REFERENCES

• Avellaneda, M., 1987, Iterated homogenization, differential effective medium theory and applications: Commun.Pure Appl.Math 40, 527-554.
• Berge, P. A., Bonner, B. P., and Berryman, J. G., 1995, Ultrasonic velocity-porosity relationships for sandstone analogs made from fused glass beads: Geophysics 60, 108-119.
• Berryman, J. G., 1980a, Long-wavelength propagation in composite elastic media. I. Spherical inclusions: J. Acoust.Soc.Am. 68, 1809-1819.
• Berryman, J. G., 1980b, Long-wavelength propagation in composite elastic media II. Ellipsoidal inclusions: J. Acoust.Soc.Am. 68, 1820-1831.
• Berryman, J. G., 1992, Single-scattering approximations for coefficients in Biot's equations of poroelasticity: J. Acoust.Soc.Am. 91, 551-571.
• Berryman, J. G., 1999, Origin of Gassmann's equations: Geophysics 64, 1627-1629.
• Berryman, J. G., Berge, P. A., and Bonner, B. P., 2000, Transformation of seismic velocity data to extract porosity and saturation values for rocks: J. Acoust.Soc.Am. 107, 3018-3027.
• Berryman, J. G., Berge, P. A., and Bonner, B. P., 2002a, Estimating rock porosity and fluid saturation using only seismic velocities: Geophysics 67, 391-404.
• Berryman, J. G., Pride, S. R., and Wang, H. F., 2002b, A differential scheme for elastic properties of rocks with dry or saturated cracks: Geophys.J. Int., accepted for publication in 2002.
• Berryman, J. G., Thigpen, L., and Chin, R. C. Y., 1988, Bulk elastic wave propagation in partially saturated porous solids: J. Acoust.Soc.Am. 84, 360-373.
• Berryman, J. G, and Wang, H. F., 2001, Dispersion in poroelastic systems: Phys.Rev.E 64, 011303-1-011303-16.
• Biot, M. A., 1956a, Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range: J. Acoust. Soc.Am. 28, 168-178.
• Biot, M. A., 1956b, Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range: J. Acoust. Soc.Am. 28, 179-1791.
• Biot, M. A., 1962, Mechanics of deformation and acoustic propagation in porous media: J. Appl.Phys. 33, 1482-1498.
• Bruggeman, D. A. G., 1935, Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen: Ann.Physik. (Leipzig) 24, 636-679.
• Chin, R. C. Y., Berryman, J. G., and Hedstrom, G. W., 1985, Generalized ray expansion for pulse propagation and attenuation in fluid-saturated porous media: Wave Motion 7, 43-66.
• Cleary, M. P., Chen, I.-W., and Lee, S.-M., 1980, Self-consistent techniques for heterogeneous media: ASCE J. Eng.Mech. 106, 861-887.
• Domenico, S. N., 1974, Effect of water saturation on seismic reflectivity of sand reservoirs encased in shale: Geophysics 39, 759-769.
• Dvorkin, J., Mavko, G., and Nur, A., 1999a, Overpressure detection from compressional- and shear-wave data: Geophys.Res.Lett. 26, 3417-3420.
• Dvorkin, J., Moos, D., Packwood, J. L., and Nur, A. M., 1999b, Identifying patchy saturation from well logs: Geophysics 64, 1756-1759.
• Dvorkin, J. and Nur, A., 1998, Acoustic signatures of patchy saturation: Int. J. Solids Struct. 35, 4803-4810.
• Eshelby, J. D., 1957, The determination of the elastic field of an ellipsoidal inclusion, and related problems: Proc.Roy.Soc.London A 241, 376-396.
• Gassmann, F., 1951, Über die elastizität poröser medien: Vierteljahrsschrift der Naturforschenden Gesellschaft in Zürich, 96, 1-23.
• Hadley, K., 1976, Comparison of calculated and observed crack densities and seismic velocities in Westerly granite: J. Geophys.Res. 81, 3484-3494.
• Hashin, Z., and Shtrikman, S., 1961, Note on a variational approach to the theory of composite elastic materials: J. Franklin Inst. 271, 336-341.
• Hashin, Z., and Shtrikman, S., 1962, A variational approach to the theory of elastic behaviour of polycrystals: J. Mech.Phys.Solids 10, 343-352.
• Johnson, D. L., 2001, Theory of frequency dependent acoustics in patchy-saturated porous media: J. Acoust.Soc.Am. 110, 682-694.
• Knight, R., and Nolen-Hoeksema, R., 1990, A laboratory study of the dependence of elastic wave velocities on pore scale fluid distribution: Geophys. Res. Lett. 17, 1529-1532.
• Korringa, J., Brown, R. J. S., Thompson, D. D., and Runge, R. J., 1979, Self-consistent imbedding and the ellipsoidal model for porous rocks: J. Geophys.Res. 84, 5591-5598 (1979).
• Mavko, G., and Jizba, D., 1991, Estimating grain-scale fluid effects on velocity dispersion in rocks: Geophysics 56, 1940-1949.
• Mavko, G., Mukerji, T., and Dvorkin, J., 1998, The Rock Physics Handbook: Tools for Seismic Analysis in Porous Media, Cambridge University Press, Cambridge, pp.307-309.
• Milton, G. W., 1985, The coherent potential approximation is a realizable effective medium scheme: Comm.Math.Phys. 99, 463-500.
• Murphy, William F., III, 1982, Effects of Microstructure and Pore Fluids on the Acoustic Properties of Granular Sedimentary Materials, Ph.D. Dissertation, Stanford University.
• Norris, A. N., 1985, A differential scheme for the effective moduli of composites: Mech.Mater. 4, 1-16.
• Nur, A., and Simmons, G., 1969, The effect of saturation on velocity in low porosity rocks: Earth and Planet.Sci.Lett. 7, 183-193.
• Plona, T. J., 1980, Observation of a second bulk compressional wave in a porous medium at ultrasonic frequencies: Appl.Phys.Lett. 36, 259-261.
• Reuss, A., 1929, Berechung der Fleissgrenze von Mischkristallen: Z. Angew.Math.Mech. 9, 55.
• Seifert, P. K., B. Kaelin, and L. R. Johnson, 1999, Effect on ultrasonic signals of viscous pore fluids in unconsolidated sand: J. Acoust.Soc.Am. 106, 3089-3094.
• Voigt, W., 1928, Lehrbuch der Kristallphysik, Teubner, Leipzig, p.962.
• Walls, J. D., 1982, Tight gas sands - permeability, pore structure: and clay: J. Petroleum Technology 34, 2708-2714.
• Walsh, J. B., 1965, The effect of cracks on the compressibility of rock: J. Geophys.Res. 70, 381-389.
• Walsh, J. B., 1980, Static deformation of rock: ASCE J. Engng.Mech. 106, 1005-1019.
• Wu, T. T., 1966, The effect of inclusion shape on the elastic moduli of a two-phase material: Int.J. Solids Struct. 2, 1-8.

 

 

Short Note
Dispersion of waves in porous cylinders with patchy saturation

James G. Berryman, Steven R. Pride

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