Mavko G., Mukerji T., Dvorkin J. The Rock Physics Handbook
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Schwerdtner, W.M., Tou, J. C.-M., and Hertz, P.B., 1965. Elastic properties of single crystals of
anhydrite. Can. J. Earth Sci., 2, 673–683.
Scott, G.D. and Kilgour, D.M., 1969. The density of random close packing of spheres. Brit.
J. Appl. Phys. (J. Phys. D), 2(2), 863–866.
Segel, L.A., 1987. Mathematics Applied to Continuum Mechanics. Mineola, NY: Dover.
Sen, P.N. and Goode, P.A., 1988. Shaley sand conductivities at low and high salinities. Trans.
Soc. Prof. Well Log Analysts, 29th Annual Logging Symposium, Paper F.
Sen, P.N., Scala, C., and Cohen, M.H., 1981. A self-similar model for sedimentary rocks with
application to the dielectric constant of fused glass beads. Geophys., 46, 781–795.
Seshagiri Rao, T., 1951. Elastic constants of barytes and celestite. Proc. Ind. Acad. Sci. A, 33,
251–256.
Shapiro, S.A. and Hubral, P., 1995. Frequency-dependent shear-wave splitting and velocity
anisotropy due to elastic multilayering. J. Seismic Explor., 4, 151–168.
Shapiro, S.A. and Hubral, P., 1996. Elastic waves in thinly layered sediments: the equivalent
medium and generalized O’Doherty–Anstey formulas. Geophys., 61, 1282–1300.
Shapiro, S.A. and Hubral, P., 1999. Elastic Waves in Random Media: Fundamentals of Seismic
Stratigraphic Filtering. Berlin: Springer-Verlag.
Shapiro, S.A. and Zien, H., 1993. The O’Doherty–Anstey formula and localization of seismic
waves. Geophys., 58, 736–740.
Shapiro, S.A., Hubral, P., and Zien, H., 1994. Frequency-dependent anisotropy of scalar waves
in a multilayered medium. J. Seismic Explor., 3, 37–52.
Sharma, M.M. and Tutuncu, A.N., 1994. Grain contact adhesion hysteresis: a mechanism for
attenuation of seismic waves. Geophys. Res. Lett. , 21, 2323–2326.
Sharma, M.M., Garrouch, A., and Dunlap, H.F., 1991. Effects of wettability, pore
geometry, and stress on electrical conduction in fluid-saturated rocks. Log Analyst,
32, 511–526.
Sharma, M.M., Tutuncu, A.N., and Podia, A. L., 1994. Grain contact adhesion hysteresis: a
mechanism for attenuation of seismic waves in sedimentary granular media. In
Extended Abstracts, Soc. Expl. Geophys., 64th Annual International Meeting, Los Angeles.
Tulsa, OK: Society of Exploration Geophysicists, pp. 1077–1080.
Shen, L.C., 1985. Problems in dielectric-constant logging and possible routes to their solution.
Log Analyst, 26, 14–25.
Sheriff, R.E., 1991. Encyclopedic Dictionary of Exploration Geophysics, 3rd edn. Tulsa, OK:
Society of Exploration Geophysics.
Sherman, M.M., 1986. The calculation of porosity from dielectric constant measurements: a
study using laboratory data. Log Analyst, Jan.–Feb., 15–24.
Sherman, M.M., 1988. A model for the frequency dependence of the dielectric permittivity of
reservoir rocks. Log Analyst, Sept.–Oct., 358–369.
Shuey, R.T., 1985. A simplification of the Zoeppritz equations. Geophys. , 50, 609–614.
Siggins, A.F. and Dewhurst, D.N., 2003. Saturation, pore pressure and effective stress from
sandstone acoustic properties.
Geophys. Res. Lett., 30,
1089 doi:10.1029/2002GL016143.
Simandoux, P.,
1963. Dielectric measurements on porous media: application to the measurement
of water saturations: study of the behavior of argillaceous formations. Rev. Inst. Franc¸ais
Petrole, 18, supplementary issue, 193–215.
Simmons, G., 1965. Single crystal elastic constants and calculated aggregate properties. J. Grad.
Res. Center, SMU, 34, 1–269.
Simmons, G. and Birch, F., 1963. Elastic constants of pyrite. J. Appl. Phys., 34, 2736–2738.
Skelt, C., 2004. Fluid substitution in laminated sands. Leading Edge, 23, 485–489.
497 References
Smith, G.C. and Gidlow, P.M., 1987. Weighted stacking for rock property estimation and detection
of gas. Geophys. Prospect., 35, 993–1014.
Smith, W.O., Foote, P.D., and Busand, P.G., 1929. Packing of homogeneous spheres. Phys. Rev. ,
34(2), 1271–1274.
Sneddon, I.N. and Lowergrub, M., 1969. Crack Problems in the Classical Theory of Elasticity. New
York: John Wiley and Sons.
Soga, N., 1967. Elastic constants of garnet under pressure and temperature. J. Geophys. Res., 72,
4227–4234.
Spangenburg, K. and Haussuhl, S., 1957. Die elastischen Konstanten der Alkalihalogenide.
Z. Kristallogr., 109, 422–437.
Spanos, T. J. T., 2002. The Thermophysics of Porous Media. Boca Raton, FL: Chapman &
Hall/CRC.
Spratt, R.S., Goins, N.R., and Fitch, T.J., 1993. Pseudo-shear – the analysis of AVO. In Offset
Dependent Reflectivity – Theory and Practice of AVO Analysis, ed. J.P. Castagna and
M. Backus, Invest. Geophys., No. 8. Tulsa, OK: Society of Exploration Geophysicists, pp. 37–56.
Stoll, R.D., 1974. Acoustic waves in saturated sediments. In Physics of Sound in Marine Sediments,
ed. L.D. Hampton. New York: Plenum, pp. 19–39.
Stoll, R.D., 1977. Acoustic waves in ocean sediments. Geophys., 42, 715–725.
Stoll, R.D., 1989. Sediment Acoustics. Berlin: Springer-Verlag, p. 154.
Stoll, R.D. and Bryan, G.M., 1970. Wave attenuation in saturated sediments. J. Acoust. Soc. Am.,
47, 1440–1447.
Stoner, E.C., 1945. The demagnetizing factors for ellipsoids. Philos. Mag., 36, 803–821.
Strandenes, S., 1991. Rock Physics Analysis of the Brent Group Reservoir in the Oseberg Field.
Stanford Rockphysics and Borehole Geophysics Project, special volume.
Sumino, Y., Kumazawa, M., Nishizawa, O., and Pluschkell, W., 1980. The elastic constants of
single-crystal Fe
1x
O, MnO, and CoO, and the elasticity of stochiometric magnesiowustite.
J. Phys. Earth, 28, 475–495.
Tang, X.-M. and Cheng, A., 2004. Quantitative Borehole Acoustic Methods. Amsterdam: Elsevier.
Tang, X.-M., Cheng, A., and Tokso
¨
z, M.N., 1991. Dynamic permeability and borehole Stoneley
waves: a simplified Biot–Rosenbaum model. J. Acoust. Soc. Am., 90, 1632–1646.
Thomas, E.C. and Stieber, S.J., 1975. The distribution of shale in sandstones and its effect upon
porosity. In Trans. 16th Annual Logging Symposium of the SPWLA , paper T.
Thomas, E.C. and Stieber, S.J., 1977. Log derived shale distributions in sandstone and its effect
upon porosity, water saturation, and permeability. In Trans. 6th Formation Evaluation
Symposium of the Canadian Well Logging Society.
Thomsen, L., 1986. Weak elastic anisotropy. Geophys., 51, 1954–1966.
Thomsen, L., 1993. Weak anisotropic reflections. In Offset Dependent Reflectivity – Theory and
Practice of AVO Analysis, ed. J.P. Castagna and M. Backus, Invest. Geophys., No. 8. Tulsa,
OK: Society of Exploration Geophysicists, pp. 103–111.
Thomson, W., 1878. Mathematical theory of elasticity. Elasticity, Encyclopedia Britannica, 7,
819–825.
Timoshenko, S.P. and Goodier, J.N., 1934. Theory of Elasticity. New York: McGraw-Hill.
Tixier, M.P. and Alger, R.P., 1967. Log evaluation of non-metallic mineral deposits. Trans. SPWLA
8th Ann. Logging Symp., Denver, June 11–14, Paper R.
Todd, T. and Simmons, G., 1972. Effect of pore pressure on the velocity of compressional waves
in low porosity rocks. J. Geophys. Res., 77, 3731–3743.
Topp, G.C., Davis, J.L., and Annan, A.P., 1980. Electromagnetic determination of soil water
content: measurements in coaxial transmission lines. Water Resource Res., 16, 574–582.
498 References
Tosaya, C.A., 1982. Acoustical Properties of Clay-bearing Rocks. Ph.D. dissertation, Stanford
University.
Tosaya, C.A. and Nur, A., 1982. Effects of diagenesis and clays on compressional velocities in
rocks. Geophys. Res. Lett., 9, 5–8.
Truesdell, C., 1965. Problems of Nonlinear Elasticity. New York: Gordon and Breach.
Tsvankin, I., 1997. Anisotropic parameters and P-wave velocity for orthorhombic media. Geophys.,
62, 1292–1309.
Tsvankin, I., 2001. Seismic Signatures and Analysis of Reflection Data in Anisotropic Media.
New York: Pergamon.
Tucker, M.E., 2001. Sedimentary Petrology, 3rd edn. Oxford: Blackwell Science.
Tutuncu, A.N., 1992. Velocity Dispersion and Attenuation of Acoustic Waves in Granular
Sedimentary Media. Ph.D. dissertation, University of Texas, Austin.
Tutuncu, A.N. and Sharma, M.M., 1992. The influence of grain contact stiffness and frame
moduli in sedimentary rocks. Geophys., 57, 1571–1582.
Urmos, J. and Wilkens, R.H., 1993. In situ velocities in pelagic carbonates: new insights from ocean
drilling program leg 130, Ontong Java. J. Geophys. Res., 98(B5), 7903–7920.
Vaughan, M.T. and Guggenheim, 1986. Elasticity of muscovite and its relationship to crustal
structure. J. Geophys. Res., 91, 4657–4664.
Vavryc
ˇ
uk, V. and Ps
ˇ
enc
ˇ
ik, I., 1998. PP-wave reflection coefficients in weakly anisotropic
elastic media. Geophys., 63(6), 2129–2141.
Verma, R.K., 1960. Elasticity of some high-density crystals. J. Geophys. Res., 65, 757–766.
Vernik, L., Bruno, M., and Bovberg, C., 1993. Empirical relations between compressive
strength and porosity of siliciclastic rocks. Int. J. Rock Mech. Min. Sci. Geomech. Abstracts,
30(7), 677–680.
Vernik, L., Fisher, D., and Bahret, S., 2002. Estimation of net-to-gross from P and S impedance in
deepwater turbidites. Leading Edge, 21, 380–387.
Voigt, W., 1890. Bestimmung der Elastizita
¨
tskonstanten des brasilianischen Turmalines. Ann. Phys.
Chem., 41, 712–729.
Voigt, W., 1907. Bestimmung der Elastizita
¨
tskonstanten von Eisenglanz. Ann. Phys., 24, 129–140.
Wachtman, J.B., Jr., Tefft, W.E., Lam, D.G., Jr., and Strinchfield, R.P., 1960. Elastic constants
of synthetic single crystal corundum at room temperature. J. Res. Natl. Bur. Stand., 64A,
213–228.
Waddell, H., 1932. Volume, shape and roundness of rock particles.
J. Geol. 40,
443–451.
Wadsworth, J., 1960.
Experimental examination of local processes in packed beds of
homogeneous spheres. Nat. Res. Council of Canada, Mech. Eng. Report MT-41 February.
Walls, J., Nur, A., and Dvorkin, J., 1991. A slug test method in reservoirs with pressure
sensitive permeability. Proc. 1991 Coalbed Methane Symp., University of Alabama,
Tuscaloosa, May 13–16, pp. 97–105.
Walsh, J.B., 1965. The effect of cracks on the compressibility of rock. J. Geophys. Res., 70 ,
381–389.
Walsh, J.B., 1969. A new analysis of attenuation in partially melted rock. J. Geophys. Res., 74,
4333.
Walsh, J.B., Brace, W.F., and England, A.W., 1965. Effect of porosity on compressibility of
glass. J. Am. Ceramic Soc., 48, 605–608.
Walton, K., 1987. The effective elastic moduli of a random packing of spheres. J. Mech. Phys.
Solids, 35, 213–226.
Wang, H.F., 2000. Theory of Linear Poroelasticity. Princeton, NJ: Princeton University Press.
499 References
Wang, Z., 2000a. Dynamic versus static properties of reservoir rocks, in seismic and acoustic
velocities in reservoir rocks. SEG Geophysics Reprint Series, 19, 531–539.
Wang, Z., 2002. Seismic anisotropy in sedimentary rocks, Parts I and II. Geophys., 67, 1415–1440.
Wang, Z. and Nur, A., 1992. Seismic and Acoustic Velocities in Reservoir Rocks, vol. 2, Theoretical
and Model Studies, Soc. Expl. Geophys., Geophysics Reprint Series. Tulsa, OK: Society of
Exploration Geophysicists.
Wang, Z. and Nur, A. (eds.), 2000. Seismic and Acoustic Velocities in Reservoir Rocks, vol. 3,
Recent Developments, Geophysics Reprint Series, no. 19. Tulsa, OK: Society of Exploration
Geophysicists.
Ward, S.H. and Hohmann, G.W., 1987. Electromagnetic theory for geophysical applications. In
Electromagnetic Methods in Applied Geophysics, vol. I, Theory , ed. M.N. Nabhigian. Tulsa,
OK: Society of Exploration Geophysicists, pp. 131–311.
Watt, J.P., Davies, G.F., and O’Connell, R.J., 1976. The elastic properties of composite materials.
Rev. Geophys. Space Phys., 14, 541–563.
Waxman, M.H. and Smits, L. J. M., 1968. Electrical conductivities in oil-bearing shaley sands. Soc.
Petrol Eng. J., 8, 107–122.
Weidner, D.J. and Carleton, H.R., 1977. Elasticity of coesite. J. Geophys. Res., 82, 1334–1346.
Weidner, D.J. and Hamaya, N., 1983. Elastic properties of the olivine and spinel polymorphs of
Mg
2
GeO
4
and evaluation of elastic analogues. Phys. Earth Planetary Interiors, 33, 275–283.
Weidner, D. J., Bass, J.D., Ringwood, E., and Sinclair, W., 1982. The single-crystal elastic moduli
of stishovite. J. Geophys. Res., 87, 4740–4746.
Weingarten, J.S. and Perkins, T.K., 1995. Prediction of sand production in wells: methods and Gulf
of Mexico case study. J. Petrol. Tech., 596–600.
Whitcombe, D.N., 2002. Elastic impedance normalization. Geophys., 67, 59–61.
Whitcombe, D.N., Connolly, P.A., Reagan, R.L., and Redshaw, T.C., 2002. Extended elastic
impedance for fluid and lithology prediction. Geophys., 67, 63–67.
White, J.E., 1975. Computed seismic speeds and attenuation in rocks with partial gas saturation.
Geophys., 40, 224–232.
White, J.E., 1983. Underground Sound: Application of Seismic Waves. New York: Elsevier.
White, J.E., 1986. Biot–Gardner theory of extensional waves in porous rods. Geophys., 51,
742–745.
Widmaier, M., Shapiro, S.A., and Hubral, P., 1996. AVO correction for a thinly layered reflector
overburden. Geophys., 61, 520–528.
Wiggins, R., Kenny, G.S., and McClure, C.D., 1983. A method for determining and displaying the
shear-velocity reflectivities of a geologic formation. European Patent Application 0113944.
Williams, D.M., 1990. The acoustic log hydrocarbon indicator. Soc. Prof. Well Log Analysts,
31st Ann. Logging Symp., Paper W.
Willis, J.R., 1977. Bounds and self-consistent estimates for the overall properties of anisotropic
composites, J. Mech. Phys. Solids, 25, 185–202.
Winkler, K., 1986. Estimates of velocity dispersion between seismic and ultrasonic frequencies.
Geophys., 51, 183–189.
Winkler, K.W., 1983. Contact stiffness in granular porous materials: comparison between theory
and experiment. Geophys. Res. Lett., 10, 1073–1076.
Winkler, K.W., 1985. Dispersion analysis of velocity and attenuation in Berea sandstone.
J. Geophys. Res., 90, 6793–6800.
Winkler, K.W. and Murphy, W.F., III, 1995. Acoustic velocity and attenuation in porous rocks.
In Rock Physics and Phase Relations, A Handbook of Physical Constants, AGU Reference
Shelf 3. Washington, DC: American Geophysical Union.
500 References
Winkler, K.W. and Nur, A., 1979. Pore fluids and seismic attenuation in rocks. Geophys. Res.
Lett., 6, 1–4.
Woeber, A.F., Katz, S., and Ahrens, T.J., 1963. Elasticity of selected rocks and minerals. Geophys.,
28, 658–663.
Wong, S.W., Kenter, C.J., Schokkenbroek, H., van Regteren, J., and De Bordes, P.F., 1993.
Optimising shale drilling in the Northern North Sea; borehole stability considerations.
SPE paper 26736, Offshore Europe Conference, Aberdeen, 7–10 September.
Wood, A.W., 1955. A Textbook of Sound. New York: McMillan Co.
Worthington, P.F., 1985. Evolution of shaley sand concepts in reservoir evaluation. Log Analyst,
26, 23–40.
Wu, T.T., 1966. The effect of inclusion shape on the elastic moduli of a two-phase material.
Int. J. Solids Structures, 2, 1–8.
Wyllie, M. R. J. and Gregory, A.R., 1953. Formation factors of unconsolidated porous media:
influence of particle shape and effect of cementation. Trans. Am. Inst. Mech. Eng., 198,
103–110.
Wyllie, M. R. J., Gregory, A.R., and Gardner, L.W., 1956. Elastic wave velocities in
heterogeneous and porous media. Geophys., 21, 41–70.
Wyllie, M. R. J., Gregory, A.R., and Gardner, G. H. F., 1958. An experimental investigation of
factors affecting elastic wave velocities in porous media. Geophys., 23, 459–493.
Wyllie, M. R. J., Gardner, G. H. F., and Gregory, A.R., 1963. Studies of elastic wave attenuation
in porous media. Geophys., 27, 569–589.
Xu, S. and White, R.E., 1994. A physical model for shear-wave velocity prediction. In Expanded
Abstracts, 56th Eur. Assoc. Expl. Geoscientists Meet. Tech. Exhib., Vienna, p. 117.
Xu, S. and White, R.E., 1995. A new velocity model for clay–sand mixtures. Geophys. Prospect.,
43, 91–118.
Yale, D.P. and Jameison, W.H., Jr., 1994. Static and dynamic rock mechanical properties in
the Hugoton and Panoma fields. Kansas Society of Petroleum Engineers, Paper 27939.
Society of Petroleum Engineers Mid-Continent Gas Symposium, Amarillo, TX, May.
Yamakawa, N., 1962. Scattering and attenuation of elastic waves. Geophys. Mag., Tokyo, 31,
63–103.
Yeganeh-Haeri, A., Weidner, D.J., and Ito, E., 1989. Single-crystal elastic moduli of magnesium
metasilicate perovskite. In Perovskite: a Structure of Great Interest to Geophysics and
Materials Science, Geophysics Monograph Series, vol. 45. Washington, D.C.: American
Geophysical Union, pp. 13–25.
Yeganeh-Haeri, A., Weidner, D.J., and Parise, J.B., 1992. Elasticity of a-cristobalite: a silicon
dioxide with a negative Poisson’s ratio. Science, 257, 650–652.
Yin, H., 1992. Acoustic Velocity and Attenuation of Rocks: Isotropy, Intrinsic Anisotropy, and
Stress-Induced Anisotropy. Ph.D. dissertation, Stanford University.
Yoneda, A., 1990. Pressure derivatives of elastic constants of single crystal MgO, MgAl
2
O
4
.
J. Phys. Earth, 38, 19–55.
Yoon, H.S. and Newnham, R.E., 1969. Elastic properties of fluorapatite. Amer. Mineralog., 54,
1193–1197.
Yoon, H.S. and Newnham, R.E., 1973. The elastic properties of beryl. Acta Cryst., A29, 507–509.
Young, H.D., 1962. Statistical Treatment of Experimental Data. New York: McGraw-Hill.
Yu, G., Vozoff, K., and Durney, W., 1993. The influence of confining pressure and water saturation
on dynamic properties of some rare Permian coals. Geophys., 58, 30–38.
Zamora, M. and Poirier, J.P., 1990. Experimental study of acoustic anisotropy and birefringence in
dry and saturated Fontainebleau sandstone. Geophys., 55, 1455–1465.
501 References
Zarembo, I.K. and Krasil’nikov, V.A., 1971. Nonlinear phenomena in the propagation of elastic
waves in solids. Sov. Phys. Usp., 13, 778–797.
Zeller, R. and Dederichs, P.H., 1973. Elastic constants of polycrystals. Phys. Stat. Sol. b, 55, 831.
Zener, C., 1948. Elasticity and Anelasticity of Metals. Chicago, IL: University of Chicago Press.
Zhao, Y. and Weidner, D.J., 1993. The single-crystal elastic moduli of neighborite. Phys. Chem.
Minerals, 20, 419–424.
Zimmerman, R.W., 1984. The elastic moduli of a solid with spherical pores: new self-consistent
method. Int. J. Rock Mech., Mining Sci. Geomech. Abstracts, 21, 339–343.
Zimmerman, R.W., 1986. Compressibility of two-dimensional cavities of various shapes. J. Appl.
Mech. Trans. Am. Soc. Mech. Eng., 53, 500–504.
Zimmerman, R.W., 1991a. Compressibility of Sandstones. New York: Elsevier.
Zimmerman, R.W., 1991b. Elastic moduli of a solid containing spherical inclusions. Mech. Mater.,
12, 17–24.
Zoback, M.D., 2007. Reservoir Geomechanics, Cambridge: Cambridge University Press.
Zoeppritz, K., 1919. Erdbebenwellen VIIIB, On the reflection and propagation of seismic waves.
Go
¨
ttinger Nachr., I, 66–84.
502 References
Index
Aki–Richards approximation, 100
see also AVO
analytic signal, 6–7
see also Hilbert transform
anellipticity, 37
anisotropy, elastic
anellipticity, 37
Backus average, 138, 179, 210–218
coordinate transformation, 18–20, 26
dispersion, 138–146
displacement discontinuity model, 219, 223
Eshelby–Cheng model, 203–205
fluid substitution, anisotropic, 284–286
frequency-dependent, 138–146
group, phase, energy velocities, 83–86
Hooke’s law, 23–35
Hudson’s model, 152, 194–203
layered media, 37–38, 138–146
ordered sphere packing, effective moduli, 264
squirt, anisotropic, 306–309
stiffness tensor, 23–35
stress-induced anisotropy, 43–47
T-matrix inclusion models, 205–210
see also AVO; effective medium models, elastic;
elasticity; NMO; granular media; Thomsen’s
weak anisotropy; Tsvankin’s parameters
API gravity, 344
Archie’s law, 425
cementation exponent, 425
saturation exponent, 425
second law, 425
attenuation electromagnetic, 418–419
attenuation, seismic, 332
Biot model, 143–146, 157, 266–271
BISQ model, 302–303
Chapman et al. squirt model, 304–305
characteristic frequency, 311
comparison among fluid-related mechanisms,
310–315
Dvorkin–Mavko attenuation model, 315
empirical relation, 384
Kennett
algorithm, 130
Kennett–Frazer
theory, 134
layered media, see stratigraphic filtering
O’Doherty–Anstey formula, 136
squirt model, 297–301, 304–309
stratigraphic filtering, 134–137
viscous fluid
see also borehole; scattering; viscoelasticity and Q
autocorrelation, 2
AVO, 93–115
Aki–Richards approximation, 100
anisotropic, 105–115
arbitrary anisotropy, 114
Bortfield approximation, 100
Gardner’s equation, 102
gradient, 102
Hilterman’s equation, 103
isotropic, 96–105
orthorhombic, 111
Poisson’s ratio trace (Hilterman’s), 103
Shuey’s approximation, 102
Smith and Gidlow’s formula, 102
transversely isotropic, 108, 110
Zoeppritz equations, 98
AVOA, see AVO, anisotropic
Backus average, 138, 179, 210–218
arbitrarily anisotropic layers, 215
fractures, parallel, 219
isotropic layers, 211
poroelastic layers, 216
transversely isotropic layers, 211
uniform shear modulus, 213
BAM, see bounding average method
bar resonance, see cylindrical rods
Batzle–Wang relations, 341–346
Bayes decision theory, 17
Berryman self-consistent model, see self-consistent
approximation
binary mixture of spheres, see granular media
binomial coefficients, 12
binomial distribution, 12
Biot coefficient, 45, 58, 280
Biot
model, 143–146, 157, 266–271
Geertsma–Smit approxima
tion, 272
partial saturation, 327–332
slow P-wave, 267–268
503
Biot model (cont.)
slow S-wave, 269–271
see also Gassmann’s equations
Biot–Rosenbaum theory, 164
Biot–White–Gardner effect in resonant
bars, 157
BISQ model, 302–303
Bond coordinate transformation, 19, 26
bootstrap, 16
borehole,
Biot–Rosenbaum theory, 164
permeable formation, 164
pseudo-Rayleigh in borehole, 160
Stoneley waves, 160, 167
stress and deformation, 70–76
waves, 160–168
Bortfield’s AVO formula, see AVO
bound water, 428
bounds, cross-property
Berryman–Milton bounds, 432
Gibiansky–Torquato bound, 432
Milton bounds, 432
bounds elastic, 169–175
bound-filling models, 224–228
bounding average method, 225, 295–296
Hashin–Shtrikman, 169–228, 258, 260
Hashin–Shtrikman–Walpole, 169–174, 224
isoframe model, 225
modified Hashin–Shtrikman bound, 224
modified Voigt bound, 348
Reuss, 172, 174–177, 224, 324
Voigt, 174–175, 177, 224, 347
Voigt–Reuss–Hill average, 177, 225
bounds electrical, 414
bound-filling models, 224–228
bounding average method, 225, 295–296
Bower’s relation, 383
Bragg scattering, 137
Brandt
model, 252
Brie mixing equation, 327
Brinkman’s
equation, 394
Brocher’s empirical relations, 359
Brown and Korringa equation, 210, 290
anisotropic form, 285
mixed mineralogy, 282–284
Buckley–Leverett equation, 390
bulk modulus, see elasticity, effective medium
models, elastic
Burger’s vector, 65
capillary forces, 396–400
capillary pressure, 398
Laplace equation, 398
carbon dioxide, properties, 474
Castagna’s empirical relations, 358
cation exchange capacity, 427
Cauchy’s formula, 76
causality, 8
cavities in elastic solid, 57–76
Biot coefficient, 58
circular hole, 70–76
crack closing stress, 48, 61, 219
cylindrical shell, 70
ellipsoidal with finite thickness, 68
elliptical borehole, 72
needle-shaped (prolate spheroid), 61
nonelliptical, 67, 220
penny-shaped crack (oblate spheroid), 60
spherical cavities, 59, 151
spherical shells, 68
three-dimensional ellipsoidal cavities, 59
two-dimensional cavities, 62–67
see also borehole; effective medium theories,
elastic; inclusion models
cementation models, 255
Chapman et al. squirt model, 304–305
classification, 17
Bayes decision theory, 17
discriminant analysis, 18
Mahalanobis distance, 18
Clausius–Mossotti formula, 415
clay
Castagna’s velocity relations, 358
electrical
conductivity, 426
Han’s velocity relation
s, 355
mudrock line, 366
Tosaya’s velocity relations, 357
V
P
–V
S
relations, 363–379
closing stress, see crack closing stress
coal, V
P
–V
S
relations, 369
Coates equation, 407
Coates–Dumanoir equation, 407
coefficient of determination, 10
coherent potential approximation, 209
Cole–Cole dielectric model, 419
complex dielectric constant, see dielectric constant,
attenuation electromagnetic
complex modulus, see viscoelasticity and Q
compliance tensor, see elasticity
compressibility
cavities in elastic solid, 57–76
definitions and pitfalls, 179–183
reservoir fluids, 341–346
see also elasticity; effective medium models,
elastic; bounds, elastic
compressive strength, see unconfined
compressive strength
constant Q model, 126
see also viscoelasticity and Q
contact angle, 398
contact stiffness, see Hertz–Mindlin–model
conversion tables, 452–456
convolution, 2
coordinate transformation, 18–20, 26
coordination number, see granular media
correlation coefficient, 9
504 Index
covariance, 10, 12
cracks, 57–76
Chapman et al. squirt model, 304–305
crack closing stress, 48, 61, 219
deformation under stress, see cavities in
elastic solid
displacement discontinuity model, 219, 223
Eshelby–Cheng model, 203–205
fracture compliance, 219–223
fractures, flow in, 410–411
Hudson model, 152, 194–203
Kuster–Tokso
¨
z model, 183–185
seismic response, 219–223
self-consistent approximation, 185–188
squirt model, 297–301, 304–309
stress-induced anisotropy, 43–47
T-matrix inclusion models, 205–210
see also cavities in elastic solid; effective
medium models, elastic; scattering
creeping flow, 396
CRIM formula, 421
critical porosity, 347
modified DEM model, 192
modified Hashin–Shtrikman bound, 224
modified Voigt bound, 347–348
V
P
–V
S
relations, 369
cross-correlation, 2
cross-property relations, 429–435
crystallographic third order constants, 42
curvilinear coordinates, 55–56
cylindrical rods, 155–159
flexural waves, 156
longitudinal waves, 156
Pochhammer equation, 156–157
porous, saturated, 157
torsional waves, 155
cylindrical shell, 70
Darcy, unit, 389
Darcy’s law, 389
Brinkman’s equation, 394
Forchheimer’s relation, 394
dead oil, 345
Debye dielectric model, 419
DEM model, 190–194, 415
density–velocity relations, see empirical velocity
relations
depolarizing factors, dielectric, 416
dielectric constant, 418–419
dielectric permittivity, 414–417
dielectric susceptibility, 418
differential effective medium model, see DEM
diffusion, 391 –392, 411–413
diffusion equation hyperbolic, 412
diffusion equation nonlinear, 411
diffusion scattering, 150
Digby model, 249
discriminant analysis, 18
dislocation theory, 66
dispersion, see velocity dispersion
displacement discontinuity model, see cracks
dissipation, see attenuation
distributions,
binomial coefficients, 12
binomial distribution, 12
logistic distribution, 15
lognormal distribution, 14
normal (Gaussian) distribution, 13
Poisson distribution, 13–14
truncated exponential distribution, 14
uniform
distribution, 13
Weibull distribution, 15
Dix
equation, 88
see also NMO
drainage, 400
dual water model, 426
Dutta–Ode
´
model, 327–332
Eaton’s pore-pressure relation, 383
Eberhart–Phillips (Han) velocity relations, 355
effective electrical properties, 414–435
effective fluid, 323
effective medium models, dielectric
bounds, 414
Clausius–Mossotti formula, 415
coherent potential approximation, 415
Cole–Cole model, 419
Debye model, 419
DEM model, 415
ellipsoidal inclusions, 416
Lorentz–Lorenz equation, 415
Maxwell–Garnett equation, 415
self-consistent approximation, 415
effective medium models, elastic, 169–228
BISQ model, 302–303
bound-filling models, 224–228
bounding average method, 225
Brandt model, 252
cavities in elastic solid, 57–76
cementation models, 255
Chapman et al. squirt model, 304–305
comparison among fluid-related dispersion
mechanisms, 310–315
compressibility and pitfalls, 179–183
contact stiffness, grain, see Hertz–Mindlin model
coordination number, 232, 245
DEM model, 190–194
Digby model, 249
Eshelby–Cheng model, 203–205
granular media, 245–265
Hashin–Shtrikman bounds, see bounds, elastic
Hertz (–Mindlin) model, 220, 246–248,
252, 258
Hudson model, 152 , 194–203
isoframe model, 225
Jenkins, et
al. model, 251
505 Index
effective medium models, elastic (cont.)
Johnson et al. model, 253
Kuster–Tokso
¨
z model, 183–185
O’Connell–Budiansky model, 186
ordered sphere packing, effective moduli, 264
self-consistent approximation, 185–188
squirt, anisotropic, 306–309
squirt model, 297–301, 304–305
stiff sand model, 260
stress-induced anisotropy, 43–47
T-matrix inclusion models, 205–210
uniform shear modulus (Hill), 178
Walton model, 248
Wood’s formula, 175
Xu–White model, 377
see also bounds, elastic
effective stress properties, 43–47
eigentensors and eigenvalues, 32
elastic compliance, see elasticity
elastic impedance, 115–121
isotropic, 118
orthorhombic, 120
transversely isotropic, 119
elastic moduli, see elasticity
elasticity
anellipticity, 37
anisotropic, 23–40, 43–47
Biot coefficient, 58
bulk modulus, 21
cavities in elastic solid, 57–76
compliance tensor, 24
compressibility, 21, 179–183
cubic, 27, 264
effective stress properties, 43–47
eigentensors and eigenvalues, 32
hexagonal, 27, 264
Hooke’s law, 21, 23–35
isotropic, 24, 26
Kelvin notation, 30–32, 207
Lame’s constant, 22
moduli, elastic, 21, 79, 80
monoclin
ic, 28
nonlinear elasticity, 40–47
orthorhombi
c, 28, 39–40, 47
P-wave modulus, 22
Poisson’s ratio, 22, 33
shear modulus, 22
Skempton coefficient, 58
static and dynamic moduli, 79
stiffness tensor, 25–35
stress-induced anisotropy, 43–47
third-order elasticity, 40–43, 53
Thomsen parameters, 35–39
transversely isotropic, 27, 35–39, 41, 210–218
triclinic, 24
Tsvankin’s parameters, 39–40
Voigt notation, 24–28, 35, 207
Young’s modulus, 22
see also AVO; bounds, elastic; effective medium
models, elastic; phase velocity
electrical conductivity, 424–429
Archie’s law, 425
dual water model, 426
Indonesia formula, 426
Sen and Goode model, 428
shaley sands, 426
Simandoux equation, 426
Waxman–Smits model, 426
Waxman–Smits–Juha
´
sz model, 426
electromagnetic waves, 418
reflection coefficients, 420
transmission coefficients, 420
ellipsoidal cavities, 57–76
see also cavities in elastic solid; effective
medium models, elastic
empirical electrical property relations, 421–429
Archie’s law, 425
CRIM formula, 421
cross-property relations, 429–435
Faust’s
relation, 429
hydraulic conductivity, 423
Knight
and Nur relation, 423
Koesoemadinata and McMechan relations, 423
Lichtnecker–Rother formula, 421
Odelevskii formula, 422
Olhoeft’s relation, 422
Topp’s relation, 422
empirical velocity relations
Brocher’s compilation, 359
Castagna’s velocity relations, 358, 363–379
coal, 369
critical porosity model, 347–349
cross-property relations, 429–435
Eberhart–Phillips (Han) relations, 355
Faust’s relation, 429
Gardner’s velocity–density relation, 102, 381
Geertsma’s modulus–porosity relation, 350
Greenberg–Castagna relations, 374
Han’s velocity relations, 355
Krief’s relation, 372
Pickett’s relation, 363
Raymer–Hunt–Gardner velocity relations, 353
static and dynamic moduli, 79
Tosaya’s velocity relations, 357
velocity–density relations, 359, 380
velocity–strength relations, 386
Vernik’s relations, 376
V
P
–V
S
relations, 361, 363–379
Williams’s relation, 377
Wyllie’s time average, 350
energy spectrum, 2
energy velocity, 84
envelope, see Hilbert transform
equations of state fluids, see Batzle–Wang
relations
Eshelby–Cheng model, 203–205
506 Index