LEADER 05505nam 2200721Ia 450 001 9910960415303321 005 20200520144314.0 010 $a9781283735124 010 $a1283735121 010 $a9780123977847 010 $a0123977843 035 $a(CKB)2550000000101222 035 $a(EBL)921025 035 $a(OCoLC)794328701 035 $a(SSID)ssj0000656148 035 $a(PQKBManifestationID)12256969 035 $a(PQKBTitleCode)TC0000656148 035 $a(PQKBWorkID)10648852 035 $a(PQKB)10188449 035 $a(Au-PeEL)EBL921025 035 $a(CaPaEBR)ebr10562134 035 $a(CaONFJC)MIL404762 035 $a(PPN)170604284 035 $a(FR-PaCSA)88812272 035 $a(MiAaPQ)EBC921025 035 $a(FRCYB88812272)88812272 035 $a(EXLCZ)992550000000101222 100 $a20120213d2012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aGeophysical data analysis $ediscrete inverse theory /$fWilliam Menke 205 $aMatlab ed., 3rd ed. 210 $aAmsterdam ;$aBoston $cElsevier/AP$d2012 215 $a1 online resource (331 p.) 300 $aDescription based upon print version of record. 311 08$a9780123971609 311 08$a0123971608 320 $aIncludes bibliographical references and index. 327 $aFront Cover; Geophysical Data Analysis: Discrete Inverse Theory; Copyright; Dedication; Preface; Reference; Companion Web Site; Contents; Introduction; I.1. Forward and Inverse Theories; I.2. MatLab as a Tool for Learning Inverse Theory; I.3. A Very Quick MatLab Tutorial; I.4. Review of Vectors and Matrices and Their Representation in MatLab; I.5. Useful MatLab Operations; I.5.1. Loops; I.5.2. Loading Data from a File; I.5.3. Plotting Data; I.5.4. Creating Character Strings Containing the Values of Variables; I.5.4 References; Chapter 1: Describing Inverse Problems 327 $a1.1. Formulating Inverse Problems1.1.1. Implicit Linear Form; 1.1.2. Explicit Form; 1.1.3. Explicit Linear Form; 1.2. The Linear Inverse Problem; 1.3. Examples of Formulating Inverse Problems; 1.3.1. Example 1: Fitting a Straight Line; 1.3.2. Example 2: Fitting a Parabola; 1.3.3. Example 3: Acoustic Tomography; 1.3.4. Example 4: X-ray Imaging; 1.3.5. Example 5: Spectral Curve Fitting; 1.3.6. Example 6: Factor Analysis; 1.4. Solutions to Inverse Problems; 1.4.1. Estimates of Model Parameters; 1.4.2. Bounding Values; 1.4.3. Probability Density Functions 327 $a1.4.4. Sets of Realizations of Model Parameters1.4.5. Weighted Averages of Model Parameters; 1.5. Problems; 1.5 References; Chapter 2: Some Comments on Probability Theory; 2.1. Noise and Random Variables; 2.2. Correlated Data; 2.3. Functions of Random Variables; 2.4. Gaussian Probability Density Functions; 2.5. Testing the Assumption of Gaussian Statistics; 2.6. Conditional Probability Density Functions; 2.7. Confidence Intervals; 2.8. Computing Realizations of Random Variables; 2.9. Problems; 2.9 References; Chapter 3: Solution of the Linear, Gaussian Inverse Problem, Viewpoint 1 327 $a3.1. The Lengths of Estimates3.2. Measures of Length; 3.3. Least Squares for a Straight Line; 3.4. The Least Squares Solution of the Linear Inverse Problem; 3.5. Some Examples; 3.5.1. The Straight Line Problem; 3.5.2. Fitting a Parabola; 3.5.3. Fitting a Plane Surface; 3.6. The Existence of the Least Squares Solution; 3.6.1. Underdetermined Problems; 3.6.2. Even-Determined Problems; 3.6.3. Overdetermined Problems; 3.7. The Purely Underdetermined Problem; 3.8. Mixed-Determined Problems; 3.9. Weighted Measures of Length as a Type of A Priori Information; 3.9.1. Weighted Least Squares 327 $a3.9.2. Weighted Minimum Length3.9.3. Weighted Damped Least Squares; 3.10. Other Types of A Priori Information; 3.10.1. Example: Constrained Fitting of a Straight Line; 3.11. The Variance of the Model Parameter Estimates; 3.12. Variance and Prediction Error of the Least Squares Solution; 3.13. Problems; 3.13References; Chapter 4: Solution of the Linear, Gaussian Inverse Problem, Viewpoint 2; 4.1. Solutions Versus Operators; 4.2. The Data Resolution Matrix; 4.3. The Model Resolution Matrix; 4.4. The Unit Covariance Matrix; 4.5. Resolution and Covariance of Some Generalized Inverses 327 $a4.5.1. Least Squares 330 $aSince 1984, Geophysical Data Analysis has filled the need for a short, concise reference on inverse theory for individuals who have an intermediate background in science and mathematics. The new edition maintains the accessible and succinct manner for which it is known, with the addition of: MATLAB examples and problem setsAdvanced color graphicsCoverage of new topics, including Adjoint Methods; Inversion by Steepest Descent, Monte Carlo and Simulated Annealing methods; and Bootstrap algorithm for determining empirical confidence intervalsOnline da 606 $aGeophysics$xMeasurement 606 $aInverse problems (Differential equations)$xNumerical solutions 606 $aOceanography$xMeasurement 615 0$aGeophysics$xMeasurement. 615 0$aInverse problems (Differential equations)$xNumerical solutions. 615 0$aOceanography$xMeasurement. 676 $a551 700 $aMenke$b William$067453 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910960415303321 996 $aGeophysical data analysis$9103390 997 $aUNINA