The Rock Physics Handbook: Tools for Seismic Analysis in Porous Media

Cover......Page 1
The Rock Physics Handbook: Tools for Seismic Analysis of Porous Media......Page 3
©......Page 5
CONTENTS......Page 6
PREFACE......Page 10
     1.1 The fourier transform......Page 12
     1.2 The hilbert transform and analytic signal......Page 19
     1.3 Statistics and linear regression......Page 21
     1.4 Coordinate transformations......Page 25
     2.1 Elastic moduli-isotropic form of Hooke\'s law......Page 28
     2.2 Anisotropic form of Hooke\'s law......Page 30
     2.3 Thomsen\'s notation for weak elastic anisotropy......Page 36
     2.4 Stress-induced anisotropy in rocks......Page 38
     2.5 Strain components and equations of motion in cylindrical and spherical coordinate systems......Page 43
     2.6 Deformation of inclusions and cavities in elastic solids......Page 45
     2.7 Deformation of a circular hole-borehole stresses......Page 56
     2.8 Mohr\'s circles......Page 59
     3.1 Seismic velocities......Page 62
     3.2 Phase, group, and energy velocities......Page 65
     3.3 Impedance, reflectivity, and transmissivity......Page 68
     3.4 Reflectivity and AVO......Page 71
     3.5 Avoz in anisotropic environments......Page 76
     3.6 Viscoelasticity and Q......Page 81
     3.7 Kramers-Kronig relations between velocity dispersion and Q......Page 86
     3.8 Waves in layered media: full-waveform synthetic seismograms......Page 88
     3.9 Waves in layered media: stratigraphic filtering and velocity dispersion......Page 93
     3.10 Waves in layered media: frequency-dependent anisotropy and dispersion......Page 97
     3.11 Scale-dependent seismic velocities in heterogeneous media......Page 102
     3.12 Scattering attenuation......Page 106
     3.13 Waves in cylindrical rods - the resonant bar......Page 111
     4.1 Hashin-Shtrikman bounds......Page 117
     4.2 Voigt and Reuss bounds......Page 121
     4.3 Wood\'s formula......Page 123
     4.4 Hill average moduli estimate......Page 125
     4.5 Composite with uniform shear modulus......Page 126
     4.6 Rock and pore compressibilities and some pitfalls......Page 128
     4.7 Kaster and Toksoz formulation for effective moduli......Page 132
     4.8 Self-consistent approximations of effective moduli......Page 134
     4.9 Differential effective medium model......Page 140
     4.10 Hudson\'s model for cracked media......Page 144
     4.11 Eshelby-Cheng model for cracked anisotropic media......Page 151
     4.12 Elastic constants in finely layered media - backus average......Page 154
     5.1 Packing of spheres - geometric relations......Page 158
     5.2 Random spherical grain packings - contact models and effective moduli......Page 160
     6.1 Biot\'s velocity relations......Page 173
     6.2 Geertsma-Smit approximations of Biot\'s relations......Page 177
     6.3 Gassmann\'s relations......Page 179
     6.4 Bam-Marion\'s bounding average method......Page 188
     6.5 Fluid substitution in anisotropic rocks: Brown and Korringa\'s relations......Page 190
     6.6 Generalized Gassmann\'s equetions for composite porous media......Page 192
     6.7 Mavko-Jizba squirt relations......Page 195
     6.8 Extension of Mavko-Jizba squirt relations for all frequencies......Page 197
     6.9 BISQ......Page 201
     6.10 Anisotropic squirt......Page 204
     6.11 Common features of fluid-related velocity dispersion mechanisms......Page 208
     6.12 Partial and multiphase saturations......Page 213
     6.13 Partial saturation: White and Dutta-Ode model for velocity dispersion and attenuation......Page 218
     6.14 Waves in pure viscous fluid......Page 224
     6.15 Physical properties of gases and fluids......Page 225
     7.1 Velocity-porosity models:critical porosity and Nur\'s modified Voigt average......Page 232
     7.2 Velocity-porosity models: Gerrtsma\'s empirical relations for compressibility......Page 236
     7.3 Velocity-porosity models: Wyllie\'s time average equetion......Page 237
     7.4 Velocity-porosity models: Raymer-Hunt-Garner relations......Page 239
     7.5 Velocity-porosity-clay models: Han\'s empirical relations for shaley sandstones......Page 242
     7.6 Velocity-porosity-clay models: Tosaya\'s empirical relations for shaley sandstones......Page 244
     7.7 Velocity-porosity-clay models: Castagna\'s empirical relations for velocities......Page 245
     7.8 Vp-Vs relations......Page 246
     7.9 Velocity-density relations......Page 261
     8.1 Darcy\'s law......Page 266
     8.2 Kozeny-Carman relation......Page 271
     8.3 Viscous flow......Page 275
     8.4 Capillary forces......Page 278
     8.5 Diffusion and filtration - special cases......Page 279
     9.1 Bounds and effective medium models......Page 282
     9.2 Velocity dispersion and attenuation......Page 286
     9.3 Empirical relations......Page 291
     9.4 Electrical coductivity in porous rocks......Page 293
     10.1 Typical rock properties......Page 299
     10.2 Conversions......Page 314
     10.3 Moduli and density of common minerals......Page 317
REFERENCES CITED IN THE TABLE......Page 319
REFERENCES......Page 323
INDEX......Page 335