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

by Gary Mavko , Tapan Mukerji , Jack Dvorkin

• ISBN13: 9780521861366
• ISBN10: 0521861365
• Edition: 2nd
• Format: Hardcover
• Copyright: 2009-05-25
• Publisher: Cambridge University Press

Summary

This fully updated text addresses the relationships between geophysical observations and the underlying physical properties of rocks. It distills a vast quantity of background theory and laboratory results into a series of concise chapters that provide practical solutions to problems in geophysical data interpretation. Now in its second edition, major new chapters are presented on statistical rock physics and velocity-porosity-clay models for clastic sediments. Other new and expanded topics include anisotropic seismic signatures, borehole waves, models for fractured media, poroelastic models, and attenuation models. Also new to this edition is an enhanced set of appendices with key empirical results, data tables, and an atlas of reservoir rock properties - extended to include carbonates, clays, gas hydrates, and heavy oils. Supported by a website hosting MATLAB routines for implementing the various rock physics formulas, this book is a vital resource for advanced students and university faculty, as well as petroleum industry geophysicists and engineers.

Table of Contents

Preface	p. xi
Basic tools	p. 1
The Fourier transform	p. 1
The Hilbert transform and analytic signal	p. 6
Statistics and probability	p. 9
Coordinate transformations	p. 18
Elasticity and Hooke's law	p. 21
Elastic moduli: isotropic form of Hooke's law	p. 21
Anisotropic form of Hooke's law	p. 23
Thomsen's notation for weak elastic anisotropy	p. 35
Tsvankin's extended Thomsen parameters for orthorhombic media	p. 39
Third-order nonlinear elasticity	p. 40
Effective stress properties of rocks	p. 43
Stress-induced anisotropy in rocks	p. 47
Strain components and equations of motion in cylindrical and spherical coordinate systems	p. 54
Deformation of inclusions and cavities in elastic solids	p. 56
Deformation of a circular hole: borehole stresses	p. 68
Mohr's circles	p. 74
Static and dynamic moduli	p. 76
Seismic wave propagation	p. 81
Seismic velocities	p. 81
Phase, group, and energy velocities	p. 83
NMO in isotropic and anisotropic media	p. 86
Impedance, reflectivity, and transmissivity	p. 93
Reflectivity and amplitude variations with offset (AVO) in isotropic media	p. 96
Plane-wave reflectivity in anisotropic media	p. 105
Elastic impedance	p. 115
Viscoelasticity and Q	p. 121
Kramers-Kronig relations between velocity dispersion and Q	p. 127
Waves in layered media: full-waveform synthetic seismograms	p. 129
Waves in layered media: stratigraphic filtering and velocity dispersion	p. 134
Waves in layered media: frequency-dependent anisotropy, dispersion, and attenuation	p. 138
Scale-dependent seismic velocities in heterogeneous media	p. 146
Scattering attenuation	p. 150
Waves in cylindrical rods: the resonant bar	p. 155
Waves in boreholes	p. 160
Effective elastic media: bounds and mixing laws	p. 169
Hashin-Shtrikman-Walpole bounds	p. 169
Voigt and Reuss bounds	p. 174
Wood's formula	p. 175
Voigt-Reuss-Hill average moduli estimate	p. 177
Composite with uniform shear modulus	p. 178
Rock and pore compressibilities and some pitfalls	p. 179
Kuster and Toksoz formulation for effective moduli	p. 183
Self-consistent approximations of effective moduli	p. 185
Differential effective medium model	p. 190
Hudson's model for cracked media	p. 194
Eshelby-Cheng model for cracked anisotropic media	p. 203
T-matrix inclusion models for effective moduli	p. 205
Elastic constants in finely layered media: Backus average	p. 210
Elastic constants in finely layered media: general layer anisotropy	p. 215
Poroelastic Backus average	p. 216
Seismic response to fractures	p. 219
Bound-filling models	p. 224
Granular media	p. 229
Packing and sorting of spheres	p. 229
Thomas-Stieber model for sand-shale systems	p. 237
Particle size and sorting	p. 242
Random spherical grain packings: contact models and effective moduli	p. 245
Ordered spherical grain packings: effective moduli	p. 264
Fluid effects on wave propagation	p. 266
Biot's velocity relations	p. 266
Geertsma-Smit approximations of Biot's relations	p. 272
Gassmann's relations: isotropic form	p. 273
Brown and Korringa's generalized Gassmann equations for mixed mineralogy	p. 282
Fluid substitution in anisotropic rocks	p. 284
Generalized Gassmann's equations for composite porous media	p. 287
Generalized Gassmann equations for solid pore-filling material	p. 290
Fluid substitution in thinly laminated reservoirs	p. 292
BAM: Marion's bounding average method	p. 295
Mavko-Jizba squirt relations	p. 297
Extension of Mavko-Jizba squirt relations for all frequencies	p. 298
Biot-squirt model	p. 302
Chapman et al. squirt model	p. 304
Anisotropic squirt	p. 306
Common features of fluid-related velocity dispersion mechanisms	p. 310
Dvorkin-Mavko attenuation model	p. 315
Partial and multiphase saturations	p. 320
Partial saturation: White and Dutta-Ode model for velocity dispersion and attenuation	p. 326
Velocity dispersion, attenuation, and dynamic permeability in heterogeneous poroelastic media	p. 331
Waves in a pure viscous fluid	p. 338
Physical properties of gases and fluids	p. 339
Empirical relations	p. 347
Velocity-porosity models: critical porosity and Nur's modified Voigt average	p. 347
Velocity-porosity models: Geertsma's empirical relations for compressibility	p. 350
Velocity-porosity models: Wyllie's time-average equation	p. 350
Velocity-porosity models: Raymer-Hunt-Gardner relations	p. 353
Velocity-porosity-clay models: Han's empirical relations for shaley sandstones	p. 355
Velocity-porosity-clay models: Tosaya's empirical relations for shaley sandstones	p. 357
Velocity-porosity-clay models: Castagna's empirical relations for velocities	p. 358
VP-VS-density models: Brocher's compilation	p. 359
VP-VS relations	p. 363
Velocity-density relations	p. 380
Eaton and Bowers pore-pressure relations	p. 383
Kan and Swan pore-pressure relations	p. 383
Attenuation and quality factor relations	p. 384
Velocity-porosity-strength relations	p. 386
Flow and diffusion	p. 389
Darcy's law	p. 389
Viscous flow	p. 394
Capillary forces	p. 396
Kozeny-Carman relation for flow	p. 401
Permeability relations with Swi	p. 407
Permeability of fractured formations	p. 410
Diffusion and filtration: special cases	p. 411
Electrical properties	p. 414
Bounds and effective medium models	p. 414
Velocity dispersion and attenuation	p. 418
Empirical relations	p. 421
Electrical conductivity in porous rocks	p. 424
Cross-property bounds and relations between elastic and electrical parameters	p. 429
Appendices	p. 437
Typical rock properties	p. 437
Conversions	p. 452
Physical constants	p. 456
Moduli and density of common minerals	p. 457
Velocities and moduli of ice and methane hydrate	p. 457
Physical properties of common gases	p. 468
Velocity, moduli, and density of carbon dioxide	p. 474
Standard temperature and pressure	p. 474
References	p. 479
Index	p. 503
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