Free Standard AU & NZ Shipping For All Book Orders Over $80!
Register      Login
Exploration Geophysics Exploration Geophysics Society
Journal of the Australian Society of Exploration Geophysicists
RESEARCH ARTICLE

A poroelastic model for ultrasonic wave attenuation in partially frozen brines

Jun Matsushima 1 4 Takao Nibe 1 2 Makoto Suzuki 1 Yoshibumi Kato 1 Shuichi Rokugawa 3
+ Author Affiliations
- Author Affiliations

1 Frontier Research Center for Energy and Resources, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.

2 JGI, Inc., Meikei Building, 1-5-21 Otsuka, Bunkyo-ku, Tokyo 112-0012, Japan.

3 Department of Technology Management for Innovation, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.

4 Corresponding author. Email: jun-matsushima@frcer.t.u-tokyo.ac.jp

Exploration Geophysics 42(1) 105-115 https://doi.org/10.1071/EG10045
Submitted: 25 August 2010  Accepted: 30 November 2010   Published: 25 February 2011

Abstract

Although there are many possible mechanisms for the intrinsic seismic attenuation in composite materials that include fluids, relative motion between solids and fluids during seismic wave propagation is one of the most important attenuation mechanisms. In our previous study, we conducted ultrasonic wave transmission measurements on an ice-brine coexisting system to examine the influence on ultrasonic waves of the unfrozen brine in the pore microstructure of ice. In order to elucidate the physical mechanism responsible for ultrasonic wave attenuation in the frequency range of 350–600 kHz, measured at different temperatures in partially frozen brines, we employed a poroelastic model based on the Biot theory to describe the propagation of ultrasonic waves through partially frozen brines. By assuming that the solid phase is ice and the liquid phase is the unfrozen brine, fluid properties measured by a pulsed nuclear magnetic resonance technique were used to calculate porosities at different temperatures. The computed intrinsic attenuation at 500 kHz cannot completely predict the measured attenuation results from the experimental study in an ice-brine coexisting system, which suggests that other attenuation mechanisms such as the squirt-flow mechanism and wave scattering effect should be taken into account.

Key words: attenuation mechanism, Biot theory, partially frozen brines, poroelastic, ultrasonic attenuation.


References

Berryman, J. G., 1980, Confirmation of Biot’s Theory: Applied Physics Letters, 37, 382–384
Confirmation of Biot’s Theory:Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DyaL3cXltlyitLg%3D&md5=34ace84bb6c132eb85700015320d18c0CAS |

Biot, M. A., 1956, Theory of propagation of elastic waves in a fluid saturated porous solid, I. Low-Frequency Range and II. High-Frequency range: The Journal of the Acoustical Society of America, 28, 168–191
Theory of propagation of elastic waves in a fluid saturated porous solid, I. Low-Frequency Range and II. High-Frequency range:Crossref | GoogleScholarGoogle Scholar |

Burridge, R., and Keller, J. B., 1981, Poroelasticity equations derived from microstructure: The Journal of the Acoustical Society of America, 70, 1140–1146
Poroelasticity equations derived from microstructure:Crossref | GoogleScholarGoogle Scholar |

Callaghan, P. T., Dykstra, R., Eccles, C. D., Haskell, T. G., and Seymour, J. D., 1999, A nuclear magnetic resonance study of Antarctic sea ice brine diffusivity: Cold Regions Science and Technology, 29, 153–171
A nuclear magnetic resonance study of Antarctic sea ice brine diffusivity:Crossref | GoogleScholarGoogle Scholar |

Carcione, J. M., and Seriani, G., 2001, Wave simulation in frozen porous media: Journal of Computational Physics, 170, 676–695
Wave simulation in frozen porous media:Crossref | GoogleScholarGoogle Scholar |

Carcione, J. M., Santos, J. E., Ravazzoli, C. L., and Helle, H. B., 2003, Wave simulation in partially frozen porous media with fractal freezing conditions: Journal of Applied Physics, 94, 7839–7847
Wave simulation in partially frozen porous media with fractal freezing conditions:Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD3sXps1Wlt7c%3D&md5=de38e5b3f567408332e5ebc185ca087fCAS |

Carcione, J. M., Campanella, O. H., and Santos, J. E., 2007, A poroelastic model for wave propagation in partially frozen orange juice: Journal of Food Engineering, 80, 11–17
A poroelastic model for wave propagation in partially frozen orange juice:Crossref | GoogleScholarGoogle Scholar |

Carman, P. C., 1937, Fluid flow through a granular bed: Transactions of the Institution of Chemical Engineers, 15, 150–166
| 1:CAS:528:DyaA1cXlt1CntQ%3D%3D&md5=6cd4736bf433c8b0b834b5195db1101eCAS |

Carr, H. Y., and Purcell, E. M., 1954, Effects of diffusion on free precession in nuclear magnetic resonance experiments: Physical Review, 94, 630–638
Effects of diffusion on free precession in nuclear magnetic resonance experiments:Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DyaG2cXksFKjtA%3D%3D&md5=e41b982a8a952957f8a42c5b15fd0f16CAS |

De Gennes, P. G., 1976, On a relation between percolation theory and the elasticity of gels: Journal de Physique Lettres, 37, 1–2
On a relation between percolation theory and the elasticity of gels:Crossref | GoogleScholarGoogle Scholar |

Deptuck, D., Harrison, J. P., and Zawadzki, P., 1985, Measurement of elasticity and conductivity of a three-dimensional percolation system: Physical Review Letters, 54, 913–916
Measurement of elasticity and conductivity of a three-dimensional percolation system:Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DyaL2MXhsVWmt7k%3D&md5=cc294fc38d5d045739de811c239135c5CAS | 10031653PubMed |

Dvorkin, J., Mavko, G., and Nur, A., 1995, Squirt flow in fully saturated rocks: Geophysics, 60, 97–107
Squirt flow in fully saturated rocks:Crossref | GoogleScholarGoogle Scholar |

Ecker, C., Dvorkin, J., and Nur, M. A., 2000, Estimating the amount of gas hydrate and free gas from marine seismic data: Geophysics, 65, 565–573
Estimating the amount of gas hydrate and free gas from marine seismic data:Crossref | GoogleScholarGoogle Scholar |

Gao, L., Poirier, J., and Aki, K., 1993, Attenuation due to partial melting: an experimental study on a model system, using the lab coda method: Journal of Geophysical Research, 98, 1853–1860
Attenuation due to partial melting: an experimental study on a model system, using the lab coda method:Crossref | GoogleScholarGoogle Scholar |

Gassmann, F., 1951, Über der Elastizität poröser Medien: Vieteljahrsschrift der Naturforschenden. Gesellschaft in Zurich, 96, 1–23

Guerin, G., and Goldberg, D., 2002, Sonic waveform attenuation in gas hydrate-bearing sediments from the Mallik 2L–38 research well, Mackenzie Delta, Canada: Journal of Geophysical Research, 107, 2088
Sonic waveform attenuation in gas hydrate-bearing sediments from the Mallik 2L–38 research well, Mackenzie Delta, Canada:Crossref | GoogleScholarGoogle Scholar |

Guerin, G., and Goldberg, D., 2005, Modeling of acoustic wave dissipation in gas hydrate - bearing sediments: Geochemistry Geophysics Geosystems, 6, Q07010
Modeling of acoustic wave dissipation in gas hydrate - bearing sediments:Crossref | GoogleScholarGoogle Scholar |

Hackert, C. L., and Parra, J. O., 2003, Estimating scattering attenuation from vugs or karsts: Geophysics, 68, 1182–1188
Estimating scattering attenuation from vugs or karsts:Crossref | GoogleScholarGoogle Scholar |

Helgerud, M., Dvorkin, J., Nur, A., Sakai, A., and Collett, T., 1999, Elastic-wave velocity in marine sediments with gas hydrates: effective medium modelling: Geophysical Research Letters, 26, 2021–2024
Elastic-wave velocity in marine sediments with gas hydrates: effective medium modelling:Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DyaK1MXkvV2ls7Y%3D&md5=8dadccf1b7303dbed21abc7e447b56d6CAS |

Johnson, D. L., Koplik, J., and Dashen, R., 1987, Theory of dynamic permeability and tortuosity in fluid-saturated porous media: Journal of Fluid Mechanics, 176, 379–402
Theory of dynamic permeability and tortuosity in fluid-saturated porous media:Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DyaL2sXitFKhs7g%3D&md5=70f3bc6b19f2ed25003cc38f70acb848CAS |

Johnston, D. H., Toksöz, M. N., and Timur, A., 1979, Attenuation of seismic waves in dry and saturated rocks: II. Mechanisms: Geophysics, 44, 691–711
Attenuation of seismic waves in dry and saturated rocks: II. Mechanisms:Crossref | GoogleScholarGoogle Scholar |

Korenaga, J., Holbrook, W. S., Singh, S. C., and Minshull, T. A., 1997, Natural gas hydrates on the Southeast U.S. margin: Constraints from full-waveform and travel time inversion of wide-angle seismic data: Journal of Geophysical Research, 102, 15345–15365
Natural gas hydrates on the Southeast U.S. margin: Constraints from full-waveform and travel time inversion of wide-angle seismic data:Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DyaK2sXlt1Cqtrw%3D&md5=7166b16c7227db924ce20bb98055d805CAS |

Kozeny, J., 1927, Über kapillare Leitung des Wassers im Boden – Aufstieg, Versickerung und Anwendung auf die Bewässerung, Sitzungsberichte der Akademie der Wissenschaften Wien: Mathematisch Naturwissenschaftliche Abteilung, 136, 271–306

Klimentos, T., and McCann, C., 1990, Relationships between compressional wave attenuation, porosity, clay content, and permeability of sandstone: Geophysics, 55, 998–1014
Relationships between compressional wave attenuation, porosity, clay content, and permeability of sandstone:Crossref | GoogleScholarGoogle Scholar |

Leclaire, P., Cohen-Tenoudji, F., and Aguirre-Puente, J., 1994, Extension of Biot’s theory of wave propagation to frozen porous media: The Journal of the Acoustical Society of America, 96, 3753–3768
Extension of Biot’s theory of wave propagation to frozen porous media:Crossref | GoogleScholarGoogle Scholar |

Lee, M. W., 2006, Is amplitude loss of sonic waveforms due to intrinsic attenuation or source coupling to the medium? Scientific Investigations Report 2006–5120, 13 pp., U.S. Geological Survey, Reston, Virginia.

Lee, S., Cornillon, P., and Kim, Y., 2002, Spatial investigation of the nonfrozen water distribution in frozen foods using NMR SPRITE: Journal of Food Science, 67, 2251–2255
Spatial investigation of the nonfrozen water distribution in frozen foods using NMR SPRITE:Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD38XmslCnsLs%3D&md5=8ae02af2d1f74389df7c0f0715129be6CAS |

Lee, S., Pyrak-Nolte, L. J., Cornillon, P., and Campanella, O., 2004, Characterization of frozen orange juice by ultrasound and wavelet analysis: Journal of the Science of Food and Agriculture, 84, 405–410
Characterization of frozen orange juice by ultrasound and wavelet analysis:Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD2cXisVKit74%3D&md5=559b6d6068fe83354813fe6a4eeea750CAS |

Matsushima, J., 2005,, Attenuation measurements from sonic waveform logs in methane hydrate-bearing sediments at the Nankai Trough exploratory well off Tokai, central Japan: Geophysical Research Letters, 32, L03306. (Correction): Geophysical Research Letters, 33, L02305
Attenuation measurements from sonic waveform logs in methane hydrate-bearing sediments at the Nankai Trough exploratory well off Tokai, central Japan: Geophysical Research Letters, 32, L03306. (Correction):Crossref | GoogleScholarGoogle Scholar |

Matsushima, J., 2006, Seismic wave attenuation in methane hydrate-bearing sediments: Vertical seismic profiling data from the Nankai Trough exploratory well, offshore Tokai, central Japan: Journal of Geophysical Research, 111, B10101
Seismic wave attenuation in methane hydrate-bearing sediments: Vertical seismic profiling data from the Nankai Trough exploratory well, offshore Tokai, central Japan:Crossref | GoogleScholarGoogle Scholar |

Matsushima, J., Suzuki, M., Kato, Y., Nibe, T., and Rokugawa, S., 2008, Laboratory experiments on compressional ultrasonic wave attenuation in partially frozen brines: Geophysics, 73, N9–N18

Meiboom, S., and Gill, D., 1958, Modified spin-echo method for measuring nuclear relaxation times: The Review of Scientific Instruments, 29, 688–691
Modified spin-echo method for measuring nuclear relaxation times:Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DyaF3cXosFWitQ%3D%3D&md5=554f77032b03d614ab0a2b5ef555de86CAS |

Pham, N. H., Carcione, J. M., Helle, H. B., and Ursin, B., 2002, Wave velocities and attenuation of shaley sandstones as a function of pore pressure and partial saturation: Geophysical Prospecting, 50, 615–627
Wave velocities and attenuation of shaley sandstones as a function of pore pressure and partial saturation:Crossref | GoogleScholarGoogle Scholar |

Plona, T. J., 1980, Observation of a second bulk compressional wave in a porous medium at ultrasonic frequencies: Applied Physics Letters, 36, 259–261
Observation of a second bulk compressional wave in a porous medium at ultrasonic frequencies:Crossref | GoogleScholarGoogle Scholar |

Prasad, M., and Dvorkin, J., 2004, Velocity and attenuation of compressional waves in brines: 74th Annual International Meeting, SEG, Expanded Abstracts, 23, 1666–1669.

Pratt, R., Bauer, K., and Weber, M., 2003, Crosshole waveform tomography velocity and attenuation images of arctic gas hydrates: 73rd SEG Annual Meeting, Extended Abstracts, 22, 2255–2258.

Priest, J. A., Best, A. I., and Clayton, C. R. I., 2006, Attenuation of seismic waves in methane gas hydrate-bearing sand: Geophysical Journal International, 164, 149–159
Attenuation of seismic waves in methane gas hydrate-bearing sand:Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD28XitFSmurw%3D&md5=be7ba31660f5e214ff2723a280442f05CAS |

Sams, M., and Goldberg, D., 1990, The validity of Q estimates from borehole data using spectral ratios: Geophysics, 55, 97–101
The validity of Q estimates from borehole data using spectral ratios:Crossref | GoogleScholarGoogle Scholar |

Spetzler, H., and Anderson, D. L., 1968, The effect of temperature and partial melting on velocity and attenuation in a simple binary system: Journal of Geophysical Research, 73, 6051–6060
The effect of temperature and partial melting on velocity and attenuation in a simple binary system:Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DyaF1cXkvVSku7Y%3D&md5=958501c3f306f3c30dbdcb15a8527c2aCAS |

Sloan, E. D., 1990, Clathrate Hydrates of Natural Gases: Marcel Dekker.

Stoll, R. D., 1977, Acoustic waves in ocean sediments: Geophysics, 42, 715–725
Acoustic waves in ocean sediments:Crossref | GoogleScholarGoogle Scholar |

Suzuki, M., Matsushima, J., Kato, Y., Nibe, T., and Rokugawa, S., 2010, Ultrasonic wave-transmission measurement system on an ice-brine coexisting system: Butsuri Tansa, 63, 239–249

Tada, R., 1999, Experimental study of the elastic wave propagation in the granular composite material: Butsuri Tansa, 52, 28–42

Tada, R., and Kimura, M., 1999, Experimental study of the elastic wave propagation in composite porous media with glass beads and ice constituents – comparison with numerical study: Butsuri Tansa, 52, 323–335

Walsh, J. B., 1966, Seismic attenuation in rock due to friction: Journal of Geophysical Research, 71, 2591–2599

Walsh, J. B., 1969, New analysis of attenuation in partially melted rock: Journal of Geophysical Research, 74, 4333–4337
New analysis of attenuation in partially melted rock:Crossref | GoogleScholarGoogle Scholar |

Winkler, K. W., and Nur, A., 1982, Seismic attenuation: Effects of pore fluids and frictional sliding: Geophysics, 47, 1–15
Seismic attenuation: Effects of pore fluids and frictional sliding:Crossref | GoogleScholarGoogle Scholar |

Wood, W. T., Stoffa, P. L., and Shipley, T. H., 1994, Quantitative detection of methane hydrate through high-resolution seismic velocity analysis: Journal of Geophysical Research, 99, 9681–9695
Quantitative detection of methane hydrate through high-resolution seismic velocity analysis:Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DyaK2MXktlOgsQ%3D%3D&md5=d194a024903a7542fd28709d49dce92bCAS |

Yang, D., and Zhang, Z., 2002, Poroelastic wave equation including the Biot/squirt mechanism and the solid/fluid coupling anisotropy: Wave Motion, 35, 223–245
Poroelastic wave equation including the Biot/squirt mechanism and the solid/fluid coupling anisotropy:Crossref | GoogleScholarGoogle Scholar |