THE ROCK PHYSICS HANDBOOK - GBV
THE ROCK PHYSICSHANDBOOKTOOLS FOR SEISMIC ANALYSISIN POROUS MEDIAGary MavkoStanford UniversityTapan MukerjiStanford UniversityJack DvorkinStanford UniversityCAMBRIDGEUNIVERSITY PRESS
CONTENTSPrefacePART 1 : BASIC TOOLS1.11.21.31.4The Fourier TransformThe Hilbert Transform and Analytic SignalStatistics and Linear RegressionCoordinate Transformationspage ix1181014PART 2: ELASTICITY AND HOOKE'S LAW172.12.22.32.42.517192526Elastic Moduli - Isotropic Form of Hooke's LawAnisotropic Form of Hooke's LawThomsen's Notation for Weak Elastic AnisotropyStress-Induced Anisotropy in RocksStrain Components and Equations of Motion in Cylindrical andSpherical Coordinate Systems2.6 Deformation of Inclusions and Cavities in Elastic Solids2.7 Deformation of a Circular Hole - Borehole Stresses2.8 Mohr's Circles32344548PART 3: SEISMIC WAVE PROPAGATION513.13.25154Seismic VelocitiesPhase, Group, and Energy Velocities
ViC O N T E N T S3.3 Impedance, Reflectivity, and Transmissivity3.4 Reflectivity and AVO3.5 AVOZ in Anisotropic Environments3.6 Viscoelasticity and Q3.7 " Kramers-Kronig Relations Between Velocity Dispersionand Q3.8 Waves in Layered Media: Full-Waveform Synthetic Seismograms3.9 Waves in Layered Media: Stratigraphic Filtering andVelocity Dispersion3.10 Waves in Layered Media: Frequency-Dependent Anisotropyand Dispersion3.11 Scale-Dependent Seismic Velocities in Heterogeneous Media3.12 Scattering Attenuation3.13 Waves in Cylindrical Rods - The Resonant Bar869195100PART 4 : E F F E C T I V E M E D I 12114115117121123129133140142Hashin-Shtrikman Bounds 'Voigt and Reuss BoundsWood's FormulaHill Average Moduli EstimateComposite with Uniform Shear ModulusRock and Pore Compressibilities and Some PitfallsKuster and Toksoz Formulation for Effective ModuliSelf-Consistent Approximations of Effective ModuliDifferential Effective Medium ModelHudson's Model for Cracked Media Eshelby-Cheng Model for Cracked Anisotropic MediaElastic Constants in Finely Layered Media - Backus Average57606570757782PART 5 : G R A N U L A R M E D I A1475.1 Packing of Spheres - Geometric Relations5.2 Random Spherical Grain Packings - Contact Models and EffectiveModuli5.3 Ordered Spherical Grain Packings - Effective Moduli147149160PART 6 : F L U I D E F F E C T S ONWAVE PROPAGATION1626.16.26.36.4162166168177Biot's Velocity RelationsGeertsma-Smit Approximations of Biot's RelationsGassmann's RelationsBAM - Marion's Bounding Average Method
C O N T E N T S6.56.66.76.86.96.106.116.126.136.146.15Fluid Substitution in Anisotropic Rocks: Brown andKorringa's RelationsGeneralized Gassmann's Equations for Composite Porous MediaMavko-Jizba Squirt RelationsExtension of Mavko-Jizba Squirt Relations for All FrequenciesBISQAnisotropic SquirtCommon Features of Fluid-Related Velocity Dispersion MechanismsPartial and Multiphase SaturationsPartial Saturation: White and Dutta-Ode Model for VelocityDispersion and AttenuationWaves in Pure Viscous FluidPhysical Properties of Gases and FluidsPART 7 : E M P I R I C A L R E L A T I O N S7.1 Velocity-Porosity Models: Critical Porosity and Nur's ModifiedVoigt Average.7.2 Velocity-Porosity Models: Geertsma's Empirical Relationsfor Compressibility7.3 Velocity-Porosity Models: Wyllie's Time Average Equation7.4 Velocity-Porosity Models: Raymer-Hunt-Gardner Relations7.5 Velocity-Porosity-Clay Models: Han's Empirical Relations forShaley Sandstones7.6 Velocity-Porosity-Clay Models: Tosaya's Empirical Relations forShaley Sandstones7.7 Velocity-Porosity-Clay Models: Castagna's Empirical Relationsfor Velocities7.8 Vp-Vs Relations7.9 Velocity-Density 5226228231233234235250PART 8 : FLOW A N D D I F F U S I O -Carman Relation for FlowViscous FlowCapillary ForcesDiffusion and Filtration - Special CasesPART 9 : E L E C T R I C A L P R O P E R T I E S2719.19.29.39.4271275279282Bounds and Effective Medium ModelsVelocity Dispersion and AttenuationEmpirical RelationsElectrical Conductivity in Porous RocksVii
ViiiCONTENTSPART 1 0 : APPENDIXES28910.1 Typical Rock Properties10.2 Conversions10.3 Moduli and Density of Common Minerals289304306ReferencesIndex313325
THE ROCK PHYSICS HANDBOOK . CAMBRIDGE UNIVERSITY PRESS. CONTENTS Preface page ix PART 1: BASIC TOOLS 1 1.1 The Fourier Transform 1 1.2 The Hilbert Transform and Analytic Signal 8 1.3 Statistics and Linear Regression 10 1.4 Coordinate Transformations 14 PART 2: ELASTICITY AND HOOKE'S LAW 17
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