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E-raamat: Geophysical Data Analysis: Discrete Inverse Theory

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(Professor of Earth and Environmental Sciences ,Columbia University)
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 10-Apr-2018
  • Kirjastus: Academic Press Inc
  • Keel: eng
  • ISBN-13: 9780128135563
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Geophysical Data Analysis: Discrete Inverse TheorySuurem pilt
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 10-Apr-2018
  • Kirjastus: Academic Press Inc
  • Keel: eng
  • ISBN-13: 9780128135563
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Geophysical Data Analysis: Diverse Inverse Theory, Fourth Edition is a revised and expanded introduction to inverse theory and tomography as it is practiced by geophysicists. It demonstrates the methods needed to analyze a broad spectrum of geophysical datasets, with special attention to those methods that generate images of the earth. Data analysis can be a mathematically complex activity, but the treatment in this volume is carefully designed to emphasize those mathematical techniques that readers will find the most familiar and to systematically introduce less-familiar ones.

Using problems and case studies, along with MATLAB computer code and summaries of methods, the book provides data scientists and engineers in geophysics with the tools necessary to understand and apply mathematical techniques and inverse theory.

  • Includes material on probability, including Bayesian influence, probability density function and metropolis algorithm
  • Offers detailed discussion of the application of inverse theory to tectonic, gravitational and geomagnetic studies
  • Contains numerous examples, color figures and end-of-chapter homework problems to help readers explore and further understand presented ideas
  • Includes MATLAB examples and problem sets
  • Updated and refined throughout to bring the text in line with current understanding and improved examples and case studies
  • Expanded sections to cover material, such as second-derivation smoothing and chi-squared tests not covered in the previous edition
Preface ix
Introduction xi
1 Describing Inverse Problems
1.1 Formulating Inverse Problems
1(2)
1.2 The Linear Inverse Problem
3(1)
1.3 Examples of Formulating Inverse Problems
4(8)
1.4 Solutions to Inverse Problems
12(3)
1.5 Problems
15(2)
Reference
15(1)
Further Reading
15(2)
2 Some Comments on Probability Theory
2.1 Noise and Random Variables
17(4)
2.2 Correlated Data
21(2)
2.3 Functions of Random Variables
23(4)
2.4 Gaussian Probability Density Functions
27(3)
2.5 Testing the Assumption of Gaussian Statistics
30(2)
2.6 Conditional Probability Density Functions
32(2)
2.7 Confidence Intervals
34(1)
2.8 Computing Realizations of Random Variables
35(2)
2.9 Problems
37(3)
Reference
37(3)
3 Solution of the Linear, Gaussian Inverse Problem, Viewpoint 1: The Length Method
3.1 The Lengths of Estimates
40(1)
3.2 Measures of Length
40(3)
3.3 Least Squares for a Straight Line
43(1)
3.4 The Least Squares Solution of the Linear Inverse Problem
44(2)
3.5 Some Examples
46(6)
3.6 The Existence of the Least Squares Solution
52(2)
3.7 The Purely Underdetermined Problem
54(1)
3.8 Mixed-Determined Problems
55(2)
3.9 Weighted Measures of Length as a Type of Prior Information
57(5)
3.10 Other Types of Prior Information
62(2)
3.11 The Variance of the Model Parameter Estimates
64(2)
3.12 Variance and Prediction Error of the Least Squares Solution
66(2)
3.13 Problems
68(4)
References
69(3)
4 Solution of the Linear, Gaussian Inverse Problem, Viewpoint 2: Generalized Inverses
4.1 Solutions Versus Operators
72(1)
4.2 The Data Resolution Matrix
72(2)
4.3 The Model Resolution Matrix
74(1)
4.4 The Unit Covariance Matrix
75(1)
4.5 Resolution and Covariance of Some Generalized Inverses
76(1)
4.6 Measures of Goodness of Resolution and Covariance
77(1)
4.7 Generalized Inverses With Good Resolution and Covariance
78(2)
4.8 Sidelobes and the Backus-Gilbert Spread Function
80(1)
4.9 The Backus-Gilbert Generalized Inverse for the Underdetermined Problem
81(3)
4.10 Including the Covariance Size
84(1)
4.11 The Trade-Off of Resolution and Variance
85(2)
4.12 Checkerboard Tests
87(2)
4.13 Problems
89(3)
References
89(3)
5 Solution of the Linear, Gaussian Inverse Problem, Viewpoint 3: Maximum Likelihood Methods
5.1 The Mean of a Group of Measurements
92(2)
5.2 Maximum Likelihood Applied to Inverse Problem
94(15)
5.3 Model Resolution in the Presence of Prior Information
109(2)
5.4 Relative Entropy as a Guiding Principle
111(1)
5.5 Equivalence of the Three Viewpoints
112(1)
5.6 Chi-Square Test for the Compatibility of the Prior and Posterior Error
113(3)
5.7 The F-test of the Error Improvement Significance
116(2)
5.8 Problems
118(3)
References
119(2)
6 Nonuniqueness and Localized Averages
6.1 Null Vectors and Nonuniqueness
121(1)
6.2 Null Vectors of a Simple Inverse Problem
122(1)
6.3 Localized Averages of Model Parameters
123(1)
6.4 Relationship to the Resolution Matrix
124(1)
6.5 Averages Versus Estimates
124(1)
6.6 Nonunique Averaging Vectors and Prior Information
125(2)
6.7 End-Member Solutions and Squeezing
127(2)
6.8 Problems
129(2)
References
130(1)
7 Applications of Vector Spaces
7.1 Model and Data Spaces
131(1)
7.2 Householder Transformations
132(4)
7.3 Designing Householder Transformations
136(1)
7.4 Transformations That Do Not Preserve Length
137(1)
7.5 The Solution of the Mixed-Determined Problem
138(1)
7.6 Singular-Value Decomposition and the Natural Generalized Inverse
139(6)
7.7 Derivation of the Singular-Value Decomposition
145(1)
7.8 Simplifying Linear Equality and Inequality Constraints
146(1)
7.9 Inequality Constraints
147(6)
7.10 Problems
153(2)
References
154(1)
8 Linear Inverse Problems and Non-Gaussian Statistics
8.1 L1 Norms and Exponential Probability Density Functions
155(2)
8.2 Maximum Likelihood Estimate of the Mean of an Exponential Probability Density Function
157(2)
8.3 The General Linear Problem
159(1)
8.4 Solving L1 Norm Problems by Transformation to a Linear Programming Problem
160(3)
8.5 Solving L1 Norm Problems by Reweighted L2 Minimization
163(3)
8.6 The L∞ Norm
166(3)
8.7 The L0 Norm and Sparsity
169(3)
8.8 Problems
172(3)
References
173(2)
9 Nonlinear Inverse Problems
9.1 Parameterizations
175(2)
9.2 Linearizing Transformations
177(1)
9.3 Error and Likelihood in Nonlinear Inverse Problems
178(2)
9.4 The Grid Search
180(3)
9.5 The Monte Carlo Search
183(1)
9.6 Newton's Method
183(4)
9.7 The Implicit Nonlinear Inverse Problem With Gaussian Data
187(5)
9.8 Gradient Method
192(2)
9.9 Simulated Annealing
194(2)
9.10 The Genetic Algorithm
196(6)
9.11 Choosing the Null Distribution for Inexact Non-Gaussian Nonlinear Theories
202(1)
9.12 Bootstrap Confidence Intervals
203(1)
9.13 Problems
204(3)
References
205(2)
10 Factor Analysis
10.1 The Factor Analysis Problem
207(5)
10.2 Normalization and Physicality Constraints
212(4)
10.3 Q-Mode and R-Mode Factor Analysis
216(1)
10.4 Empirical Orthogonal Function Analysis
217(3)
10.5 Problems
220(3)
References
222(1)
11 Continuous Inverse Theory and Tomography
11.1 The Backus-Gilbert Inverse Problem
223(2)
11.2 Resolution and Variance Trade-Off
225(1)
11.3 Approximating Continuous Inverse Problems as Discrete Problems
226(1)
11.4 Tomography and Continuous Inverse Theory
227(1)
11.5 Tomography and the Radon Transform
228(1)
11.6 The Fourier Slice Theorem
229(2)
11.7 Correspondence Between Matrices and Linear Operators
231(3)
11.8 The Frechet Derivative
234(1)
11.9 The Frechet Derivative of Error
234(1)
11.10 Backprojection
235(3)
11.11 Frechet Derivatives Involving a Differential Equation
238(4)
11.12 Derivative With Respect to a Parameter in a Differential Equation
242(5)
11.13 Problems
247(2)
References
248(1)
12 Sample Inverse Problems
12.1 An Image Enhancement Problem
249(3)
12.2 Digital Filter Design
252(3)
12.3 Adjustment of Crossover Errors
255(3)
12.4 An Acoustic Tomography Problem
258(1)
12.5 One-Dimensional Temperature Distribution
259(4)
12.6 L1, L2, and L∞ Fitting of a Straight Line
263(1)
12.7 Finding the Mean of a Set of Unit Vectors
264(3)
12.8 Gaussian and Lorentzian Curve Fitting
267(3)
12.9 Earthquake Location
270(3)
12.10 Vibrational Problems
273(3)
12.11 Problems
276(1)
References
276(1)
13 Applications of Inverse Theory to Solid Earth Geophysics
13.1 Earthquake Location and Determination of the Velocity Structure of the Earth From Travel Time Data
277(3)
13.2 Moment Tensors of Earthquakes
280(1)
13.3 Adjoint Methods in Seismic Imaging
281(4)
13.4 Wavefield Tomography
285(2)
13.5 Finite-Frequency Travel Time Tomography
287(3)
13.6 Banana-Doughnut Kernels
290(2)
13.7 Seismic Migration
292(1)
13.8 Velocity Structure From Free Oscillations and Seismic Surface Waves
293(2)
13.9 Seismic Attenuation
295(1)
13.10 Signal Correlation
295(1)
13.11 Tectonic Plate Motions
296(1)
13.12 Gravity and Geomagnetism
296(2)
13.13 Electromagnetic Induction and the Magnetotelluric Method
298(1)
13.14 Problems
298(3)
References
298(2)
Further Reading
300(1)
Appendices 301(10)
Index 311
William Menke is a Professor of Earth and Environmental Sciences at Columbia University. His research focuses on the development of data analysis algorithms for time series analysis and imaging in the earth and environmental sciences and the application of these methods to volcanoes, earthquakes, and other natural hazards. He has thirty years of experience teaching data analysis methods to both undergraduates and graduate students. Relevant courses that he has taught include, at the undergraduate level, Environmental Data Analysis and The Earth System, and at the graduate level, Geophysical Inverse Theory, Quantitative Methods of Data Analysis, Geophysical Theory and Practical Seismology.
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