REFERENCES

• Abramowitz, M., and Stegun, I. A., 1965, Handbook of Mathematical Functions, Dover, New York, Chapter 9.
• Avellaneda, M., 1987, Iterated homogenization, differential effective medium theory and applications: Commun.Pure Appl.Math 40, 527-554.
• Bancroft, D., 1941, The velocity of longitudinal waves in cylindrical bars: Phys.Rev., 59, 588-593.
• 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., 1983, Dispersion of extensional waves in fluid-saturated porous cylinders at ultrasonic frequencies: J. Acoust.Soc.Am., 74, 1805-1812.
• 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.
• 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. |item Chree, C., 1886, Longitudinal vibrations of a circular bar: Quart.J. Pure Appl.Math., 21, 287-298.
• Deresiewicz, H., and Skalak, R., 1963, On uniqueness in dynamic poroelasticity: Bull.Seismol.Soc.Am., 53, 783-788.
• 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.
• 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.
• Pochhammer, L., 1876, Über Fortpflanzungsgeschwindigkeiten kleiner Schwingungen in einem unbegrenzten isotropen Kreiscylinder: J. Reine Angew.Math. (Crelle), 81, 324-336.
• Pride, S. R., and Flekkoy, E. G., 1999, Two-phase flow through porous media in the fixed-contact-line regime: Phys.Rev.E, 60, 4285-4299.
• Pride, S. R., Tromeur, E., and Berryman, J. G., 2002, Biot slow-wave effects in stratified rock: Geophysics, 67, 271-281.

 

 

Short Note
Exploring the relationship between uncertainty of AVA attributes and rock information

Weitian Chen and Robert Clapp

chen@sep.stanford.edu, bob@sep.stanford.edu