05375nam 2200661Ia 450 991077917530332120230105231541.01-283-73512-10-12-397784-3(CKB)2550000000101222(EBL)921025(OCoLC)794328701(SSID)ssj0000656148(PQKBManifestationID)12256969(PQKBTitleCode)TC0000656148(PQKBWorkID)10648852(PQKB)10188449(MiAaPQ)EBC921025(Au-PeEL)EBL921025(CaPaEBR)ebr10562134(CaONFJC)MIL404762(PPN)170604284(EXLCZ)99255000000010122220120213d2012 uy 0engur|n|---|||||txtccrGeophysical data analysis[electronic resource] discrete inverse theory /William MenkeMatlab ed., 3rd ed.Amsterdam ;Boston Elsevier/AP20121 online resource (331 p.)Description based upon print version of record.0-12-397160-8 Includes bibliographical references and index.Front 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 Problems1.1. 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 Functions1.4.4. 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 13.1. 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 Squares3.9.2. 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 Inverses4.5.1. Least SquaresSince 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 daGeophysicsMeasurementInverse problems (Differential equations)Numerical solutionsOceanographyMeasurementGeophysicsMeasurement.Inverse problems (Differential equations)Numerical solutions.OceanographyMeasurement.551Menke William67453MiAaPQMiAaPQMiAaPQBOOK9910779175303321Geophysical data analysis103390UNINA