Global optimization methods in geophysical inversion / / Mrinal K. Sen, University of Texas, Austin, USA and Paul L. Stoffa, The University of Texas, Austin, USA [[electronic resource]]

• Record Nr.: UNINA9910792070103321
• Autore: Sen Mrinal K.
• Pubbl/distr/stampa: Cambridge : , : Cambridge University Press, , 2013
• ISBN: 1-108-44584-5; 1-107-23477-8; 1-139-61021-X; 1-139-60864-9; 1-139-62509-8; 0-511-99757-4; 1-139-61579-3; 1-139-61207-7; 1-299-25764-X
• Edizione: [2nd ed.]
• Descrizione fisica: 1 online resource (xii, 289 pages) : digital, PDF file(s)
• Classificazione: SCI032000
• Disciplina: 550.1/515357
• Soggetti: Geological modeling; Geophysics - Mathematical models; Inverse problems (Differential equations); Mathematical optimization
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Title from publisher's bibliographic system (viewed on 05 Oct 2015).
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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' rule1.8 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 Existence2.3.2 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 principle2.4.6 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 methods4 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
• Sommario/riassunto: Providing an up-to-date overview of the most popular global optimization methods used in interpreting geophysical observations, this new edition includes a detailed description of the theoretical development underlying each method and a thorough explanation of the design, implementation and limitations of algorithms. New and expanded chapters provide details of recently developed methods, such as the neighborhood algorithm, particle swarm optimization, 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.