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Geophysical data analysis : discrete inverse theory / / William Menke
| Geophysical data analysis : discrete inverse theory / / William Menke |
| Autore | Menke William |
| Pubbl/distr/stampa | London, United Kingdom : , : Academic Press, an imprint of Elsevier, , [2018] |
| Descrizione fisica | 1 online resource (539 pages) |
| Disciplina | 551.01519 |
| Soggetto topico |
Geophysics - Measurement
Oceanography - Measurement Inverse problems (Differential equations) - Numerical solutions |
| ISBN |
0-12-813556-5
0-12-813555-7 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Describing inverse problems -- Some comments on probability theory -- Solution of the linear, Gaussian inverse problem, viewpoint 1 : the length method -- Solution of the linear, Gaussian inverse problem, viewpoint 2 : generalized inverses -- Solution of the linear, Gaussian inverse problem, viewpoint 3 : maximum likelihood methods -- Nonuniqueness and localized averages -- Applications of vector spaces -- Linear inverse problems and non-Gaussian statistics -- Nonlinear inverse problems -- Factor analysis -- Continuous inverse theory and tomography -- Sample inverse problems -- Applications of inverse theory to solid earth geophysics. |
| Record Nr. | UNINA-9910583476103321 |
Menke William
|
||
| London, United Kingdom : , : Academic Press, an imprint of Elsevier, , [2018] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Geophysical data analysis [[electronic resource] ] : discrete inverse theory / / William Menke
| Geophysical data analysis [[electronic resource] ] : discrete inverse theory / / William Menke |
| Autore | Menke William |
| Edizione | [Matlab ed., 3rd ed.] |
| Pubbl/distr/stampa | Amsterdam ; ; Boston, : Elsevier/AP, 2012 |
| Descrizione fisica | 1 online resource (331 p.) |
| Disciplina | 551 |
| Soggetto topico |
Geophysics - Measurement
Inverse problems (Differential equations) - Numerical solutions Oceanography - Measurement |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-283-73512-1
0-12-397784-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 Problems
1.1. 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 1.4.4. 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 3.1. 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 3.9.2. 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 4.5.1. Least Squares |
| Record Nr. | UNINA-9910452072303321 |
|
Menke William
|
||
| Amsterdam ; ; Boston, : Elsevier/AP, 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Geophysical data analysis [[electronic resource] ] : discrete inverse theory / / William Menke
| Geophysical data analysis [[electronic resource] ] : discrete inverse theory / / William Menke |
| Autore | Menke William |
| Edizione | [Matlab ed., 3rd ed.] |
| Pubbl/distr/stampa | Amsterdam ; ; Boston, : Elsevier/AP, 2012 |
| Descrizione fisica | 1 online resource (331 p.) |
| Disciplina | 551 |
| Soggetto topico |
Geophysics - Measurement
Inverse problems (Differential equations) - Numerical solutions Oceanography - Measurement |
| ISBN |
1-283-73512-1
0-12-397784-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 Problems
1.1. 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 1.4.4. 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 3.1. 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 3.9.2. 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 4.5.1. Least Squares |
| Record Nr. | UNINA-9910779175303321 |
|
Menke William
|
||
| Amsterdam ; ; Boston, : Elsevier/AP, 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Geophysical data analysis : discrete inverse theory / / William Menke
| Geophysical data analysis : discrete inverse theory / / William Menke |
| Autore | Menke William |
| Edizione | [Matlab ed., 3rd ed.] |
| Pubbl/distr/stampa | Amsterdam ; ; Boston, : Elsevier/AP, 2012 |
| Descrizione fisica | 1 online resource (331 p.) |
| Disciplina | 551 |
| Soggetto topico |
Geophysics - Measurement
Inverse problems (Differential equations) - Numerical solutions Oceanography - Measurement |
| ISBN |
9781283735124
1283735121 9780123977847 0123977843 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 Problems
1.1. 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 1.4.4. 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 3.1. 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 3.9.2. 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 4.5.1. Least Squares |
| Record Nr. | UNINA-9910960415303321 |
|
Menke William
|
||
| Amsterdam ; ; Boston, : Elsevier/AP, 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Geophysical data analysis : discrete inverse theory / William Menke
| Geophysical data analysis : discrete inverse theory / William Menke |
| Autore | Menke, William |
| Edizione | [3rd ed.] |
| Pubbl/distr/stampa | Amsterdarm : Elsevier, 2012 |
| Descrizione fisica | xiii, 293 p. : ill. ; 24 cm |
| Disciplina | 551 |
| Soggetto topico |
Geophysics - Measurement
Inverse problems (Differential equations) - Numerical solutions Oceanography - Measurement |
| ISBN | 9780123971609 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991002944549707536 |
|
Menke, William
|
||
| Amsterdarm : Elsevier, 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
Geophysical inverse theory and regularization problems / / Michael S. Zhdanov
| Geophysical inverse theory and regularization problems / / Michael S. Zhdanov |
| Autore | Zhdanov Mikhail Semenovich |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Amsterdam, : Elsevier, 2002 |
| Descrizione fisica | 1 online resource (635 p.) |
| Disciplina |
550
550.1515 622.150151 |
| Collana | Methods in geochemistry and geophysics |
| Soggetto topico |
Inversion (Geophysics)
Geophysics - Measurement Functional analysis Mathematical optimization |
| ISBN |
1-281-04863-1
9786611048631 0-08-053250-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; 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
2.5 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 4.3 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 6.2 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 8.4 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 Chapter 11. Electromagnetic migration imaging |
| Record Nr. | UNINA-9911004759003321 |
|
Zhdanov Mikhail Semenovich
|
||
| Amsterdam, : Elsevier, 2002 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Inverse theory and applications in geophysics / / Michael S. Zhdanov
| Inverse theory and applications in geophysics / / Michael S. Zhdanov |
| Autore | Zhdanov Mikhail Semenovich |
| Edizione | [Second edition.] |
| Pubbl/distr/stampa | Amsterdam, Netherlands : , : Elsevier, , 2015 |
| Descrizione fisica | 1 online resource (731 p.) |
| Disciplina | 550.1515 |
| Collana | Methods in Geochemistry and Geophysics |
| Soggetto topico |
Inversion (Geophysics)
Geophysics - Measurement Functional analysis |
| ISBN | 0-444-62712-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Front 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
1.3 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 2.3.3 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 3.1.2 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 3.5.2 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 Chapter 4: Iterative Solutions of the Linear Inverse Problem |
| Record Nr. | UNINA-9910797356103321 |
|
Zhdanov Mikhail Semenovich
|
||
| Amsterdam, Netherlands : , : Elsevier, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Inverse theory and applications in geophysics / / Michael S. Zhdanov
| Inverse theory and applications in geophysics / / Michael S. Zhdanov |
| Autore | Zhdanov Mikhail Semenovich |
| Edizione | [Second edition.] |
| Pubbl/distr/stampa | Amsterdam, Netherlands : , : Elsevier, , 2015 |
| Descrizione fisica | 1 online resource (731 p.) |
| Disciplina | 550.1515 |
| Collana | Methods in Geochemistry and Geophysics |
| Soggetto topico |
Inversion (Geophysics)
Geophysics - Measurement Functional analysis |
| ISBN | 0-444-62712-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Front 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
1.3 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 2.3.3 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 3.1.2 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 3.5.2 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 Chapter 4: Iterative Solutions of the Linear Inverse Problem |
| Record Nr. | UNINA-9910811684503321 |
|
Zhdanov Mikhail Semenovich
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| Amsterdam, Netherlands : , : Elsevier, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
