Mavko G., Mukerji T., Dvorkin J. The Rock Physics Handbook

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exponential distribution, 14

eye, gnat’s, see gnat’s eye

fast path effect, 147

Faust’s relation, 429

FFT, see Fourier transform

flexural waves

bar, 156

Floquet solution, 137

fluid

Batzle–Wang relations for physical properties,

341–346

nonwetting, 398

wetting, 398

fluid flow

Brinkman’s equation, 394

creeping flow, 396

Darcy’s law, 389

diffusion equation nonlinear, 411

diffusivity, 391

drainage, 400

Forchheimer’s relation, 394

fractured formation, 410–411

imbibition, 400

Kozeny–Carman relation, 401–406

multiphase flow, 390

pipe, 395

relative permeability, 390–391

viscous flow, 394–396

fluid substitution, 274, 279, 284–286

Batzle–Wang relations for fluid properties, 341–346

bounding average method, 225, 295–296

Brown and Korringa equations, 210, 282–285

Gassmann’s equations, 273–281, 284–285

partial saturations, 320–332

thinly laminated sands, 292

Fontainebleau sandstone, 407

Forchheimer’s relation, 394

formation factor, 424

Fourier transform, 1–6

fractures, see cracks

Fresnel’s equations, electromagnetic, 420

Gardner’s equation, 102, 381

gases, properties, 468–474

Gassmann equations, 273–281, 290

anisotropic

form, 284–285

Batzle–Wang relations

for fluid properties, 341–346

Biot coefficient form, 280

bounding average method, 295–296

compressibility form, 275

dry rock caveat, 273, 320

generalized form for composite porous media,

287–289

linear form, 276

P-wave modulus form, 277

partial saturations, 320–332

pore stiffness interpretation, 278

Reuss average form, 276

solid pore-filling material, 290–291

thinly laminated sands, 292

velocity form, 277

-only form (no V

), 281

see also AVO

Koesoemadinata and McMechan relations, 423

Kozeny–Carman relation, 401–406

Kramers–Kronig relations, 127

Krief’s relation, 372

Kuster–Tokso

z model, 183–185

Lame’s constant, see elasticity

Landau’s third-order constants, 42

Laplace equation for capillary pressure, 398

layered media, 129–146

anisotropy and dispersion, 138–146

Bragg scattering, 137

dielectric constant, 417

electromagnetic waves, 421

Floquet solution, 137

Kennett algorithm, 130

Kennett–Frazer theory, 134

O’Doherty–Anstey formula, 136

periodic, 137

poroelastic, 143–146

synthetic seismograms, 129

uniform shear modulus, 179

see also Backus average; stratigraphic filtering;

velocity dispersion

Lichtnecker–Rother formula, 421

linear regression, 10

live oil, 344

local flow model, see squirt

model

logarithmic decrement, 123

see

also viscoelasticity and Q

logistic distribution, 15

lognormal distribution, 14

longitudinal waves, 156

see also viscoelasticity and Q

Mohr’s circles, 76–79

monoclinic symmetry, see elasticity

Monte Carlo simulations, 15

mudrock line, 366

Murnaghan third-order constants, 42

Navier–Stokes equations, 395

nearly constant Q model, 126

see also viscoelasticity and Q

Newtonian flow, 394–396

NMO, 86–93

anisotropic, 88–93

Dix equation, 88

elliptical anisotropy, 90–91

interval velocity, 88

isotropic, 86

orthorhombic, 92–93

transversely isotropic, 89–90

nonlinear elasticity, 40–43

normal distribution, 13

Nyquist frequency, 3

O’Connell–Budiansky model, 186

Odelevskii formula, 422

O’Doherty–Anstey formula, 136

oil properties

Batzle–Wang relations, 341–346

dead oil, 345

live oil, 344

Olhoeft’s relation, 422

optical potential approximation, 208

orthorhombic symmetry, see AVO, elasticity, phase

velocity, reflectivity

packing, 320–327, see granular media

partial saturations, 320–327

Brie mixing equation, 327

effective fluid, 323

patchy saturation, 325

relaxation scale, 324

relaxation time, 324

Reuss average mixing, 324

Voigt average mixing, 327

White–Dutta–Ode

model, 327–332

see

also

fluid substitution; Gassmann’s

equations; Biot model

patchy saturation, 325, 327–332

see also viscoelasticity and Q

quality factor, 123

see also viscoelasticity and Q

ray parameter, 93, 98

Rayleigh scattering, 150

Rayleigh wave velocity, 82

pseudo-Rayleigh in borehole, 160

Raymer form, V

relation, 379

509 Index

Raymer–Hunt–Gardner velocity relations, 353

reflectivity, electromagnetic, 420

reflectivity, seismic, 93–115

see also AVO

regression, 9

residual oil, 400

resistivity, electrical, 424–429

see also AVO

Snell’s law

sorting, see granular media

specific surface area, 229, 402

spectral ratio, 124

see also viscoelasticity and Q

spectrum, 2

sphere packs, see granular media

spherical inclusions, see cavities in elastic solid,

effective medium models, elastic, scattering

spherical shells, 68

squirt model, 297–298, 304–305

anisotropic, 306–309

Chapman et al. squirt model, 304–305

extended to all frequencies, 298–301

standard deviation, 9

standard linear solid, see viscoelasticity and Q

standard temperature and pressure (STP), 474

statistical classification, 17

statistics and probability, 9–18

see also distributions; Monte Carlo; bootstrap;

classification; Bayes

stiff sand model, 260

stiffness tensor, see elasticity

stochastic (Mie) scattering, 150

Stoneley waves in borehole, 160, 167

stratigraphic filtering, 134–137

Floquet

solution, 137

O’Doherty–Anstey formula, 136

stratigraphic

slowness, 134

strength, see unconfined compressive strength

stress-induced anisotropy, 43–47

surface tension, 396

contact angle, 398

Young’s relation, 397

suspensions, see Wood’s formula

synthetic seismograms, 129–146

see also Kennett algorithm; layered media

tensor transformation, see coordinate transformation

third-order elasticity, 40–43, 53

Thomas–Stieber model for sand–shale systems, 237–242

Thomsen’s weak anisotropy, 35–39

time-average equation, 350

time-domain reflectometry (TDR)

Timur equation, 407

Tixier equation, 407

T-matrix inclusion models, 205–210

coherent potential approximation, 209

optical potential approximation, 208

self-consistent approximation, 209

Topp’s relation, 422

torsional waves, 155

see also AVO

transverse isotropy, see AVO, elasticity, NMO,

phase velocity, reflectivity

truncated exponential distribution, 14

Tsvankin’s parameters, 39–40

Udden–Wentworth scale, 242

uncemented (soft) sand model, 258

unconfined compressive strength (UCS), empirical

relations, 386

uniform distribution, 13

variance, 9

variogram, 12

velocity, dispersion, 84, 134–146, 332

anomalous normal

Biot model, 143–146, 157, 266–271

BISQ model, 302–303

Bragg scattering, 137

Chapman et al. squirt model, 304–305

characteristic frequency, 311

comparison among fluid-related mechanisms, 310–315

cylindrical rods, 155–159

Dvorkin–Mavko attenuation model, 315

electromagnetic, 418

fast path effect, 147

Floquet solution, 137

group, phase, energy velocities, 83–86

heterogeneous media, 146–150

layered poroelastic, 143–146

O’Doherty–Anstey formula, 136

resonant bar, see cylindrical bar

saturation-related, 320–332

scattering attenuation, 150–155

squirt model, 297–301, 304–309

stratigraphic filtering, 134–137

stratigraphic slowness, 134

three-dimensional heterogeneous media, 147

waves in pure viscous fluid, 339

see also layered media; viscoelasticity and Q

velocity, electromagnetic, 418

velocity,

seismic, 81–83

cylindrical rods, 155–159

dispersion, 84

group, phase,

energy velocities, 83–86

isotropic, 81

phase velocity, 36

Rayleigh wave, 82

RMS, see NMO

signal velocity, 86

stratigraphic filtering, 134–137

viscous fluid, in, 339

see also anisotropy; empirical velocity relations;

velocity dispersion

velocity–density relations, 359, 380

velocity–porosity relation, see empirical velocity

relations

Vernik’s V

–V

relations, 376

viscoelasticity and Q, 121–129, 138–146, 332

characteristic frequency, 311

comparison among fluid-related mechanisms,

310–315

constant Q model, 126

dispersion, 84

Dvorkin–Mavko attenuation model, 315

group, phase, energy velocities, 83–86

logarithmic decrement, 123

Maxwell solid, 122

modulus defect, 126, 310

nearly constant Q model, 126

quality factor (Q), 123

saturation-related, 320–332

spectral ratio, 124

standard linear solid, 122, 124

Voigt solid, 122