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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]]
| 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]] |
| Autore | Sen Mrinal K. |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2013 |
| Descrizione fisica | 1 online resource (xii, 289 pages) : digital, PDF file(s) |
| Disciplina | 550.1/515357 |
| Soggetto topico |
Geological modeling
Geophysics - Mathematical models Inverse problems (Differential equations) Mathematical optimization |
| ISBN |
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 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910465378203321 |
Sen Mrinal K.
|
||
| Cambridge : , : Cambridge University Press, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
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]]
| 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]] |
| Autore | Sen Mrinal K. |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2013 |
| Descrizione fisica | 1 online resource (xii, 289 pages) : digital, PDF file(s) |
| Disciplina | 550.1/515357 |
| Soggetto topico |
Geological modeling
Geophysics - Mathematical models Inverse problems (Differential equations) Mathematical optimization |
| 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 |
| Classificazione | SCI032000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910792070103321 |
|
Sen Mrinal K.
|
||
| Cambridge : , : Cambridge University Press, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
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]]
| 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]] |
| Autore | Sen Mrinal K. |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2013 |
| Descrizione fisica | 1 online resource (xii, 289 pages) : digital, PDF file(s) |
| Disciplina | 550.1/515357 |
| Soggetto topico |
Geological modeling
Geophysics - Mathematical models Inverse problems (Differential equations) Mathematical optimization |
| 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 |
| Classificazione | SCI032000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910822272103321 |
|
Sen Mrinal K.
|
||
| Cambridge : , : Cambridge University Press, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||