| Edition |
2nd ed. |
| Description |
1 online resource |
| Physical Medium |
polychrome |
| Description |
text file |
| Summary |
"Making inferences about systems in the Earth's subsurface from remotely-sensed, sparse measurements is a challenging task. Geophysical inversion aims to find models which explain geophysical observations - a model-based inversion method attempts to infer model parameters by iteratively fitting observations with theoretical predictions from trial models. Global optimization often enables the solution of non-linear models, employing a global search approach to find the absolute minimum of an objective function, so that predicted data best fits the observations. This new edition provides an up-to-date overview of the most popular global optimization methods, including a detailed description of the theoretical development underlying each method, and a thorough explanation of the design, implementation, and limitations of algorithms. A new chapter provides details of recently-developed methods, such as the neighborhood algorithm, and particle swarm optimization. An expanded chapter on uncertainty estimation includes a succinct description on how to use optimization methods for model space exploration to characterize uncertainty, and now discusses other new methods such as hybrid Monte Carlo and multi-chain MCMC methods. Other chapters include new examples of applications, from uncertainty in climate modeling to whole earth studies. Several different examples of geophysical inversion, including joint inversion of disparate geophysical datasets, are provided to help readers design algorithms for their own applications. This is an authoritative and valuable text for researchers and graduate students in geophysics, inverse theory, and exploration geoscience, and an important resource for professionals working in engineering and petroleum exploration."-- Provided by publisher. |
| Bibliography |
Includes bibliographical references and index. |
| Contents |
Cover -- Global Optimization Methods in Geophysical Inversion -- Title -- Copyright -- Contents -- Preface to the first edition (1995) -- Preface to the second edition (2013) -- 1 Preliminary statistics -- 1.1 Random variables -- 1.2 Random numbers -- 1.3 Probability -- 1.4 Probability distribution, distribution function, and density function -- 1.4.1 Examples of distribution and density functions -- 1.4.1.1 Normal or Gaussian distribution -- 1.4.1.2 Cauchy distribution -- 1.4.1.3 Gibbs' distribution -- 1.5 Joint and marginal probability distributions -- 1.6 Mathematical expectation, moments, variances, and covariances -- 1.7 Conditional probability and Bayes' rule -- 1.8 Monte Carlo integration -- 1.9 Importance sampling -- 1.10 Stochastic processes -- 1.11 Markov chains -- 1.12 Homogeneous, inhomogeneous, irreducible, and aperiodic Markov chains -- 1.13 The limiting probability -- 2 Direct, linear, and iterative-linear inverse methods -- 2.1 Direct inversion methods -- 2.2 Model-based inversion methods -- 2.2.1 Linear/linearized methods -- 2.2.2 Iterative-linear or gradient-based methods -- 2.2.3 Enumerative or grid-search method -- 2.2.4 Monte Carlo method -- 2.2.4.1 Directed Monte Carlo methods -- 2.3 Linear/linearized inverse methods -- 2.3.1 Existence -- 2.3.2 Uniqueness -- 2.3.3 Stability -- 2.3.4 Robustness -- 2.4 Solution of linear inverse problems -- 2.4.1 Method of least squares -- 2.4.1.1 Maximum-likelihood methods -- 2.4.2 Stability and uniqueness -- singular-value-decomposition (SVD) analysis -- 2.4.3 Methods of constraining the solution -- 2.4.3.1 Positivity constraint -- 2.4.3.2 Prior model -- 2.4.3.3 Model smoothness -- 2.4.4 Uncertainty estimates -- 2.4.5 Regularization -- 2.4.5.1 Method for choosing the regularization parameter -- The L-curve -- Generalized cross-validation (GCV) method -- Morozov's discrepancy principle. |
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Engl's modified discrepancy principle -- 2.4.6 General Lp Norm -- 2.4.6.1 IRLS -- 2.4.6.2 Total variation regularization (TVR) -- 2.5 Iterative methods for non-linear problems: local optimization -- 2.5.1 Quadratic function -- 2.5.2 Newton's method -- 2.5.3 Steepest descent -- 2.5.4 Conjugate gradient -- 2.5.5 Gauss-Newton -- 2.6 Solution using probabilistic formulation -- 2.6.1 Linear case -- 2.6.2 Case of weak non-linearity -- 2.6.3 Quasi-linear case -- 2.6.4 Non-linear case -- 2.7 Summary -- 3 Monte Carlo methods -- 3.1 Enumerative or grid-search techniques -- 3.2 Monte Carlo inversion -- 3.3 Hybrid Monte Carlo-linear inversion -- 3.4 Directed Monte Carlo methods -- 4 Simulated annealing methods -- 4.1 Metropolis algorithm -- 4.1.1 Mathematical model and asymptotic convergence -- 4.1.1.1 Irreducibility -- 4.1.1.2 Aperiodicity -- 4.1.1.3 Limiting probability -- 4.2 Heat bath algorithm -- 4.2.1 Mathematical model and asymptotic convergence -- 4.2.1.1 Transition probability matrix -- 4.2.1.2 Irreducibility -- 4.2.1.3 Aperiodicity -- 4.2.1.4 Limiting probability -- 4.3 Simulated annealing without rejected moves -- 4.4 Fast simulated annealing (FSA) -- 4.5 Very fast simulated reannealing -- 4.6 Mean field annealing -- 4.6.1 Neurons and neural networks -- 4.6.2 Hopfield neural networks -- 4.6.3 Avoiding local minimum: SA -- 4.6.4 Mean field theory (MFT) -- 4.7 Using SA in geophysical inversion -- 4.7.1 Bayesian formulation -- 4.8 Summary -- 5 Genetic algorithms -- 5.1 A classical GA -- 5.1.1 Coding -- 5.1.2 Selection -- 5.1.2.1 Fitness-proportionate selection -- 5.1.2.2 Rank selection -- 5.1.2.3 Tournament selection -- 5.1.3 Crossover -- 5.1.4 Mutation -- 5.2 Schemata and the fundamental theorem of genetic algorithms -- 5.3 Problems -- 5.4 Combining elements of SA into a new GA -- 5.5 A mathematical model of a GA. |
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5.6 Multimodal fitness functions, genetic drift, GA with sharing, and repeat (parallel) GA -- 5.7 Uncertainty estimates -- 5.8 Evolutionary programming -- a variant of GA -- 5.9 Summary -- 6 Other stochastic optimization methods -- 6.1 The neighborhood algorithm (NA) -- 6.1.1 Voronoi diagrams -- 6.1.2 Voronoi diagrams in SA and GA -- 6.1.3 Neighborhood sampling algorithm -- 6.2 Particle swarm optimization (PSO) -- 6.3 Simultaneous perturbation stochastic approximation (SPSA) -- 7 Geophysical applications of simulated annealing and genetic algorithms -- 7.1 1D seismic waveform inversion -- 7.1.1 Application of heat bath SA -- 7.1.2 Application of GAs -- 7.1.3 Real-data examples -- 7.1.4 Hybrid GA/LI inversion using different measures of fitness -- 7.1.5 Hybrid VFSA inversion using different strategies -- 7.2 Prestack migration velocity estimation -- 7.2.1 1D earth structure -- 7.2.2 2D earth structure -- 7.2.3 Multiple and simultaneous VFSA for imaging -- 7.3 Inversion of resistivity sounding data for 1D earth models -- 7.3.1 Exact parameterization -- 7.3.2 Overparameterization with smoothing -- 7.4 Inversion of resistivity profiling data for 2D earth models -- 7.4.1 Inversion of synthetic data -- 7.4.2 Inversion of field data -- 7.5 Inversion of magnetotelluric sounding data for 1D earth models -- 7.6 Stochastic reservoir modeling -- 7.7 Seismic deconvolution by mean field annealing (MFA) and Hopfield network -- 7.7.1 Synthetic example -- 7.7.2 Real-data example -- 7.8 Joint inversion -- 7.8.1 Joint travel time and gravity inversion -- 7.8.2 Time-lapse (4D) seismic and well production joint inversion -- 8 Uncertainty estimation -- 8.1 Methods of numerical integration -- 8.1.1 Grid search or enumeration -- 8.1.2 Monte Carlo integration -- 8.1.3 Importance sampling -- 8.1.4 Multiple MAP estimation -- 8.2 Simulated annealing: the Gibbs sampler. |
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8.3 Genetic algorithm: the parallel Gibbs sampler -- 8.4 Numerical examples -- 8.4.1 Inversion of noisy synthetic vertical electric sounding data -- 8.4.2 Quantifying climate uncertainty -- 8.5 Hybrid Monte Carlo -- 8.5.1 Langevin MCMC -- 8.5.2 Hybrid or Hamiltonian Monte Carlo (HMC) -- 8.6 Summary -- Bibliography -- Index. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Geological modeling.
|
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Geological modeling. |
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Geophysics -- Mathematical models.
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Geophysics -- Mathematical models. |
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Geophysics. |
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Inverse problems (Differential equations)
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Inverse problems (Differential equations) |
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Mathematical optimization.
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Mathematical optimization. |
| Genre/Form |
Electronic books.
|
| Added Author |
Stoffa, Paul L., 1948-
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| Other Form: |
Print version: Sen, Mrinal K. Global optimization methods in geophysical inversion. 2nd ed. Cambridge : Cambridge University Press, 2013 9781107011908 (DLC) 2012033212 (OCoLC)812071260 |
| ISBN |
9781139625098 (electronic book) |
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1139625098 (electronic book) |
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9781139615792 |
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1139615793 |
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9780511997570 (electronic book) |
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0511997574 (electronic book) |
|
9781107011908 |
|
1107011906 |
|
