Comparative review of theoretical models for elastic wave attenuation and dispersion in partially saturated rocks

Soil Dynamics and Earthquake Engineering

Volumn 26, Issue 6-7, 2006, Pages 548-565

  Toms, J ^a   Muller T M ^b   Ciz, R ^c   Gurevich, B ^a,c  

^a CURTIN UNIVERSITY   (Australia)

^b UNIVERSITY OF KARLSRUHE   (Germany)

^c CSIRO   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

ATTENUATION; DISPERSION (WAVES); FLOW OF FLUIDS; MATHEMATICAL MODELS; ROCKS; SATURATION (MATERIALS COMPOSITION); SEISMIC WAVES; WAVE PROPAGATION;

MESOSCOPIC FLUID HETEROGENEITIES; PARTIAL FLUID SATURATION; WAVE-INDUCED FLUID FLOW;

ELASTIC WAVES;

ELASTIC WAVE; MODELING; POROUS MEDIUM; ROCK; SEISMIC ATTENUATION; SEISMIC WAVE; THEORETICAL STUDY; WAVE ATTENUATION; WAVE DISPERSION; WAVE PROPAGATION;

EID: 33746019322     PISSN: 02677261     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.soildyn.2006.01.008     Document Type: Article

References (84)

1. Biot M.A. Theory of propagation of elastic waves in a fluid in a fluid saturated porous solid. I-Low frequency range. J Acoust Soc Am 28 (1956) 168-178
2. Biot M.A. Theory of propagation of elastic waves in a fluid saturated porous solid. II. Higher frequency range. J Acoust Soc Am 28 (1956) 179-191
3. Biot M.A. Mechanics of deformation and acoustic propagation in porous media. J Appl Phys 33 (1962) 1482-1498
4. Gassmann F. Elastic waves through a packing of spheres. Geophysics 16 (1951) 673-685
5. Bear J. Dynamics of fluids in porous media (1988), Dover, New York
6. Wood A.B. A textbook of sound (1941), Bell, London
7. White J.E. Computed seismic speeds and attenuation in rocks with partial gas saturation. Geophysics 40 (1975) 224-232
8. Johnson D.L. Theory of frequency dependent acoustics in patchy-saturated porous media. J Acoust Soc Am 110 (2001) 682-694
9. Pride S.R., Berryman J.G., and Harris J.M. Seismic attenuation due to wave-induced flow. J Geophys Res 109 B1 (2004) B01201
10. Gurevich B., and Lopatnikov S.L. Velocity and attenuation of elastic waves in finely layered porous rocks. Geophys J Int 121 (1995) 933-947
11. Müller T.M., and Gurevich B. One-dimensional random patchy saturation model for velocity and attenuation in porous rocks. Geophysics 69 (2004) 1166-1172
12. Ciz R, Toms J, Gurevich B. Attenuation and dispersion of elastic waves in a poroelastic medium with spherical inclusions. In: Abousleiman YN, Cheng AHD, Ulm FJ, editors. Proceedings of the 3rd Biot Conference on Poromechanics, University of Oklahoma, AA. Balkema Publishers, 2005. p. 201-7.
13. Toms J, Müller T, Gurevich B. 3D random patchy saturation model for velocity and attenuation in porous rock. In: Proceedings of the 75th annual international meeting: Society of Exploration Geophysicists, Houston, 2005, Expanded Abstracts, paper SM 1.1, p. 1747-50.
14. Pride S.R., Gangi A.F., and Morgan F.D. Deriving the equations of motion for porous isotropic media. J Acoust Soc Am 92 (1992) 3278-3290
15. Levy T. Propagation of waves in a fluid-saturated porous elastic solid. Int J Eng Sci 17 (1979) 1005-1014
16. Auriault J.L. Dynamic behaviour of a porous medium saturated by a Newtonian fluid. Int J Eng Sci 18 (1980) 775-785
17. Burridge R., and Keller J.B. Poroelasticity equations derived from microstructure. J Acoust Soc Am 70 (1981) 1140-1145
18. Biot M.A., and Willis D.G. The elastic coefficients of the theory of consolidation. J Appl Mech 24 (1957) 594-601
19. Bourbie T., Coussy O., and Zinszner B. Acoustics of porous media (1987), Technip, Paris
20. Berryman J.G. Seismic wave attenuation in fluid saturated porous media. PAGEOPHY 128 (1998) 424-432
21. Wang Z. Fundamentals of seismic rock physics. Geophysics 66 (2001) 398-412
22. Smith T.M., Sondergeld C.H., and Rai C.S. Gassmann fluid substitutions: a tutorial. Geophysics 68 (2003) 430-440
23. Johnston D.H., Toksöz M.N., and Timur A. Attenuation of seismic waves in dry and saturated rocks: mechanisms. Geophysics 44 (1979) 691-711
24. Winkler K. Dispersion analysis of velocity and attenuation in Berea sandstone. J Geophys Res 90 (1985) 6793-6800
25. Gist G.A. Interpreting laboratory velocity measurements in partially gas-saturated rocks. Geophysics 59 (1994) 1100-1109
26. Buckingham M.J. Wave propagation, stress relaxation, and grain-to-grain shearing in saturated, unconsolidated marine sediments. J Acoust Soc Am 108 (2000) 2796-2815
27. Plona T.J. Observation of a second bulk compressional wave in a porous medium at ultrasonic frequencies. Appl Phys Lett 36 (1980) 259-261
28. Nagy P.B., Alder L., and Bonner B.P. Slow wave propagation in air-filled porous materials and natural rocks. Appl Phys Lett 56 (1990) 2504-2506
29. Kelder O., and Smeulders D.M.J. Observation of the Biot slow wave in water-saturated Nivelsteiner sandstone. Geophysics 62 (1997) 1794-1796
30. White J.E., Mikhaylova N.G., and Lyakhovitskiy F.M. Low-frequency seismic waves in fluid-saturated layered rocks. Phys Solid Earth Trans Izv 11 (1976) 654-659
31. Domenico S.N. Effect of brine-gas mixture on velocity in an unconsolidated sand reservoir. Geophysics 41 (1976) 882-894
32. Gregory A.R. Fluid saturation effects on dynamic elastic properties of sedimentary rocks. Geophysics 41 (1976) 895-921
33. Murphy W.F. Acoustic measures of partial gas saturation in tight sandstones. J Geophys Res 89 B13 (1984) 11549-11559
34. Murphy W.F. Sonic and ultrasonic velocities: theory versus experiment. Geophys Res Lett 12 (1985) 85-88
35. Cadoret T., Marion D., and Zinszner B. Influence of frequency and fluid distribution on elastic wave velocities in partially saturated limestones. J Geophys Res 100 (1995) 9789-9803
36. Cadoret T., Mavko G., and Zinszner B. Fluid distribution effect on sonic attenuation in partially saturated limestones. Geophysics 63 (1998) 154-160
37. Dutta N.C., and Ode H. Attenuation and dispersion of compressional waves in fluid-filled porous rocks with partial gas saturation (White model)-Part I. Biot theory. Geophysics 44 (1979) 1777-1788
38. Dutta N.C., and Ode H. Attenuation and dispersion of compressional waves in fluid-filled porous rocks with partial gas saturation (White model)-Part II. Results. Geophysics 44 (1979) 1789-1805
39. Dutta N.C., and Seriff A.J. On White's model of attenuation in rocks with partial gas saturation. Geophysics 44 (1979) 1806-1812
40. Carcione J.M., Helle H.B., and Pham N.H. White's model for wave propagation in partially saturated rocks, comparison with poroelastic numerical experiments. Geophysics 67 (2003) 1389-1398
41. Helle H.B., Pham N.H., and Carcione J.M. Velocity and attenuation in partially saturated rock, poroelastic numerical experiments. Geophys Prospect 51 (2003) 551-566
42. Mavko G., and Nur A. Wave propagation in partially saturated rocks. Geophysics 44 (1979) 161-178
43. Palmer I.D., and Traviola M.L. Attenuation by squirt flow in undersaturated gas sands. Geophysics 45 (1980) 1780-1792
44. Murphy W.A., Winkler K.W., and Kleinberg R.A. Acoustic relaxation in sedimentary rocks-dependence on grain contacts and fluid saturation. Geophysics 51 (1986) 757-766
45. Jones T.D. Pore fluids and frequency-dependent wave propagation in rocks. Geophysics 51 (1986) 1939-1953
46. Bedford A., and Stern M. A model for wave propagation in gassy sediments. J Acoust Soc Am 73 (1982) 409-417
47. Lopatnikov S.L., and Gorbachev P.Y. Propagation and attenuation of longitudinal waves in a partially gas-saturated porous media. Izv Earth Phys 23 (1987) 683-689
48. Smeulders D.M.J., and van Dongen M.E.H. Wave propagation in porous media containing a dilute gas-liquid mixture: theory and experiments. J Fluid Mech 343 (1997) 351-373
49. Auriault J.L., Boutin C., Royer P., and Schmitt D. Acoustics of a porous medium saturated by a bubbly fluid undergoing phase change. Transport Porous Media 46 (2002) 43-76
50. Assefa S., McCann C., and Sothcott J. Attenuation of P- and S-waves in limestones. Geophys Prospect 47 (1999) 359-392
51. Best A.I., McCann C., and Sothcott J. The relationship between the velocities, attenuations and petrophysical properties of reservoir sedimentary rocks. Geophys Prospect 42 (1994) 151-178
52. Silberman E.J. Sound velocity and attenuation in bubbly mixtures measured in standing wave tubes. J Acoust Soc Am 29 (1957) 925-933
53. van Wijngaarden L. One dimensional flow of liquids containing small gas bubbles. Annu Rev Fluid Mech 4 (1972) 369-396
54. Commander K.W., and Prosperetti A. Linear pressure waves in bubbly fluids. Comparison between theory and experiments. J Acoust Soc Am 85 (1989) 732-746
55. Knight R., Chapman A., and Knoll M. Numerical modelling of microscopic fluid distribution in porous media. J Appl Phys 68 (1990) 994-1001
56. Silverstein D.L., and Fort T. Prediction of air-water interfacial air in wet unsaturated porous media. Langmuir 16 (2000) 829-834
57. Silverstein D.L., and Fort T. Incorporating low hydraulic conductivity in a numerical model for predicting air-water interfacial area in wet unsaturated particulate porous media. Langmuir 16 (2000) 835-838
58. Silverstein D.L., and Fort T. Prediction of water configuration in wet unsaturated porous media. Langmuir 16 (2000) 839-844
59. Berkowitz B., and Hansen D. A numerical study of the distribution of water in partially saturated porous rock. Transport Porous Media 45 (2001) 303-319
60. Monsen K., and Johnstad S.E. Improved understanding of velocity-saturation relationships using 4D computer-tomography acoustic measurements. Geophys Prospect 53 (2005) 173-181
61. Knight R., and Nolen-Hoeskema R. A laboratory study of the dependence of elastic wave propagation of elastic wave velocities on porescale distribution. Geophys Res Lett 17 (1990) 1529-1532
62. Mavko G., and Mukerji T. Bounds on low frequency seismic velocities in partially saturated rocks. Geophysics 63 (1998) 918-924
63. Norris A.N. Low-frequency dispersion and attenuation in partially saturated rocks. J Acoust Soc Am 94 (1993) 359-370
64. Hill R. Elastic properties of reinforced solids: some theoretical principles. J Mech Phys Solids 11 (1963) 357-372
65. Tserkovnyak Y., and Johnson D.L. Can one hear the shape of a saturation patch. Geophys Res Lett 29 (2002) 1108-1112
66. Pride S.R., and Berryman J.G. Linear dynamics of double-porosity and dual-permeability materials. I. Governing equations and acoustic attenuation. Phys Rev E 68 (2003) 036,603
67. Pride S.R., and Berryman J.G. Linear dynamics of double-porosity and dual permeability materials. II. Fluid transport equations. Phys Rev E 68 (2003) 036,604
68. Pride S.R., Morgan F.D., and Gangi A.F. Drag forces of porous-medium acoustics. Phys Rev B 47 (1993) 4964-4978
69. Lopatnikov S.L., and Gurevich B. Attenuation of elastic waves in a randomly inhomogeneous saturated porous medium. Dokl Earth Sci Sect 291 6 (1986) 19-22
70. Gelinsky S., Shapiro S.A., Müller T.M., and Gurevich B. Dynamic poroelasticity of thinly layered structures. Int J Solids Struct 35 (1998) 4739-4752
71. Shapiro S.A., and Müller T.M. Seismic signatures of permeability in heterogeneous porous media. Geophysics 64 (1999) 99-103
72. Müller TM, Lambert G, Gurevich B. Dynamic permeability of random porous rocks and its seismic signatures. In: Proceedings of the 75th annual international Meeting: Society of Exploration Geophysicists, Houston, 2005, Expanded Abstracts, paper RP 1.8, p. 1497-500.
73. Ciz R, Gurevich B. Seismic attenuation in a porous rock with spherical heterogeneities. In: Proceedings of the 74th annual international meeting: Society of Exploration Geophysicists, Denver, 2004, Expanded Abstracts, paper 466, p. 1686-9.
74. Müller T.M., and Gurevich B. A first order statistical smoothing approximation for the coherent wave field in random porous media. J Acoust Soc Am 117 (2005) 1796-1805
75. Müller T.M., and Gurevich B. Wave induced fluid flow in random porous media: attenuation and dispersion of elastic waves. J Acoust Soc Am 117 (2005) 2732-2741
76. Ciz R., and Gurevich B. Amplitude of Biot's slow wave scattered by a spherical inclusion in a fluid-saturated poroelastic medium. Geophys J Int 160 (2005) 991-1005
77. Waterman P.C., and Truell R. Multiple scattering of waves. J Math Phys 2 4 (1961) 512-537
78. Berryman J.G. Scattering by a spherical inhomogeneity in a fluid-saturated porous medium. J Math Phys 26 6 (1985) 1408-1419
79. Deresiewicz H., and Skalak R. On uniqueness in dynamic poroelasticity. Bull Seism Soc Am 53 (1963) 409-416
80. Yamakawa N. Scattering and attenuation of elastic waves. Geophys Mag Tokyo 31 (1962) 63-97
81. Knight R., Dvorkin J., and Nur A. Acoustic signatures of partial saturation. Geophysics 63 (1998) 132-138
82. Karal F.C., and Keller J.B. Elastic, electromagnetic and other waves in random. J Math Phys 5 (1964) 537-547
83. Torquato S. Random heterogeneous materials: microstructure and macroscopic properties (2001), Springer, New York
84. Murphy W.F. Effects of partial water saturation on attenuation in Massilon sandstone and Vycor porous glass. J Acoust Soc Am 71 (1982) 1458-1468