Global optimization methods in geophysical inversion /
"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 fi...
Clasificación: | Libro Electrónico |
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Autor principal: | |
Otros Autores: | |
Formato: | Electrónico eBook |
Idioma: | Inglés |
Publicado: |
Cambridge :
Cambridge University Press,
2013.
|
Edición: | 2nd ed. |
Temas: | |
Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.
- 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.
- 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.
- 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.