What is included with this book?
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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