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Geophysical Data Analysis: Discrete Inverse Theory: MATLAB Edition 3rd edition, Volume 45 [Pehme köide]

4.17/5 (6 hinnangut Goodreads-ist)
(Professor of Earth and Environmental Sciences ,Columbia University)
  • Formaat: Paperback / softback, 330 pages, kõrgus x laius: 229x152 mm, kaal: 540 g, Approx. 125 illustrations (125 in full color); Illustrations, unspecified
  • Sari: International Geophysics
  • Ilmumisaeg: 19-Aug-2016
  • Kirjastus: Academic Press Inc
  • ISBN-10: 0128100486
  • ISBN-13: 9780128100486
Teised raamatud teemal:
Geophysical Data Analysis: Discrete Inverse Theory: MATLAB Edition 3rd edition, Volume 45Suurem pilt
  • Formaat: Paperback / softback, 330 pages, kõrgus x laius: 229x152 mm, kaal: 540 g, Approx. 125 illustrations (125 in full color); Illustrations, unspecified
  • Sari: International Geophysics
  • Ilmumisaeg: 19-Aug-2016
  • Kirjastus: Academic Press Inc
  • ISBN-10: 0128100486
  • ISBN-13: 9780128100486
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780128100486.html
Märksõnad:

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 examples and problem sets
  • Advanced color graphics
  • Coverage of new topics, including Adjoint Methods; Inversion by Steepest Descent, Monte Carlo and Simulated Annealing methods; and Bootstrap algorithm for determining empirical confidence intervals
  • Online data sets and MATLAB scripts that can be used as an inverse theory tutorial.
  • Additional material on probability, including Bayesian influence, probability density function, and metropolis algorithm
  • Detailed discussion of application of inverse theory to tectonic, gravitational and geomagnetic studies
  • Numerous examples and end-of-chapter homework problems help you explore and further understand the ideas presented
  • Use as classroom text facilitated by a complete set of exemplary lectures in Microsoft PowerPoint format and homework problem solutions for instructors
  • Check out the companion website: http://www.elsevierdirect.com/companion.jsp ISBN=9780123971609 and the Instructor website: http://textbooks.elsevier.com/web/manuals.aspx isbn=9780123971609

Arvustused

"This is a practical book on data analysis based on numerical Matlab procedures for solving inverse problems with a special application in seismology. The book is useful both as a textbook for graduate students in geophysics and as a numerical data processing reference book for researchers not only in geophysics but also those involved in acoustic tomography and X-ray imaging data processing." --Zentrallblatt MATH 1250

Praise for the second edition:"The author has produced a meaningful guide to the subject; one which a student (or professional unfamiliar with the field) can follow without great difficulty and one in which many motivational guideposts are provided....I think that the value of the book is outstanding....It deserves a prominent place on the shelf of every scientist or engineer who has data to interpret." --GEOPHYSICS

"As a meteorologist, I have used least squares, maximum likelihood, maximum entropy, and empirical orthogonal functions during the course of my work, but this book brought together these somewhat disparate techniques into a coherent, unified package....I recommend it to meteorologists involved with data analysis and parameterization." --Roland B. Stull, THE BULLETIN OF THE AMERICAN METEOROLOGICAL SOCIETY

"This book provides an excellent introductory account of inverse theory with geophysical applications....My experience in using this book, along with supplementary material in a course for the first year graduate students, has been very positive. I unhesitatingly recommend it to any student or researcher in the geophysical sciences." --PACEOPH

Muu info

Provides readers with the tools to make useful inferences from complicated data using inverse theory
Introduction xv
1 Describing Inverse Problems
1.1 Formulating Inverse Problems
1(2)
1.1.1 Implicit Linear Form
2(1)
1.1.2 Explicit Form
2(1)
1.1.3 Explicit Linear Form
3(1)
1.2 The Linear Inverse Problem
3(1)
1.3 Examples of Formulating Inverse Problems
4(7)
1.3.1 Example 1: Fitting a Straight Line
4(1)
1.3.2 Example 2: Fitting a Parabola
5(1)
1.3.3 Example 3: Acoustic Tomography
6(1)
1.3.4 Example 4: X-ray Imaging
7(2)
1.3.5 Example 5: Spectral Curve Fitting
9(1)
1.3.6 Example 6: Factor Analysis
10(1)
1.4 Solutions to Inverse Problems
11(2)
1.4.1 Estimates of Model Parameters
11(1)
1.4.2 Bounding Values
12(1)
1.4.3 Probability Density Functions
12(1)
1.4.4 Sets of Realizations of Model Parameters
13(1)
1.4.5 Weighted Averages of Model Parameters
13(1)
1.5 Problems
13(2)
2 Some Comments on Probability Theory
2.1 Noise and Random Variables
15(4)
2.2 Correlated Data
19(2)
2.3 Functions of Random Variables
21(5)
2.4 Gaussian Probability Density Functions
26(3)
2.5 Testing the Assumption of Gaussian Statistics
29(1)
2.6 Conditional Probability Density Functions
30(3)
2.7 Confidence Intervals
33(1)
2.8 Computing Realizations of Random Variables
34(3)
2.9 Problems
37(2)
3 Solution of the Linear, Gaussian Inverse Problem, Viewpoint 1: The Length Method
3.1 The Lengths of Estimates
39(1)
3.2 Measures of Length
39(4)
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(3)
3.5.1 The Straight Line Problem
46(1)
3.5.2 Fitting a Parabola
47(1)
3.5.3 Fitting a Plane Surface
48(1)
3.6 The Existence of the Least Squares Solution
49(3)
3.6.1 Underdetermined Problems
51(1)
3.6.2 Even-Determined Problems
52(1)
3.6.3 Overdetermined Problems
52(1)
3.7 The Purely Underdetermined Problem
52(2)
3.8 Mixed-Determined Problems
54(2)
3.9 Weighted Measures of Length as a Type of A Priori Information
56(4)
3.9.1 Weighted Least Squares
58(1)
3.9.2 Weighted Minimum Length
58(1)
3.9.3 Weighted Damped Least Squares
58(2)
3.10 Other Types of A Priori Information
60(3)
3.10.1 Example: Constrained Fitting of a Straight Line
62(1)
3.11 The Variance of the Model Parameter Estimates
63(1)
3.12 Variance and Prediction Error of the Least Squares Solution
64(3)
3.13 Problems
67(2)
4 Solution of the Linear, Gaussian Inverse Problem, Viewpoint 2: Generalized Inverses
4.1 Solutions Versus Operators
69(1)
4.2 The Data Resolution Matrix
69(3)
4.3 The Model Resolution Matrix
72(1)
4.4 The Unit Covariance Matrix
72(2)
4.5 Resolution and Covariance of Some Generalized Inverses
74(1)
4.5.1 Least Squares
74(1)
4.5.2 Minimum Length
75(1)
4.6 Measures of Goodness of Resolution and Covariance
75(1)
4.7 Generalized Inverses with Good Resolution and Covariance
76(2)
4.7.1 Overdetermined Case
76(1)
4.7.2 Underdetermined Case
77(1)
4.7.3 The General Case with Dirichlet Spread Functions
77(1)
4.8 Sidelobes and the Backus-Gilbert Spread Function
78(1)
4.9 The Backus-Gilbert Generalized Inverse for the Underdetermined Problem
79(4)
4.10 Including the Covariance Size
83(1)
4.11 The Trade-off of Resolution and Variance
84(2)
4.12 Techniques for Computing Resolution
86(2)
4.13 Problems
88(1)
5 Solution of the Linear, Gaussian Inverse Problem, Viewpoint 3: Maximum Likelihood Methods
5.1 The Mean of a Group of Measurements
89(3)
5.2 Maximum Likelihood Applied to Inverse Problem
92(16)
5.2.1 The Simplest Case
92(1)
5.2.2 A Priori Distributions
92(5)
5.2.3 Maximum Likelihood for an Exact Theory
97(3)
5.2.4 Inexact Theories
100(2)
5.2.5 The Simple Gaussian Case with a Linear Theory
102(2)
5.2.6 The General Linear, Gaussian Case
104(3)
5.2.7 Exact Data and Theory
107(1)
5.2.8 Infinitely Inexact Data and Theory
108(1)
5.2.9 No A Priori Knowledge of the Model Parameters
108(1)
5.3 Relative Entropy as a Guiding Principle
108(2)
5.4 Equivalence of the Three Viewpoints
110(1)
5.5 The F-Test of Error Improvement Significance
111(2)
5.6 Problems
113(2)
6 Nonuniqueness and Localized Averages
6.1 Null Vectors and Nonuniqueness
115(1)
6.2 Null Vectors of a Simple Inverse Problem
116(1)
6.3 Localized Averages of Model Parameters
117(1)
6.4 Relationship to the Resolution Matrix
117(1)
6.5 Averages Versus Estimates
118(1)
6.6 Nonunique Averaging Vectors and A Priori Information
119(2)
6.7 Problems
121(2)
7 Applications of Vector Spaces
7.1 Model and Data Spaces
123(1)
7.2 Householder Transformations
124(3)
7.3 Designing Householder Transformations
127(2)
7.4 Transformations That Do Not Preserve Length
129(1)
7.5 The Solution of the Mixed-Determined Problem
130(2)
7.6 Singular-Value Decomposition and the Natural Generalized Inverse
132(6)
7.7 Derivation of the Singular-Value Decomposition
138(1)
7.8 Simplifying Linear Equality and Inequality Constraints
138(2)
7.8.1 Linear Equality Constraints
139(1)
7.8.2 Linear Inequality Constraints
139(1)
7.9 Inequality Constraints
140(7)
7.10 Problems
147(2)
8 Linear Inverse Problems and Non-Gaussian Statistics
8.1 Li Norms and Exponential Probability Density Functions
149(2)
8.2 Maximum Likelihood Estimate of the Mean of an Exponential Probability Density Function
151(2)
8.3 The General Linear Problem
153(1)
8.4 Solving L1 Norm Problems
153(5)
8.5 The L∞ Norm
158(2)
8.6 Problems
160(3)
9 Nonlinear Inverse Problems
9.1 Parameterizations
163(2)
9.2 Linearizing Transformations
165(1)
9.3 Error and Likelihood in Nonlinear Inverse Problems
166(1)
9.4 The Grid Search
167(3)
9.5 The Monte Carlo Search
170(1)
9.6 Newton's Method
171(4)
9.7 The Implicit Nonlinear Inverse Problem with Gaussian Data
175(5)
9.8 Gradient Method
180(1)
9.9 Simulated Annealing
181(3)
9.10 Choosing the Null Distribution for Inexact Non-Gaussian Nonlinear Theories
184(1)
9.11 Bootstrap Confidence Intervals
185(1)
9.12 Problems
186(3)
10 Factor Analysis
10.1 The Factor Analysis Problem
189(5)
10.2 Normalization and Physicality Constraints
194(5)
10.3 Q-Mode and R-Mode Factor Analysis
199(1)
10.4 Empirical Orthogonal Function Analysis
199(5)
10.5 Problems
204(3)
11 Continuous Inverse Theory and Tomography
11.1 The Backus-Gilbert Inverse Problem
207(2)
11.2 Resolution and Variance Trade-Off
209(1)
11.3 Approximating Continuous Inverse Problems as Discrete Problems
209(2)
11.4 Tomography and Continuous Inverse Theory
211(1)
11.5 Tomography and the Radon Transform
212(1)
11.6 The Fourier Slice Theorem
213(1)
11.7 Correspondence Between Matrices and Linear Operators
214(4)
11.8 The Frechet Derivative
218(1)
11.9 The Frechet Derivative of Error
218(1)
11.10 Backprojection
219(3)
11.11 Frechet Derivatives Involving a Differential Equation
222(5)
11.12 Problems
227(4)
12 Sample Inverse Problems
12.1 An Image Enhancement Problem
231(3)
12.2 Digital Filter Design
234(2)
12.3 Adjustment of Crossover Errors
236(4)
12.4 An Acoustic Tomography Problem
240(1)
12.5 One-Dimensional Temperature Distribution
241(4)
12.6 L1, L2, and Fitting of a Straight Line
245(1)
12.7 Finding the Mean of a Set of Unit Vectors
246(4)
12.8 Gaussian and Lorentzian Curve Fitting
250(2)
12.9 Earthquake Location
252(4)
12.10 Vibrational Problems
256(3)
12.11 Problems
259(2)
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
261(3)
13.2 Moment Tensors of Earthquakes
264(1)
13.3 Waveform "Tomography"
265(2)
13.4 Velocity Structure from Free Oscillations and Seismic Surface Waves
267(2)
13.5 Seismic Attenuation
269(1)
13.6 Signal Correlation
270(1)
13.7 Tectonic Plate Motions
271(1)
13.8 Gravity and Geomagnetism
271(2)
13.9 Electromagnetic Induction and the Magnetotelluric Method
273(4)
14 Appendices
14.1 Implementing Constraints with Lagrange multipliers
277(1)
14.2 L2 Inverse Theory with Complex Quantities
278(3)
Index 281
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.