LEADER 06524nam 22008052 450 001 9910792070103321 005 20160309145115.0 010 $a1-108-44584-5 010 $a1-107-23477-8 010 $a1-139-61021-X 010 $a1-139-60864-9 010 $a1-139-62509-8 010 $a0-511-99757-4 010 $a1-139-61579-3 010 $a1-139-61207-7 010 $a1-299-25764-X 035 $a(CKB)2560000000098635 035 $a(EBL)1099853 035 $a(OCoLC)827944810 035 $a(SSID)ssj0000833303 035 $a(PQKBManifestationID)11436134 035 $a(PQKBTitleCode)TC0000833303 035 $a(PQKBWorkID)10935535 035 $a(PQKB)10533198 035 $a(UkCbUP)CR9780511997570 035 $a(Au-PeEL)EBL1099853 035 $a(CaPaEBR)ebr10659320 035 $a(CaONFJC)MIL457014 035 $a(MiAaPQ)EBC1099853 035 $a(PPN)261318314 035 $a(EXLCZ)992560000000098635 100 $a20110111d2013|||| uy| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGlobal optimization methods in geophysical inversion /$fMrinal K. Sen, University of Texas, Austin, USA and Paul L. Stoffa, The University of Texas, Austin, USA$b[electronic resource] 205 $a2nd ed. 210 1$aCambridge :$cCambridge University Press,$d2013. 215 $a1 online resource (xii, 289 pages) $cdigital, PDF file(s) 300 $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). 311 $a1-107-01190-6 311 $a1-139-62137-8 320 $aIncludes bibliographical references and index. 327 $aCover; 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 327 $a1.7 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 327 $a2.3.1 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 327 $aEngl'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 327 $a3.4 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 327 $a4.6.2 Hopfield neural networks 330 $aProviding 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. 606 $aGeological modeling 606 $aGeophysics$xMathematical models 606 $aInverse problems (Differential equations) 606 $aMathematical optimization 615 0$aGeological modeling. 615 0$aGeophysics$xMathematical models. 615 0$aInverse problems (Differential equations) 615 0$aMathematical optimization. 676 $a550.1/515357 686 $aSCI032000$2bisacsh 700 $aSen$b Mrinal K.$01530569 702 $aStoffa$b Paul L.$f1948- 801 0$bUkCbUP 801 1$bUkCbUP 906 $aBOOK 912 $a9910792070103321 996 $aGlobal optimization methods in geophysical inversion$93775709 997 $aUNINA