Note: Cover -- Half-title -- Title -- Copyright -- Contents -- Preface to the Second Edition -- 1 Basic tools -- 1.1 The Fourier transform -- Synopsis -- Evenness and oddness -- Convolution theorem -- Energy spectrum -- Phase spectrum -- Sampling theorem -- Numerical details -- Spectral estimation and windowing -- Fourier transform theorems -- 1.2 The Hilbert transform and analytic signal -- Synopsis -- Causality -- 1.3 Statistics and probability -- Synopsis -- Regression -- Variogram and covariance function -- Distributions -- Monte Carlo simulations -- Bootstrap -- Statistical classification -- 1.4 Coordinate transformations -- Synopsis -- Assumptions and limitations -- 2 Elasticity and Hookes law -- 2.1 Elastic moduli isotropic form of Hookes law -- Synopsis -- Assumptions and limitations -- 2.2 Anisotropic form of Hookes law -- Synopsis -- Voigt notation -- Voigt stiffness matrix structure for common anisotropy classes -- Isotropic: two independent constants -- Cubic: three independent constants -- Hexagonal or transversely isotropic: five independent constants -- Orthorhombic: nine independent constants -- Monoclinic: 13 independent constants -- Phase velocities for several elastic symmetry classes -- Kelvin notation -- Elastic eigentensors and eigenvalues -- Poissons ratio defined for anisotropic elastic materials -- Assumptions and limitations -- 2.3 Thomsens notation for weak elastic anisotropy -- Synopsis -- Uses -- Assumptions and limitations -- 2.4 Tsvankin's extended Thomsen parameters for orthorhombic media -- Uses -- Assumptions and limitations -- 2.5 Third-order nonlinear elasticity -- Synopsis -- Uses -- Assumptions and limitations -- 2.6 Effective stress properties of rocks -- Synopsis -- Uses -- Assumptions and limitations -- 2.7 Stress-induced anisotropy in rocks -- Synopsis -- Uses -- Assumptions and limitations. , 2.8 Strain components and equations of motion in cylindrical and spherical coordinate systems -- Synopsis -- Uses -- Assumptions and limitations -- 2.9 Deformation of inclusions and cavities in elastic solids -- Synopsis -- General pore deformation -- Effective dry compressibility -- Stress-induced pore pressure: Skempton's coefficient -- Saturated stress-induced pore-volume change -- Low-frequency saturated compressibility -- Three-dimensional ellipsoidal cavities -- Spherical cavity -- Penny-shaped crack: oblate spheroid -- Needle-shaped pore: prolate spheroid -- Two-dimensional tubes -- Plane strain -- Two-dimensional thin cracks -- Ellipsoidal cracks of finite thickness -- Deformation of spherical shells -- Uses -- Assumptions and limitations -- 2.10 Deformation of a circular hole: borehole stresses -- Synopsis -- Hollow cylinder with internal and external pressures -- Circular hole with principal stresses at infinity -- Stress concentration around an elliptical hole -- Stress around an inclined cylindrical hole -- Stress around a vertical cylindrical hole in a poroelastic medium -- Uses -- Assumptions and limitations -- Extensions -- 2.11 Mohr's circles -- Synopsis -- Three-dimensional Mohr's circle -- Two-dimensional Mohr's circle -- Uses -- 2.12 Static and dynamic moduli -- Assumptions and limitations -- 3 Seismic wave propagation -- 3.1 Seismic velocities -- Synopsis -- Assumptions and limitations -- 3.2 Phase, group, and energy velocities -- Synopsis -- Assumptions and limitations -- 3.3 NMO in isotropic and anisotropic media -- Synopsis -- NMO in an anisotropic Earth -- VTI symmetry with horizontal reflector -- Vertical symmetry axis with dipping reflector -- Tilted TI symmetry with dipping reflector -- Orthorhombic symmetry with horizontal reflector -- NMO in a horizontally layered anisotropic Earth -- Synopsis. , 3.4 Impedance, reflectivity, and transmissivity -- Synopsis -- Simple band-limited inverse of reflectivity time series -- Rough surfaces -- Uses -- Assumptions and limitations -- 3.5 Reflectivity and amplitude variations with offset (AVO) in isotropic media -- Synopsis -- AVO: amplitude variations with offset -- Approximate forms -- Assumptions and limitations -- 3.6 Plane-wave reflectivity in anisotropic media -- Synopsis -- Transversely isotropic media: VTI -- Transversely isotropic media: HTI -- Orthorhombic media -- Arbitrary anisotropy -- Assumptions and limitations -- 3.7 Elastic impedance -- Elastic impedance expressions: isotropic -- Elastic impedance expressions: VTI anisotropic -- Elastic impedance expressions: orthorhombic x1-x3 symmetry plane -- Elastic impedance expressions: orthorhombic x2-x3 symmetry plane -- Uses -- Assumptions and limitations -- 3.8 Viscoelasticity and Q -- Synopsis -- Uses -- Assumptions and limitations -- 3.9 Kramers-Kronig relations between velocity dispersion and Q -- Synopsis -- Uses -- Assumptions and limitations -- 3.10 Waves in layered media: full-waveform synthetic seismograms -- Synopsis -- Uses -- Assumptions and limitations -- 3.11 Waves in layered media: stratigraphic filtering and velocity dispersion -- Synopsis -- Uses -- Assumptions and limitations -- 3.12 Waves in layered media: frequency-dependent anisotropy, dispersion, and attenuation -- Synopsis -- One-dimensional layered poroelastic medium -- Uses -- Assumptions and limitations -- 3.13 Scale-dependent seismic velocities in heterogeneous media -- Synopsis -- Layered (one-dimensional) media -- Uses -- Assumptions and limitations -- 3.14 Scattering attenuation -- Synopsis -- Uses -- Assumptions and limitations -- 3.15 Waves in cylindrical rods: the resonant bar -- Synopsis -- Torsional waves -- Longitudinal waves -- Flexural waves -- Bar resonance. , Porous, fluid-saturated rods -- Uses -- Assumptions and limitations -- 3.16 Waves in boreholes -- Synopsis -- Isotropic elastic formation -- Transversely isotropic (TI) elastic formation -- Isotropic, poroelastic, permeable formation -- Uses -- Assumptions and limitations -- Extensions -- 4 Effective elastic media: bounds and mixing laws -- 4.1 Hashin-Shtrikman-Walpole bounds -- Synopsis -- Uses -- Assumptions and limitations -- 4.2 Voigt and Reuss bounds -- Synopsis -- Uses -- Assumptions and limitations -- 4.3 Woods formula -- Synopsis -- Uses -- Assumptions and limitations -- 4.4 Voigt-Reuss-Hill average moduli estimate -- Synopsis -- Uses -- Assumptions and limitations -- 4.5 Composite with uniform shear modulus -- Synopsis -- Uses -- Assumptions and limitations -- 4.6 Rock and pore compressibilities and some pitfalls -- Synopsis -- More on dry-rock compressibility -- Assumptions and limitations -- 4.7 Kuster and Toksöz formulation for effective moduli -- Synopsis -- Assumptions and limitations -- 4.8 Self-consistent approximations of effective moduli -- Synopsis -- Assumptions and limitations -- 4.9 Differential effective medium model -- Synopsis -- Modified DEM with critical porosity constraints -- Uses -- Assumptions and limitations -- 4.10 Hudson's model for cracked media -- Synopsis -- Special cases of crack distributions -- Heavily faulted structures -- Uses -- Assumptions and limitations -- 4.11 Eshelby-Cheng model for cracked anisotropic media -- Synopsis -- Uses -- Assumptions and limitations -- Extensions -- 4.12 T-matrix inclusion models for effective moduli -- Synopsis -- Uses -- Assumptions and limitations -- 4.13 Elastic constants in finely layered media: Backus average -- Synopsis -- Uses -- Assumptions and limitations -- 4.14 Elastic constants in finely layered media: general layer anisotropy -- 4.15 Poroelastic Backus average. , Synopsis -- Uses -- Assumptions and limitations -- 4.16 Seismic response to fractures -- Synopsis -- Quasi-static fracture compliance -- Dynamic response -- Use -- Assumptions and limitations -- 4.17 Bound-filling models -- Synopsis -- Uses -- Assumptions and limitations -- 5 Granular media -- 5.1 Packing and sorting of spheres -- Synopsis -- Packings of identical spheres -- Porosity -- Coordination number -- Binary mixtures of spheres -- Other practical parameters affecting packing -- Uses -- Assumptions and limitations -- 5.2 Thomas-Stieber model for sand-shale systems -- Synopsis -- Assumptions and limitations -- Extensions -- 5.3 Particle size and sorting -- Synopsis -- Particle size -- Sorting -- 5.4 Random spherical grain packings: contact models and effective moduli -- Synopsis -- Contact stiffnesses and effective moduli -- The Hertz-Mindlin Model -- The Walton model -- The Digby model -- The Jenkins et al. model -- The Brandt model -- The Johnson et al. model -- The cemented-sand model -- The uncemented (soft) sand model -- The stiff-sand and intermediate stiff-sand models -- Caveat on the use of effective medium models for granular media -- Uses -- Assumptions and limitations -- Extensions -- 5.5 Ordered spherical grain packings: effective moduli -- Synopsis -- Simple cubic packing -- Hexagonal close packing -- Face-centered cubic packing -- Uses -- Assumptions and limitations -- 6 Fluid effects on wave propagation -- 6.1 Biots velocity relations -- Synopsis -- Slow S-wave -- Uses -- Assumptions and limitations -- Extensions -- 6.2 Geertsma-Smit approximations of Biots relations -- Synopsis -- Uses -- Assumptions and limitations -- 6.3 Gassmann's relations: isotropic form -- Synopsis -- Compressibility form -- Reuss average form -- Linear form -- P-wave modulus form -- Velocity form -- Pore stiffness interpretation -- Biot coefficient. , VP but no VS.

Note: Cover -- Title Page -- Copyright Page -- Contents -- Preface -- Acknowledgments -- Chapter 1 Review of Probability and Statistics -- 1.1 Introduction to Probability and Statistics -- 1.2 Probability -- 1.3 Statistics -- 1.3.1 Univariate Distributions -- 1.3.2 Multivariate Distributions -- 1.4 Probability Distributions -- 1.4.1 Bernoulli Distribution -- 1.4.2 Uniform Distribution -- 1.4.3 Gaussian Distribution -- 1.4.4 Log-Gaussian Distribution -- 1.4.5 Gaussian Mixture Distribution -- 1.4.6 Beta Distribution -- 1.5 Functions of Random Variable -- 1.6 Inverse Theory -- 1.7 Bayesian Inversion -- Chapter 2 Rock Physics Models -- 2.1 Rock Physics Relations -- 2.1.1 Porosity - Velocity Relations -- 2.1.2 Porosity - Clay Volume - Velocity Relations -- 2.1.3 P-Wave and S-Wave Velocity Relations -- 2.1.4 Velocity and Density -- 2.2 Effective Media -- 2.2.1 Solid Phase -- 2.2.2 Fluid Phase -- 2.3 Critical Porosity Concept -- 2.4 Granular Media Models -- 2.5 Inclusion Models -- 2.6 Gassmann's Equations and Fluid Substitution -- 2.7 Other Rock Physics Relations -- 2.8 Application -- Chapter 3 Geostatistics for Continuous Properties -- 3.1 Introduction to Spatial Correlation -- 3.2 Spatial Correlation Functions -- 3.3 Spatial Interpolation -- 3.4 Kriging -- 3.4.1 Simple Kriging -- 3.4.2 Data Configuration -- 3.4.3 Ordinary Kriging and Universal Kriging -- 3.4.4 Cokriging -- 3.5 Sequential Simulations -- 3.5.1 Sequential Gaussian Simulation -- 3.5.2 Sequential Gaussian Co-Simulation -- 3.6 Other Simulation Methods -- 3.7 Application -- Chapter 4 Geostatistics for Discrete Properties -- 4.1 Indicator Kriging -- 4.2 Sequential Indicator Simulation -- 4.3 Truncated Gaussian Simulation -- 4.4 Markov Chain Models -- 4.5 Multiple-Point Statistics -- 4.6 Application -- Chapter 5 Seismic and Petrophysical Inversion -- 5.1 Seismic Modeling -- 5.2 Bayesian Inversion. , 5.3 Bayesian Linearized AVO Inversion -- 5.3.1 Forward Model -- 5.3.2 Inverse Problem -- 5.4 Bayesian Rock Physics Inversion -- 5.4.1 Linear - Gaussian Case -- 5.4.2 Linear - Gaussian Mixture Case -- 5.4.3 Non-linear - Gaussian Mixture Case -- 5.4.4 Non-linear - Non-parametric Case -- 5.5 Uncertainty Propagation -- 5.6 Geostatistical Inversion -- 5.6.1 Markov Chain Monte Carlo Methods -- 5.6.2 Ensemble Smoother Method -- 5.6.3 Gradual Deformation Method -- 5.7 Other Stochastic Methods -- Chapter 6 Seismic Facies Inversion -- 6.1 Bayesian Classification -- 6.2 Bayesian Markov Chain Gaussian Mixture Inversion -- 6.3 Multimodal Markov Chain Monte Carlo Inversion -- 6.4 Probability Perturbation Method -- 6.5 Other Stochastic Methods -- Chapter 7 Integrated Methods -- 7.1 Sources of Uncertainty -- 7.2 Time-Lapse Seismic Inversion -- 7.3 Electromagnetic Inversion -- 7.4 History Matching -- 7.5 Value of Information -- Chapter 8 Case Studies -- 8.1 Hydrocarbon Reservoir Studies -- 8.1.1 Bayesian Linearized Inversion -- 8.1.2 Ensemble Smoother Inversion -- 8.1.3 Multimodal Markov Chain Monte Carlo Inversion -- 8.2 CO2 Sequestration Study -- Appendix: MATLAB Codes -- A.1 Rock Physics Modeling -- A.2 Geostatistical Modeling -- A.3 Inverse Modeling -- A.3.1 Seismic Inversion -- A.3.2 Petrophysical Inversion -- A.3.3 Ensemble Smoother Inversion -- A.4 Facies Modeling -- References -- Index -- EULA.

Note: Cover -- Half-title -- Title page -- Copyright information -- Table of contents -- Preface -- Acknowledgments -- 1 Introduction -- 1.1 What is the value of information? -- 1.2 Motivating examples from the Earth sciences -- 1.3 Contributions of this book -- 1.4 Organization -- 1.5 Intended audience and prerequisites -- 1.6 Bibliographic notes -- 2 Statistical models and methods -- 2.1 Uncertainty quantification, information gathering, and data examples -- 2.2 Notation and probability models -- 2.2.1 Univariate probability distributions -- 2.2.2 Multivariate probability distributions -- 2.3 Conditional probability, graphical models, and Bayes' rule -- 2.3.1 Conditional probability -- 2.3.2 Graphical models -- 2.3.3 Bayesian updating from data -- 2.3.4 Examples -- Treasure Island: The pirate example -- Gotta get myself connected: Bayesian network example -- Never break the chain: Markov chain example -- For whom the bell tolls: Gaussian projects example -- 2.4 Inference of model parameters -- 2.4.1 Maximum likelihood estimation -- 2.4.2 Examples -- I love rock and ore: mining oxide grade example -- Never break the chain: Markov chain example -- 2.5 Monte Carlo methods and other approximation techniques -- 2.5.1 Analysis by simulation -- 2.5.2 Solving integrals -- 2.5.3 Sampling methods -- 2.5.4 Example -- Risky business: petroleum prospect risking example -- 2.6 Bibliographic notes -- Models -- Estimation and sampling -- 3 Decision analysis -- 3.1 Background -- 3.2 Decision situations: terminology and notation -- 3.2.1 Decisions, uncertainties, and values -- 3.2.2 Utilities and certain equivalent -- 3.2.3 Maximizing expected utility -- 3.2.4 Examples -- Treasure island: the pirate example -- For whom the bell tolls: Gaussian projects example -- 3.3 Graphical models -- 3.3.1 Decision trees -- 3.3.2 Influence diagrams -- 3.3.3 Examples. , For whom the bell tolls: Gaussian projects example -- MacKenna's gold: oil and gold example -- Time after time: time-lapse seismic example -- Value from 4-D seismic monitoring -- Influence diagrams for 4-D seismic monitoring -- Observable property nodes -- Reservoir property nodes -- Seismic property nodes -- 3.4 Value of information -- 3.4.1 Definition -- 3.4.2 Perfect versus imperfect information -- 3.4.3 Relevant, material, and economic information -- 3.4.4 Examples -- Treasure island: the pirate example -- For whom the bell tolls: Gaussian projects example -- 3.5 Bibliographic notes -- Decision analysis fundamentals -- Graphical models -- VOI fundamentals -- VOI for canonical problems -- Computational issues and application reviews -- 4 Spatial modeling -- 4.1 Goals of stochastic modeling of spatial processes -- 4.2 Random fields, variograms, and covariance -- 4.3 Prediction and simulation -- 4.3.1 Spatial prediction and Kriging -- 4.3.2 Common geostatistical stochastic simulation methods -- 4.4 Gaussian models -- 4.4.1 The spatial regression model -- 4.4.2 Optimal spatial prediction: Kriging -- 4.4.3 Multivariate hierarchical spatial regression model -- 4.4.4 Examples -- Norwegian wood: forestry example -- I love rock and ore: mining oxide grade example -- 4.5 Non-Gaussian response models and hierarchical spatial models -- 4.5.1 Skew-normal models -- 4.5.2 Spatial generalized linear models -- 4.5.3 Example -- We will rock you: rock hazard example -- 4.6 Categorical spatial models -- 4.6.1 Indicator random variables -- 4.6.2 Truncated Gaussian and pluri-Gaussian models -- 4.6.3 Categorical Markov random field models -- 4.6.4 Example -- Black gold in a white plight: reservoir characterization example -- 4.7 Multiple-point geostatistics -- 4.7.1 Algorithms -- 4.7.2 Example -- Go with the flow: petroleum simulation example -- 4.8 Bibliographic notes. , Traditional geostatistics books describing variogram methods, Kriging, and simulation -- Sequential simulation techniques and related topics -- Spatial statistics -- Non-Gaussian response models -- Markov random fields -- Multiple-point geostatistics -- Spatiotemporal models -- 5 Value of information in spatial decision situations -- 5.1 Introduction -- 5.1.1 Spatial decision situations -- 5.1.2 Information gathering in spatial decision situations -- 5.1.3 Overview of models -- 5.2 Value of information: a formulation for static models -- 5.2.1 Prior value -- 5.2.2 Posterior value -- Perfect information -- Imperfect information -- 5.2.3 Special cases: an overview -- 5.3 Special case: low decision flexibility and decoupled value -- 5.3.1 Prior value -- 5.3.2 Posterior value -- 5.3.3 Computational notes -- 5.3.4 Example -- Norwegian wood: forestry example -- Framing the decision situation -- Information gathering -- Modeling -- VOI analysis -- 5.4 Special case: high decision flexibility and decoupled value -- 5.4.1 Prior value -- 5.4.2 Posterior value -- 5.4.3 Computational notes -- 5.4.4 Examples -- Never break the chain: Markov chain example -- Framing the decision situation -- Information gathering -- Modeling -- VOI analysis -- The tree amigos: conservation biology example -- Framing the decision situation -- Information gathering -- Modeling -- VOI analysis -- Norwegian wood: forestry example -- Framing the decision situation -- Information gathering -- Modeling -- VOI analysis -- 5.5 Special case: low decision flexibility and coupled value -- 5.5.1 Prior value -- 5.5.2 Posterior value -- 5.5.3 Computational notes -- 5.5.4 Example -- Go with the flow: petroleum simulation example -- Framing the decision situation -- Information gathering -- Modeling -- VOI analysis -- 5.6 Special case: high decision flexibility and coupled value. , 5.6.1 Prior value -- 5.6.2 Posterior value -- 5.6.3 Computational notes -- 5.6.4 Example -- Frozen: hydropower example -- Framing the decision situation -- Information gathering -- Modeling -- VOI analysis -- 5.7 More complex decision situations -- 5.7.1 Generalized risk preferences -- 5.7.2 Additional constraints -- The tree amigos: conservation biology example -- 5.7.3 Sequential decision situations -- Gotta get myself connected: Bayesian network example -- 5.8 Sequential information gathering -- For whom the bell tolls: Gaussian projects example -- 5.9 Other information measures -- 5.9.1 Entropy -- 5.9.2 Prediction variance -- Norwegian wood: forestry example -- 5.9.3 Prediction error -- The tree amigos: conservation biology example -- 5.10 Bibliographic notes -- Low decision flexibility and decoupled value -- Low decision flexibility and coupled value -- High decision flexibility and decoupled value -- High decision flexibility and coupled value -- More complex decision situations -- Other information measures -- 6 Earth sciences applications -- 6.1 Workflow -- 6.2 Exploration of petroleum prospects -- 6.2.1 Gotta get myself connected: Bayesian network example -- Framing the decision situation -- Information gathering -- Modeling -- VOI analysis -- 6.2.2 Basin street blues: basin modeling example -- Framing the decision situation -- Information gathering -- Modeling -- VOI analysis -- 6.2.3 Risky business: petroleum prospect risking example -- Framing the decision situation -- Information gathering -- Modeling -- VOI analysis -- 6.3 Reservoir characterization from geophysical data -- 6.3.1 Black gold in a white plight: reservoir characterization example -- Framing the decision situation -- Information gathering -- Modeling -- VOI analysis -- 6.3.2 Reservoir dogs: seismic and electromagnetic data example -- Framing the decision situation. , Information gathering -- Modeling -- VOI analysis -- 6.4 Mine planning and safety -- 6.4.1 I love rock and ore: mining oxide grade example -- Framing the decision situation -- Information gathering -- Modeling -- VOI analysis -- 6.4.2 We will rock you: rock hazard example -- Framing the decision situation -- Information gathering -- Modeling -- VOI analysis -- 6.5 Groundwater management -- 6.5.1 Salt water wells in my eyes: groundwater management example -- Framing the decision situation -- Information gathering -- Modeling -- VOI analysis -- 6.6 Bibliographic notes -- Petroleum -- Mining planning and safety -- Groundwater, hydrology, and geothermal resources -- Environmental applications -- Biological conservation, forestry, and fishing -- Agriculture and climate forecasting -- 7 Problems and projects -- 7.1 Problems and tutorial hands-on projects -- 7.1.1 Problem sets -- 7.1.2 Hands-on projects -- The tree amigos: conservation biology example -- Part I: parameter specification -- Part II: value of information -- Go with the flow: petroleum simulation example -- Part I: downloading realization outputs -- Part II: generate realizations from geologic scenario -- Part III: VOI analysis using approximate Bayesian computing -- Frozen: hydropower example -- Time after time: time-lapse seismic example -- Norwegian wood: forestry example -- Part I: parameter estimation and Kriging -- Part II: VOI analysis and spatial design -- 7.2 Hands on: exploration of petroleum prospects -- 7.2.1 Gotta get myself connected: Bayesian network example -- Part I: small network -- Part II: North Sea network with 25 segments -- 7.2.2 Basin street blues: basin modeling example -- 7.2.3 Risky business: petroleum prospect risking example -- 7.3 Hands on: reservoir characterization from geophysical data -- 7.3.1 Black gold in a white plight: reservoir characterization example. , Part I: modeling and prediction from seismic amplitude versus offset data.

Note: Literaturverz. S. 313 - 324