LEADER 05458nam 2200685 450 001 9910811684503321 005 20200520144314.0 010 $a0-444-62712-X 035 $a(CKB)3710000000448791 035 $a(EBL)2095614 035 $a(SSID)ssj0001560553 035 $a(PQKBManifestationID)16193294 035 $a(PQKBTitleCode)TC0001560553 035 $a(PQKBWorkID)14825048 035 $a(PQKB)11156080 035 $a(Au-PeEL)EBL2095614 035 $a(CaPaEBR)ebr11079050 035 $a(CaONFJC)MIL104863 035 $a(OCoLC)914434570 035 $a(MiAaPQ)EBC2095614 035 $a(PPN)198673892 035 $a(EXLCZ)993710000000448791 100 $a20150728h20152015 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aInverse theory and applications in geophysics /$fMichael S. Zhdanov 205 $aSecond edition. 210 1$aAmsterdam, Netherlands :$cElsevier,$d2015. 210 4$dİ2015 215 $a1 online resource (731 p.) 225 1 $aMethods in Geochemistry and Geophysics ;$vv.36 300 $aDescription based upon print version of record. 311 $a0-444-62674-3 320 $aIncludes bibliographical references and index. 327 $aFront Cover; Inverse Theory and Applications in Geophysics; Copyright; Dedication; Contents; Preface to the Second Edition; Preface; Part I: Introduction to Inversion Theory; Chapter 1: Forward and Inverse Problems in Science and Engineering; 1.1 Formulation of Forward and Inverse Problems for Different Physical Fields; 1.1.1 Gravity Field; 1.1.2 Magnetic Field; 1.1.3 Electromagnetic Field; 1.1.4 Seismic Wavefield; 1.2 Existence and Uniqueness of the Inverse Problem Solutions; 1.2.1 Existence of the Solution; 1.2.2 Uniqueness of the Solution; 1.2.3 Practical Uniqueness 327 $a1.3 Instability of the Inverse Problem Solution References; Chapter 2: Ill-Posed Problems and the Methods of Their Solution; 2.1 Sensitivity and Resolution of Geophysical Methods; 2.1.1 Formulation of the Inverse Problem in General Mathematical Spaces; 2.1.2 Sensitivity; 2.1.3 Resolution; 2.2 Formulation of Well-Posed and Ill-Posed Problems; 2.2.1 Well-Posed Problems; 2.2.2 Conditionally Well-Posed Problems; 2.2.3 Quasi-Solution of the Ill-Posed Problem; 2.3 Foundations of Regularization Methods of Inverse Problem Solution; 2.3.1 Regularizing Operators; 2.3.2 Stabilizing Functionals 327 $a2.3.3 Tikhonov Parametric Functional2.4 Family of Stabilizing Functionals; 2.4.1 Stabilizing Functionals Revisited; 2.4.2 Representation of a Stabilizing Functional in the Form of a Pseudo-Quadratic Functional; 2.5 Definition of the Regularization Parameter; 2.5.1 Optimal Regularization Parameter Selection; 2.5.2 L-Curve Method of Regularization Parameter Selection; References; Part II: Methods of the Solution of Inverse Problems; Chapter 3: Linear Discrete Inverse Problems; 3.1 Linear Least-Squares Inversion; 3.1.1 The Linear Discrete Inverse Problem 327 $a3.1.2 Systems of Linear Equations and Their General SolutionsMinimization of the misfit functional; 3.1.3 The Data Resolution Matrix; 3.2 Solution of the Purely Underdetermined Problem; 3.2.1 Underdetermined System of Linear Equations; 3.2.2 The Model Resolution Matrix; 3.3 Weighted Least-Squares Method; 3.4 Applying the Principles of Probability Theory to a Linear Inverse Problem; 3.4.1 Some Formulae and Notations from Probability Theory; 3.4.2 Maximum Likelihood Method; 3.4.3 Chi-Square Fitting; 3.5 Regularization Methods; 3.5.1 The Tikhonov Regularization Method 327 $a3.5.2 Application of SLDM Method in Regularized Linear Inverse Problem Solution3.5.3 Integrated Sensitivity; 3.5.4 Definition of the Weighting Matrices for the Model Parameters and Data; 3.5.5 Controlled Sensitivity; 3.5.6 Approximate Regularized Solution of the Linear Inverse Problem; 3.5.7 The Levenberg-Marquardt Method; 3.5.8 The Maximum a Posteriori Estimation Method (the Bayes Estimation); 3.6 The Backus-Gilbert Method; 3.6.1 The Data Resolution Function; 3.6.2 The Spread Function; 3.6.3 Regularized Solution in the Backus-Gilbert Method; References 327 $aChapter 4: Iterative Solutions of the Linear Inverse Problem 330 $a Geophysical Inverse Theory and Applications, Second Edition, brings together fundamental results developed by the Russian mathematical school in regularization theory and combines them with the related research in geophysical inversion carried out in the West. It presents a detailed exposition of the methods of regularized solution of inverse problems based on the ideas of Tikhonov regularization, and shows the different forms of their applications in both linear and nonlinear methods of geophysical inversion. It's the first book of its kind to treat many kinds of inversion and imaging techni 410 0$aMethods in Geochemistry and Geophysics 606 $aInversion (Geophysics) 606 $aGeophysics$xMeasurement 606 $aFunctional analysis 615 0$aInversion (Geophysics) 615 0$aGeophysics$xMeasurement. 615 0$aFunctional analysis. 676 $a550.1515 700 $aZhdanov$b Mikhail Semenovich$0771808 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910811684503321 996 $aInverse theory and applications in geophysics$94097709 997 $aUNINA