992
).46.
J. L.
Buchanan
, “A comparison of broadband models for sand sediments
,” J. Acoust. Soc. Am.
120
(6
), 3584
–3598
(2006
).47.
D. M. J.
Smeulders
and M. E. H.
Van Dongen
, “Wave propagation in porous media containing a dilute gas-liquid mixture
,” J. Fluid Mech.
343
, 351
–373
(1997
).48.
A. L.
Anderson
, F.
Abegg
, J. A.
Hawkins
, M. E.
Duncan
, and A. P.
Lyons
, “Bubble populations and acoustic interaction with the gassy floor of Eckernforde Bay
,” Cont. Shelf Res.
18
, 1807
–1838
(1998
).49.
S. G.
Kargl
, K. L.
Williams
, and R.
Lim
, “Double monopole resonance of a gas-filled, spherical cavity in a sediment
,” J. Acoust. Soc. Am.
103
(1
), 265
–274
(1998
).50.
F. A.
Boyle
and N. P.
Chotiros
, “A model for acoustic backscatter from muddy sediments
,” J. Acoust. Soc. Am.
98
(1
), 525
–530
(1995
).51.
F. A.
Boyle
and N. P.
Chotiros
, “A model for high-frequency acoustic backscatter from gas bubbles in sandy sediments at shallow grazing angles
,” J. Acoust. Soc. Am.
98
(1
), 531
–541
(1995
).52.
A. L.
Anderson
and L. D.
Hampton
, “Acoustics of gas-bearing sediments. I. Background
,” J. Acoust. Soc. Am.
67
(6
), 1865
–1889
(1980
).53.
A. L.
Anderson
and L. D.
Hampton
, “Acoustics of gas-bearing sediment. II. Measurements and models
,” J. Acoust. Soc. Am.
67
(6
), 1890
–1903
(1980
).54.
A. I.
Best
, M. D. J.
Tuffin
, J. K.
Dix
, and J. M.
Bull
, “Tidal height and frequency dependence of acoustic velocity and attenuation in shallow gassy marine sediments
,” J. Geophys. Res. B
109
, 08101
, doi: (2004
).55.
T. G.
Leighton
, S. D.
Meers
, and P. R.
White
, “Propagation through nonlinear time-dependent bubble clouds and the estimation of bubble populations from measured acoustic characteristics
,” Proc. R. Soc. London Ser. A
460
(2049
), 2521
–2550
(2004
).56.
A. P.
Lyons
, M. E.
Duncan
, and A. L.
Anderson
, “Predictions of the acoustic scattering response of free-methane bubbles in muddy sediments
,” J. Acoust. Soc. Am.
99
(1
),163
–172
(1996
).57.
M. A.
Ainslie
and T. G.
Leighton
, “Near resonant bubble acoustic cross-section corrections, including examples from oceanography, volcanology, and biomedical ultrasound
,” J. Acoust. Soc. Am.
126
(5
), 2163
–2175
(2009
).58.
M. A.
Ainslie
and T. G.
Leighton
, “Review of scattering and extinction cross-sections, damping factors, and resonance frequencies of a spherical gas bubble
,” J. Acoust. Soc. Am.
130
(5
), 3184
–3208
(2011
).59.
J. W. L.
Clarke
and T. G.
Leighton
, “A method for estimating time-dependent acoustic cross-sections of bubbles and bubble clouds prior to the steady state
,” J. Acoust. Soc. Am.
107
(4
) 1922
–1929
(2000
).60.
A. D.
Phelps
, D. G.
Ramble
, and T. G.
Leighton
, “The use of a combination frequency technique to measure the surf zone bubble population
,” J. Acoust. Soc. Am.
101
(4
) 1981
–1989
(1997
).61.
A. D.
Phelps
and T. G.
Leighton
, “Oceanic bubble population measurements using a buoy-deployed combination frequency technique
,” IEEE J. Oceanic Eng.
23
, 400
–410
(1998
).62.
T. G.
Leighton
, R. J.
Lingard
, A. J.
Walton
, and J. E.
Field
, “Acoustic bubble sizing by the combination of subharmonic emissions with an imaging frequency
,” Ultrasonics
29
, 319
–323
(1991
).63.
L. A.
Ostrovsky
, A. M.
Sutin
, I. A.
Soustova
, A. L.
Matveyev
, A. I.
Potapov
, and Z.
Kluzek
, “Nonlinear scattering of acoustic waves by natural and artificially generated subsurface bubble layers in sea
,” J. Acoust. Soc. Am.
113
(2
), 741
–749
(2003
).64.
A. M.
Sutin
, S. W.
Yoon
, E. J.
Kim
, and I. N.
Didenkulov
, “Nonlinear acoustic method for bubble density measurements in water
,” J. Acoust. Soc. Am.
103
(5
), 2377
–2384
(1998
).65.
J. G.
Berryman
, “Long-wavelength propagation in composite elastic media. I. Spherical inclusions
,” J. Acoust. Soc. Am.
68
(6
), 1808
–1819
(1980
).66.
J. G.
Berryman
, “Long-wavelength propagation in composite elastic media. II. Elipsoidal inclusions
,” J. Acoust. Soc. Am.
68
(6
), 1820
–1831
(1980
).67.
X.
Yang
and C. C.
Church
, “A model for dynamics of gas bubbles in soft tissue
,” J. Acoust. Soc. Am.
118
(6
), 3595
–3606
(2005
).68.
A.
Prosperetti
, L.
Crum
, and K.
Commander
, “Nonlinear bubble dynamics
,” J. Acoust. Soc. Am.
83
, 502
–514
(1988
).69.
J. P. Y.
Maa
and A. J.
Mehta
, “Soft mud properties: Voigt model
,” J. Waterw., Port, Coastal, Ocean Eng.
114
(6
), 765
–770
(1988
).70.
H.
Macpherson
, “The attenuation of water waves over a non-rigid bed
,” J. Fluid Mech.
97
(4
), 721
–742
(1980
).71.
H. T.
Chou
, M. A.
Foda
, and J. R.
Hunt
, “Rheological response of cohesive sediments to oscillatory forcing
,” in Nearshore and Estuarine Cohesive Sediment Transport, Coastal Estuarine Sci. Ser.
(AGU Washington
, DC
, 2013
), Vol. 42
, pp. 126
–147
.72.
M. A.
Foda
, J. R.
Hunt
, and H. T.
Chou
, “A nonlinear model for the fluidization of marine muds by waves
,” J. Geophys. Res.
98
(C4
), 7039
–7047
, doi: (1993
).73.
M.
Jain
and A. J.
Mehta
, “Role of basic rheological models in determination of wave attenuation over muddy seabeds
,” Cont. Shelf Res.
29
, 642
–651
(2009
).74.
K. W.
Commander
and A.
Prosperetti
, “Linear pressure waves in bubbly liquids: Comparison between theory and experiment
,” J. Acoust. Soc. Am.
85
, 732
–746
(1989
).75.
G. E.
Claypool
and I. R.
Kaplan
, “The origin and distribution of methane in marine sediments
,” in Natural Gases in Marine Sediments
(Plenum
, New York
, 1974
), pp. 99
–139
.76.
G.
Mavko
, T.
Mukerij
, and J.
Dvorkin
, The Rock Physics Handbook
(Cambridge University Press
, Cambridge, UK
, 1998
), pp. 1
–511
.77.
R.
Duraiswami
, S.
Prabhukumar
, and G. L.
Chahine
, “Bubble counting using an inverse acoustic scattering method
,” J. Acoust. Soc. Am.
104
, 2699
–2717
(1998
).78.
T. G.
Leighton
, A.
Mantouka
, P. R.
White
, and Z.
Klusek
, “Towards field measurements of populations of methane gas bubbles in marine sediment: An inversion method required for interpreting two-frequency insonification data from sediment containing gas bubbles
,” Hydroacoustics
11
, 203
–224
(2008
).79.
A.
Mantouka
, “Development of a two-frequency technique for gas-bubble sizing in marine sediment
,” Ph.D. thesis, University of Southampton, 2010
.80.
N. P.
Chotiros
and M. J.
Isakson
, “A broadband model of sandy ocean sediments: Biot—Stoll with contact squirt flow and shear drag
,” J. Acoust. Soc. Am.
116
(4
), 2011
–2022
(2004
).© 2016 Acoustical Society of America.
2016
Acoustical Society of America
You do not currently have access to this content.