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...

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Bibliographic Details
Main Author: Sen, Mrinal K.
Other Authors: Stoffa, Paul L., 1948-
Format: eBook
Language:English
Published: Cambridge : Cambridge University Press, 2013.
Edition:2nd ed.
Subjects:
Online Access:CONNECT
CONNECT
Table of 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.
  • 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.