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Geophysical Data Analysis : MATLAB Edition.
Since 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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Burlington :
Elsevier Science,
2012.
|
| Edición: | 3rd ed. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.