LEADER 05484nam 2200709 a 450 001 9911004759003321 005 20200520144314.0 010 $a1-281-04863-1 010 $a9786611048631 010 $a0-08-053250-0 035 $a(CKB)1000000000383969 035 $a(EBL)317136 035 $a(OCoLC)182788742 035 $a(SSID)ssj0000072065 035 $a(PQKBManifestationID)11123254 035 $a(PQKBTitleCode)TC0000072065 035 $a(PQKBWorkID)10093539 035 $a(PQKB)10178257 035 $a(MiAaPQ)EBC317136 035 $a(EXLCZ)991000000000383969 100 $a20081021d2002 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aGeophysical inverse theory and regularization problems /$fMichael S. Zhdanov 205 $a1st ed. 210 $aAmsterdam $cElsevier$d2002 215 $a1 online resource (635 p.) 225 1 $aMethods in geochemistry and geophysics,$x0076-6895 ;$v36 300 $aDescription based upon print version of record. 311 $a0-444-51089-3 320 $aIncludes bibliographical references and index. 327 $aCover; Contents; Preface; Part I: Introduction to Inversion Theory; Chapter 1. Forward and inverse problems in geophysics; 1.1 Formulation of forward and inverse problems for different geophysical fields; 1.2 Existence and uniqueness of the inverse problem solutions; 1.3 Instability of the inverse problem solution; Chapter 2. ILL-Posed problems and the methods of their solution; 2.1 Sensitivity and resolution of geophysical methods; 2.2 Formulation of well-posed and ill-posed problems; 2.3 Foundations of regularization methods of inverse problem solution; 2.4 Family of stabilizing functionals 327 $a2.5 Definition of the regularization parameterPart II: Methods of the Solution of Inverse Problems; Chapter 3. Linear discrete inverse problems; 3.1 Linear least-squares inversion; 3.2 Solution of the purely underdetermined problem; 3.3 Weighted least-squares method; 3.4 Applying the principles of probability theory to a linear inverse problem; 3.5 Regularization methods; 3.6 The Backus-Gilbert Method; Chapter 4. Iterative solutions of the linear inverse problem; 4.1 Linear operator equations and their solution by iterative methods; 4.2 A generalized minimal residual method 327 $a4.3 The regularization method in a linear inverse problem solutionChapter 5. Nonlinear inversion technique; 5.1 Gradient-type methods; 5.2 Regularized gradient-type methods in the solution of nonlinear inverse problems; 5.3 Regularized solution of a nonlinear discrete inverse problem; 5.4 Conjugate gradient re-weighted optimization; Part III: Geopotential Field Inversion; Chapter 6. Integral representations in forward modeling of gravity and magnetic fields; 6.1 Basic equations for gravity and magnetic fields 327 $a6.2 Integral representations of potential fields based on the theory of functions of a complex variableChapter 7. Integral representations in inversion of gravity and magnetic data; 7.1 Gradient methods of gravity inversion; 7.2 Gravity field migration; 7.3 Gradient methods of magnetic anomaly inversion; 7.4 Numerical methods in forward and inverse modeling; Part IV: Electromagnetic Inversion; Chapter 8. Foundations of electromagnetic theory; 8.1 Electromagnetic field equations; 8.2 Electromagnetic energy flow; 8.3 Uniqueness of the solution of electromagnetic field equations 327 $a8.4 Electromagnetic Green's tensorsChapter 9. Integral representations in electromagnetic forward modeling; 9.1 Integral equation method; 9.2 Family of linear and nonlinear integral approximations of the electromagnetic field; 9.3 Linear and non-linear approximations of higher orders; 9.4 Integral representations in numerical dressing; Chapter 10. Integral representations in electromagnetic inversion; 10.1 Linear inversion methods; 10.2 Nonlinear inversion; 10.3 Quasi-linear inversion; 10.4 Quasi-analytical inversion; 10.5 Magnetotelluric (MT) data inversion 327 $aChapter 11. Electromagnetic migration imaging 330 $aThis book presents state-of-the-art geophysical inverse theory developed in modern mathematical terminology. The book brings together fundamental results developed by the Russian mathematical school in regularization theory and combines them with the related research in geophysical inversion carried out in the West. It presents a detailed exposition of the methods of regularized solution of inverse problems based on the ideas of Tikhonov regularization, and shows the different forms of their applications in both linear and nonlinear methods of geophysical inversion. This text is the first t 410 0$aMethods in geochemistry and geophysics ;$v36. 606 $aInversion (Geophysics) 606 $aGeophysics$xMeasurement 606 $aFunctional analysis 606 $aMathematical optimization 615 0$aInversion (Geophysics) 615 0$aGeophysics$xMeasurement. 615 0$aFunctional analysis. 615 0$aMathematical optimization. 676 $a550 676 $a550.1515 676 $a622.150151 676 $a550 700 $aZhdanov$b Mikhail Semenovich$0771808 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911004759003321 996 $aGeophysical inverse theory and regularization problems$94388487 997 $aUNINA