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Preface | p. xi |
Introduction | p. 1 |
The forward problem | p. 1 |
The inverse problem | p. 3 |
Examples of inverse problems | p. 6 |
Density of the Earth | p. 6 |
Acoustic tomography | p. 7 |
Steady-state 1D flow in porous media | p. 11 |
History matching in reservoir simulation | p. 18 |
Summary | p. 22 |
Estimation for linear inverse problems | p. 24 |
Characterization of discrete linear inverse problems | p. 25 |
Solutions of discrete linear inverse problems | p. 33 |
Singular value decomposition | p. 49 |
Backus and Gilbert method | p. 55 |
Probability and estimation | p. 67 |
Random variables | p. 69 |
Expected values | p. 73 |
Bayes' rule | p. 78 |
Descriptive geostatistics | p. 86 |
Geologic constraints | p. 86 |
Univariate distribution | p. 86 |
Multi-variate distribution | p. 91 |
Gaussian random variables | p. 97 |
Random processes in function spaces | p. 110 |
Data | p. 112 |
Production data | p. 112 |
Logs and core data | p. 119 |
Seismic data | p. 121 |
The maximum a posteriori estimate | p. 127 |
Conditional probability for linear problems | p. 127 |
Model resolution | p. 131 |
Doubly stochastic Gaussian random field | p. 137 |
Matrix inversion identities | p. 141 |
Optimization for nonlinear problems using sensitivities | p. 143 |
Shape of the objective function | p. 143 |
Minimization problems | p. 146 |
Newton-like methods | p. 149 |
Levenberg-Marquardt algorithm | p. 157 |
Convergence criteria | p. 163 |
Scaling | p. 167 |
Line search methods | p. 172 |
BFGS and LBFGS | p. 180 |
Computational examples | p. 192 |
Sensitivity coefficients | p. 200 |
The Frechet derivative | p. 200 |
Discrete parameters | p. 206 |
One-dimensional steady-state flow | p. 210 |
Adjoint methods applied to transient single-phase flow | p. 217 |
Adjoint equations | p. 223 |
Sensitivity calculation example | p. 228 |
Adjoint method for multi-phase flow | p. 232 |
Reparameterization | p. 249 |
Examples | p. 254 |
Evaluation of uncertainty with a posteriori covariance matrix | p. 261 |
Quantifying uncertainty | p. 269 |
Introduction to Monte Carlo methods | p. 270 |
Sampling based on experimental design | p. 274 |
Gaussian simulation | p. 286 |
General sampling algorithms | p. 301 |
Simulation methods based on minimization | p. 319 |
Conceptual model uncertainty | p. 334 |
Other approximate methods | p. 337 |
Comparison of uncertainty quantification methods | p. 340 |
Recursive methods | p. 347 |
Basic concepts of data assimilation | p. 347 |
Theoretical framework | p. 348 |
Kalman filter and extended Kalman filter | p. 350 |
The ensemble Kalman filter | p. 353 |
Application of EnKF to strongly nonlinear problems | p. 355 |
1D example with nonlinear dynamics and observation operator | p. 358 |
Example - geologic facies | p. 359 |
References | p. 367 |
Index | p. 378 |
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The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.
The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.