Rock Physics Handbook, First Edition, 1998
The Rock Physics Handbook, First Edition, 1998
Gary Mavko,
Tapan Mukerji, and
Jack Dvorkin
Rock Physics Laboratory
Stanford University
The Rock Physics Handbook is published by
Cambridge University Press.
Second Edition, 2009
Table of Contents | Errata
Over the last three decades enormous strides have been made to understand
the connections between physical properties of rocks and geophysical
observables -- the science now known as Rock Physics. Scientists have
discovered an increasing amount of order in relations that
once appeared disappointingly scattered, such as seismic wave velocity
versus porosity, porosity versus permeabiity, velocity versus fluid
saturation and lithology. The Rock Physics Handbook conveniently brings
together the theoretical and
empirical relations that form the foundations of rock physics, with particular
emphasis on seismic properties. It also includes commonly used models and
relations for electrical and dielectric rock properties.
76 stand-alone articles concisely summarize a wide range of topics, including wave
propagation, AVO-AVOZ, effective media, poroelasticity, pore fluid flow
and diffusion. The book contains overviews of dispersion mechanisms, fluid
substitution, and Vp-Vs relations. Useful empirical results on reservoir
rocks and sediments, granular media, tables of mineral data, and an atlas
of reservoir rock properties complete the text.
This distillation of an otherwise scattered and eclectic mass of knowledge is
presented in a form that can be immediately applied to solve real
problems. Geophysics professionals, researchers and students as well as
petroleum engineers, well log analysists, and environmental geoscientists
will value the Rock Physics Handbook as a resource for practical
problem solving.
When we wrote the Rock Physics Handbook, we focused on collecting useful
equations -- those relations that we derive once every two years and then
forget, or find
ourselves searching for in piles of articles, or somewhere in that shelf of books, or on
scraps of paper taped to the side of the filing cabinet.
Our approach was to present results, with a few of the key assumptions and limitations,
and almost never any derivations. Our intention was to create a reference, and not a
textbook. We assume that the reader will be generally aware of the various topics, and if
not, we provide a few references to the more complete descriptions in books and journals.
The Rock Physics Handbook is presented as 76 stand-alone articles. We wanted the user
to be able to go directly to the topic of interest and to find all of the necessary information
within a few pages, without the need to refer to previous chapters, as in a conventional
textbook. As a result, there is an occasional redundancy in the explanatory text.
We wish to thank the faculty, students, and industrial affiliates of the
Stanford Rock
Physics and Borehole Geophysics (SRB) project for many valuable
comments and
insights. We found particularly useful discussions with Zhijing Wang, Thierry Cadoret,
Ivar Brevik, Sue Raikes, Sverre Strandenes, Mike Batzle, and Jim Berryman. Li Teng
contributed the chapter on anisotropic AVOZ, and Ran Bachrach contributed to the
chapter on dielectric rock properties. Ranie Lynds helped with the graphics and
did a marvelous job of proofing and editing. Thanks to Barbara Mavko for many useful
comments on content and style. And as always, we are indebted to
Amos Nur whose
work, past and present, has helped to make the field of Rock Physics what it is today.
We hope you find this handbook useful.
Table of Contents
- Part 1: Basic Tools
- 1.1 The Fourier Transform
- 1.2 The Hilbert Transform and Analytic Signal
- 1.3 Statistics and Linear Regression
- 1.4 Coordinate Transformations
- Part 2: Elasticity and Hooke's Law
- 2.1 Elastic Moduli -- Isotropic Form of Hooke's Law
- 2.2 Anisotropic Form of Hooke's Law
- 2.3 Thomsen's Notation for Weak Elastic Anisotropy
- 2.4 Stress-Induced Anisotropy in Rocks
- 2.5 Strain Components and Equations of Motion in Cylindrical and Spherical
Coordinate Systems
- 2.6 Deformation of Inclusions and Cavities in Elastic Solids
- 2.7 Deformation of a Circular Hole -- Borehole Stresses
- 2.8 Mohr's Circles
- Part 3: Seismic Wave Propagation
- 3.1 Seismic Velocities
- 3.2 Phase, Group, and Energy Velocities
- 3.3 Impedance, Reflectivity, and Transmissivity
- 3.4 Reflectivity and AVO
- 3.5 AVOZ in Anisotropic Environments
- 3.6 Viscoelasticity and Q
- 3.7 Kramers-Kronig Relations Between Velocity Dispersion and Q
- 3.8 Waves in Layered Media: Full Waveform Synthetic Seismograms
- 3.9 Waves in Layered Media: Stratigraphic Filtering and Velocity Dispersion
- 3.10 Waves in Layered Media: Frequency Dependent Anisotropy and
Dispersion
- 3.11 Scale-dependent Seismic Velocities in Heterogeneous Media
- 3.12 Scattering Attenuation
- 3.13 Waves in Cylindrical Rods -- The Resonant Bar
- Part 4: Effective Media
- 4.1 Hashin-Shtrikman Bounds
- 4.2 Voigt and Reuss Bounds
- 4.3 Wood's Formula
- 4.4 Hill Average Moduli Estimate
- 4.5 Composite with Uniform Shear Modulus
- 4.6 Rock and Pore Compressibilities and Some Pitfalls
- 4.7 Kuster Toksoz Formulation for Effective Moduli
- 4.8 Self-Consistent Approximations of Effective Moduli
- 4.9 Differential Effective Medium Model
- 4.10 Hudson's Model for Cracked Media
- 4.11 Eshelby-Cheng Model for Cracked Anisotropic Media
- 4.12 Elastic Constants in Finely Layered Media -- Backus Average
- Part 5: Granular Media
- 5.1 Packing of Spheres -- Geometric Relations
- 5.2 Random Spherical Grain Packings -- Contact Models and Effective Moduli
- 5.3 Ordered Spherical Grain Packings -- Effective Moduli
- Part 6: Fluid Effects on Wave Propagation
- 6.1 Biot's Velocity Relations
- 6.2 Geertsma-Smit Approximations of Biot's Relations
- 6.3 Gassmann's Relations
- 6.4 BAM -- Marion's Bounding Average Method
- 6.5 Fluid Substitution in Anisotropic Rocks: Brown and Korringa's Relations
- 6.6 Generalized Gassmann's Equations for Composite Porous Media
- 6.7 Mavko-Jizba Squirt Relations
- 6.8 Extension of Mavko-Jizba Squirt Relations for All Frequencies
- 6.9 BISQ
- 6.10 Anisotropic Squirt
- 6.11 Common Features of Fluid-Related Velocity Dispersion Mechanisms
- 6.12 Partial and Multi-Phase Saturations
- 6.13 Partial Saturation: White and Dutta-Ode Model for Velocity Dispersion and Attenuation
- 6.14 Waves in Pure Viscous Fluid
- 6.15 Physical Properties of Gases and Fluids
- Part 7: Empirical Relations
- 7.1 Velocity-Porosity Models: Critical Porosity and Nur's Modified Voigt Average
- 7.2 Velocity-Porosity Models: Geertsma's Empirical Relations for
Compressibility
- 7.3 Velocity-Porosity Models: Wyllie's Time Average Equation
- 7.4 Velocity-Porosity Models: Raymer-Hunt-Gardner Relations
- 7.5 Velocity-Porosity-Clay Models: Han's Empirical Relations for Shaly
Sandstones
- 7.6 Velocity-Porosity-Clay Models: Tosaya's Empirical Relations for Shaly
Sandstones
- 7.7 Velocity-Porosity-Clay Models: Castagna's Empirical Relations for
Velocities
- 7.8 Vp-Vs Relations
- 7.9 Velocity-Density Relations
- Part 8: Flow and Diffusion
- 8.1 Darcy's Law
- 8.2 Kozeny-Carman Relation for Flow
- 8.3 Viscous Flow
- 8.4 Capillary Forces
- 8.5 Diffusion and Filtration -- Special Cases
- Part 9: Electrical Properties
- 9.1 Electrical Properties: Bounds and Effective Medium Models
- 9.2 Electrical Properties: Velocity Dispersion and Attenuation
- 9.3 Electrical Properties: Empirical Relations
- 9.4 Electrical Conductivity in Porous Rocks
- Part 10: Appendices
- 10.1 Typical Rock Properties
- 10.2 Conversions
- 10.3 Moduli and Density of Common Minerals
- Index
Errata for the 1st Edition (1998) of the Rock Physics Handbook
Thanks to careful readers, we have identified the following errors. Please
let us know if you find any more errors.
- Page 219: Physical Properties of Gases and Fluids
The equation for Bo should have ...+T+17.8 within the brackets and not
...+T+1.78. This correction also applies to the worked example on page 219.
- Pages 244-249: Empirical Relations
The section headings for "Greenberg-Castagna" (page 246), "Williams" (page 248),
and "Xu and White" (page 249) should be two levels higher. They are not meant
to be sub-sections within "Krief's Relation" but are separate sections by
themselves.
- Page 71: Viscoelasticity and Q
The third displayed equation for 1/Q from the bottom of the page should be
an approximate equality and not an exact equality.
- Page 155: Cemented Sand Model
Equation for C_tau, shoud have +10^(-4) as in Geophysics paper
Dvorkin & Nur 1996, not -10^(-4).
- Reference to J.G. Berryman, 1995 "A Handbook of
Physical Constants", AGU - the citation should read "Rock Physics &
Phase Relations: A Handbook of Physical Constants".
-
Section 7.1, top of page 222: It says: "In the suspension
domain, POR > POR_crit, the effective bulk and shear moduli can be
estimated quite accurately using by the Reuss (iso-stress) average".
Either the word "using" or the word "by" in this sentence needs to be
removed.
-
Section 7.8, page 245: It says that Beta = POR/POR_crit for
0<=POR<=POR_crit and that Beta = 1 for POR < POR_crit. The last inequality
is incorrect. It should be "... for POR > POR_crit".
-
Equation S=(3/2)(1-Phi)/d in the middle
of page 261 should be S=6(1-Phi)/d
-
Page 157: Typo in the denominator of the Geff calculation.
(3/6)*(9*2+8*6)/(2+2*3) = 2.625
Then Geff = 3.97
-
page 217, equation at the very bottom:
1/b = 0.306 - 7.6/M is right.
The one in RPH and Batzle-Wang equation (16) giving
b = 0.306 - 7.6/M is a typo.
-
NOT A TYPO!
Page 215, third line from the bottom: 1820S^2 should NOT be 820S^2
RPH is correct (1820 S^2).
820 S^2 in Batzle & Wang Geophysics paper is typo.
-
Page 70 eqn.2 last term should be 2*mu*epsilon_ij.
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Jack Dvorkin|
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